Archiwum seminariów
29.01.5201 Paweł Idziak 
Informatyka Teoretyczna Modular circuits satisfiability of intermediate complexity 
In our paper [LICS'18] a generalization of Boolean circuits to arbitrary finite algebras was introduced and applied to sketch P versus NPcomplete borderline for circuits satisfiability over algebras from congruence modular varieties. However nilpotent but not supernilpotent algebras have not been put on any side of this borderline. This paper provides a broad class of examples, lying in this grey area, and show that, under the Exponential Time Hypothesis and Strong Exponential Size Hypothesis (saying that Boolean circuits need exponentially many modular counting gates to produce Boolean conjunctions of any arity), satisfiability over these algebras have intermediate complexity. We also sketch how these examples could be used as paradigms to fill the nilpotent versus supernilpotent gap in general. Our examples are striking in view of the natural strong connections between circuits satisfiability and Constraint Satisfaction Problem for which the dichotomy was shown by Bulatov and Zhuk. Joint work with Piotr Kawałek and Jacek Krzaczkowski 
29.01.5201 Krzysztof Turowski 
Informatyka Teoretyczna Degree Distribution of Dynamic Graphs Generated by a DuplicationDivergence Models 
We analyze the structure of dynamic graphs generated from duplication models in which a new vertex selects an existing vertex and copies some of its neighbors and then we add some random divergence. We analyze various graph parameters like mean degree, number of open triangles, number of triangles, number of vertices of degree k or maximum degree in a graph generated from such models. We provide asymptotic analysis of expected values and tail behavior of these parameters. We also point to further extensions of this approach towards computing symmetries in these graphs and algorithms for graph compression.

05.12.29864 Bartosz Wodziński 
Optymalizacja Kombinatoryczna On the unique games conjecture 
For many hard problems, instead of solving them directly, we need good approximation algorithms. Apart from good their time complexity and decent approximation factor guarantee, we would like to know whether they achieve the best possible approximation ratio (assuming P ≠ NP) possible. Unfortunately, for many NPcomplete problems, there is a huge gap between bestknown approximation ratio and the ratio that is proved to be unachievable in polynomial time. For instance, for Vertex Cover problem, we don't know any algorithm having a better ratio than 2, and it has been proved in 2005 that it is impossible to get a better ratio than ~1.36. As an attempt to fill in this gap, in 2002, the socalled Unique Games Conjecture was formulated by Khot. It states that having a (1𝜀)satisfiable instance of Unique Label Cover problem, it is NPhard to find a solution satisfying even epsilon fraction of constraints. Assuming it, we are able to prove many tight inapproximability results, for example, it implies that GoemansWilliamson Algorithm for MaxCut problem achieves the best possible approximation rate. It also follows that we cannot get any better ratio than 2 in the case of Vertex Cover problem. The Unique Games Conjecture is an unusual open problem since the academic world is about evenly divided on whether it is true or not. During the seminar, I will cover this conjecture in more details giving more examples of its influence and presenting recent progress in order to prove it.
(the seminar will only be online) 
28.08.29841 Gabriela Czarska 
Optymalizacja Kombinatoryczna The Lonely Runner Conjecture 
Abstract. Suppose that k runners having different constant speeds run laps on a circular track of unit length. The Lonely Runner Conjecture states that, sooner or later, any given runner will be at distance at least 1/k from all the other runners. We prove that with probability tending to one, a much stronger statement holds for random sets in which the bound 1/k is replaced by 1/2 − ε. The proof uses Fourier analytic methods. We also point out some consequences of our result for colouring of random integer distance graphs. (the seminar will only be online) 
21.02.29732 Wojciech Grabis 
Podstawy Informatyki Decidability of regular language genus computation by Guillaume Bonfante and Florian L. Deloup 
This article continues the study of the genus of regular languages that the authors introduced in a 2013 paper (published in 2018). In order to understand further the genus g(L) of a regular language L, we introduce the genus size of L_gen to be the minimal size of all finite deterministic automata of genus g(L) computing L.We show that the minimal finite deterministic automaton of a regular language can be arbitrarily far away from a finite deterministic automaton realizing the minimal genus and computing the same language, in terms of both the difference of genera and the difference in size. In particular, we show that the genus size Lgen can grow at least exponentially in size L. We conjecture, however, the genus of every regular language to be computable. This conjecture implies in particular that the planarity of a regular language is decidable, a question asked in 1976 by R. V. Book and A. K. Chandra. We prove here the conjecture for a fairly generic class of regular languages having no short cycles. The methods developed for the proof are used to produce new genusbased hierarchies of regular languages and in particular, we show a new family of regular languages on a twoletter alphabet having arbitrary high genus. 
21.02.29732 Wojciech Grabis 
Decidability of regular language genus computation by Guillaume Bonfante and Florian L. Deloup 
This article continues the study of the genus of regular languages that the authors introduced in a 2013 paper (published in 2018). In order to understand further the genus g(L) of a regular language L, we introduce the genus size of Lgen to be the minimal size of all finite deterministic automata of genus g(L) computing L.We show that the minimal finite deterministic automaton of a regular language can be arbitrarily far away from a finite deterministic automaton realizing the minimal genus and computing the same language, in terms of both the difference of genera and the difference in size. In particular, we show that the genus size Lgen can grow at least exponentially in size L. We conjecture, however, the genus of every regular language to be computable. This conjecture implies in particular that the planarity of a regular language is decidable, a question asked in 1976 by R. V. Book and A. K. Chandra. We prove here the conjecture for a fairly generic class of regular languages having no short cycles. The methods developed for the proof are used to produce new genusbased hierarchies of regular languages and in particular, we show a new family of regular languages on a twoletter alphabet having arbitrary high genus. 
21.02.29732 Wojciech Grabis 
Decidability of regular language genus computation by Guillaume Bonfante and Florian L. Deloup 
This article continues the study of the genus of regular languages that the authors introduced in a 2013 paper (published in 2018). In order to understand further the genus g(L) of a regular language L, we introduce the genus size of Lgen to be the minimal size of all finite deterministic automata of genus g(L) computing L.We show that the minimal finite deterministic automaton of a regular language can be arbitrarily far away from a finite deterministic automaton realizing the minimal genus and computing the same language, in terms of both the difference of genera and the difference in size. In particular, we show that the genus size Lgen can grow at least exponentially in size L. We conjecture, however, the genus of every regular language to be computable. This conjecture implies in particular that the planarity of a regular language is decidable, a question asked in 1976 by R. V. Book and A. K. Chandra. We prove here the conjecture for a fairly generic class of regular languages having no short cycles. The methods developed for the proof are used to produce new genusbased hierarchies of regular languages and in particular, we show a new family of regular languages on a twoletter alphabet having arbitrary high genus. 
21.02.29732 Wojciech Grabis 
Decidability of regular language genus computation by Guillaume Bonfante and Florian L. Deloup 
This article continues the study of the genus of regular languages that the authors introduced in a 2013 paper (published in 2018). In order to understand further the genus g(L) of a regular language L, we introduce the genus size of L_gen to be the minimal size of all finite deterministic automata of genus g(L) computing L. We show that the minimal finite deterministic automaton of a regular language can be arbitrarily far away from a finite deterministic automaton realizing the minimal genus and computing the same language, in terms of both the difference of genera and the difference in size. In particular, we show that the genus size L_gen can grow at least exponentially in size L. We conjecture, however, the genus of every regular language to be computable. This conjecture implies in particular that the planarity of a regular language is decidable, a question asked in 1976 by R. V. Book and A. K. Chandra. We prove here the conjecture for a fairly generic class of regular languages having no short cycles. The methods developed for the proof are used to produce new genusbased hierarchies of regular languages and in particular, we show a new family of regular languages on a twoletter alphabet having arbitrary high genus. 
27.06.13437 Paweł Mader 
Optymalizacja Kombinatoryczna Oblivious routing on 2d grid 
Oblivious routing is a routing problem, in which a packet path is selected independently from path choices of other packets. One of the open problems is to find networks for which there exists an oblivious routing algorithm, which allows simultaneously optimizing stretch and congestion of the network. We are presenting an algorithm for oblivious routing on 2dgrid, which is O(log n) approximation for congestion and Θ(1) approximation of stretch. (the seminar will only be online) 
20.03.13414 Raja L'hamri Mohammed V University 
Optymalizacja Kombinatoryczna Examples of codes from zerodivisor graphs 
In 2013, Dankelmann, Key, and Rodrigues introduced and investigated codes from incidence matrices of a graph. Several authors have been developed their study to several context. In this talk, we present some properties of codes associated with zero divisor graphs. Recall, the zero divisor graph of R denoted by Γ(R), is the simple graph associated with R whose set of vertices consists of all nonzero zerodivisors of R such that two distinct vertices x and y are joined by an edge if xy = 0. This is joint work with K. Abdelmoumen, D. Bennis, and F. Taraza.
(the seminar will only be online) 
16.10.10566 Ruslan Yevdokymov 
Podstawy Informatyki Learnability can be undecidable by Shai BenDavid, Pavel Hrubes, Shay Moran, Amir Shpilka and Amir Yehudayoff 
The mathematical foundations of machine learning play a key role in the development of the field. They improve our understanding and provide tools for designing new learning paradigms. The advantages of mathematics, however, sometimes come with a cost. Gödel and Cohen showed, in a nutshell, that not everything is provable. Here we show that machine learning shares this fate. We describe simple scenarios where learnability cannot be proved nor refuted using the standard axioms of mathematics. Our proof is based on the fact the continuum hypothesis cannot be proved nor refuted. We show that, in some cases, a solution to the ‘estimating the maximum’ problem is equivalent to the continuum hypothesis. The main idea is to prove an equivalence between learnability and compression. 
04.03.79147 Michał Stobierski 
Optymalizacja Kombinatoryczna The 123 Conjecture 
We all know how important mathematical theorems are in general. Less obvious is the fact that theorems in one area like algebra or number theory could have a significant impact on another. In our case, these will be combinatorial problems. In this presentation, We will go through a few simple graph coloring questions (based on the original 123 Conjecture), which unfortunately don't have simple solutions at all and we'll classify them. Moreover, thanks to Combinatorial Nullstellensatz and some greedy techniques, we will be able to prove some weaker versions of our original claims. And finally, we will see how one simple question, through a chain of small modifications, can lead us to completely different problems. (the seminar will only be online) 
25.11.79123 Rafał Byczek 
Optymalizacja Kombinatoryczna Wegner’s conjecture  colouring the square of a planar graph 
The square G^{2} of a graph G is the graph with the same vertex set in which two vertices are joined by an edge if their distance in G is at most two. The chromatic number of the square of a graph G is between D + 1 and D^{2 }+ 1, where D is the maximum degree of G. Equivalently, the square coloring of a graph is to color the vertices of a graph at distance at most 2 with different colors. In 1977, Gerd Wegner proved that the square of cubic planar graphs is 8colorable. He conjectured that his bound can be improved  the chromatic number of G^{2} is at most 7, if D = 3, at most D + 5, if 4 ≤ D ≤ 7, and [3D / 2] + 1, otherwise. Wegner also gave some examples to illustrate that these upper bounds can be obtained. C. Thomassen (2006) proved the conjecture is true for planar graphs with D = 3. The conjecture is still open for planar graphs with D ≥ 4. However several upper bounds in terms of maximum degree D have been proved as follows. In 1993, Jonas proved that χ(G^{2}) ≤ 9D19, for planar graphs with D ≥ 5. Agnarsson and Halldorson showed that for every planar graph G with maximum degree D ≥ 749, χ(G^{2}) ≤ [9D / 5] + 2. Van den Heuvel and McGuinness (2003) showed that χ(G^{2}) ≤ 2D + 25, Bordin (2002) proved that χ(G^{2}) ≤ [9D / 5] + 1, if D ≥ 47, and Molloy and Salavatipour (2005) proved χ(G^{2}) ≤ [5D / 3] + 78, moreover, χ(G^{2}) ≤ [5D / 3] + 25 if D ≥ 241. Moreover, conjecture is confirmed in the case of outerplanar graphs and graphs without K_{4} minor. The aim of the seminar will be to present the main facts about Wegner’s conjecture and main techniques and ideas which were used to prove some upper bounds. The presentation will be based on my master thesis. (the seminar will only be online) 
14.05.76272 Szymaon Kapała 
Podstawy Informatyki Searching for shortest and least programs by Cristian Caludea, Sanjay Jain, Wolfgang Merkle and Frank Stephan 
The Kolmogorov complexity of a string x is defined as the length of a shortest program p of x for some appropriate universal machine U, that is, U(p) =x and p is a shortest string with this property. Neither the plain nor the prefixfree version of Kolmogorov complexity are recursive but for both versions it is wellknown that there are recursive exact Solovay functions, that is, recursive upper bounds for Kolmogorov complexity that are infinitely often tight. Let a coding function for a machine M be a function f such that f(x) is always a program of x for M. From the existence of exact Solovay functions it follows easily that for every universal machine there is a recursive coding function that maps infinitely many strings to a shortest program. Extending a recent line of research, in what follows it is investigated in which situations there is a coding function for some universal machine that maps infinitely many strings to the lengthlexicographically least program. The main results which hold in the plain as well as in the prefixfree setting are the following. For every universal machine there is a recursive coding function that maps infinitely many strings to their least programs. There is a partial recursive coding function (defined in the natural way) for some universal machine that for every set maps infinitely many prefixes of the set to their least programs. Exactly for every set that is Bennett shallow (not deep), there is a recursive coding function for some universal machine that maps all prefixes of the set to their least programs. Differences between the plain and the prefixfree frameworks are obtained by considering effective sequences I_1, I_2, ...of mutually disjoint finite sets and asking for a recursive coding function for some universal machine that maps at least one string in each set I_n to its least code. Such coding functions do not exist in the prefixfree setting but exist in the plain setting in case the sets I_n are not too small. 
Poprzednie referaty
20.07.59958 Wojtek Grabis 
Optymalizacja Kombinatoryczna Algorithms for Destructive Shift Bribery. 
Destructive Shift Bribery is a problem in which we are given an election with a set of candidates and a set of voters, a budget , a despised candidate and price for shifting the despised candidate in the voters rankings. Our objective is to ensure that selected candidate cannot win the election. We're going to study the complexity of this problem under diffrent election methods.
(the seminar will only be online) 
16.02.57111 Piotr Mikołajczyk 
Podstawy Informatyki Lambda Calculus and Probabilistic Computation by Claudia Faggian and Simona Ronchi della Rocca 
We introduce two extensions of the lambda calculus with a probabilistic choice operators, modeling respectively callbyvalue and callbyname probabilistic computation. We prove that both enjoys confluence and standardization, in an extended way: we revisit these two fundamental notions to take into account the asymptotic behaviour of terms. The common root of the two calculi is a further calculus based on Linear Logic ! which allows us to develop a unified, modular approach. 
21.06.40816 Jan Mełech 
Optymalizacja Kombinatoryczna Upper Bounds for the domination numbers of graphs 
Sharareh Alipour and Amir Jafari showed various upper bounds for minimal cardinality of (a,b)dominating set. For positive integers a and b, a subset S ⊆ V(G) is an (a,b)dominating set if every vertex v ∈ S is adjacent to at least a vertices inside S and every vertex v ∈ V\S is adjacent to at least b vertices inside S. To achieve upper bounds, the authors used Turan's Theorem and Lovasz Local Lemma. These tools allowed them to obtain wellknown bounds in a simpler way or new improved bounds in some special cases, including regular graphs.
(the seminar will only be online) 
14.03.40793 Szymon Kapała 
Optymalizacja Kombinatoryczna Goldbach conjectures (weak and strong). 
(the seminar will only be online) 
11.10.37945 Przemysław Simajchel 
Podstawy Informatyki Dance of the Starlings by Henk Barendregt, Jorg Endrullis, Jan Klop and Johannes Waldmann 
In this birdwatching paper our binoculars are focused upon a particular bird from Smullyan's enchanted forest of combinatory birds, to wit the Starling. In the feathers of lambda calculus this bird has the plumage \abc:ac(bc). This term is usually named S, reminiscent of its inventor Schonfinkel and also the combinatory ornithologist Smullyan. The combinator S is important for a variety of reasons. First, it is part of the \{ S, K\} basis for Combinatory Logic (CL). Second, there are several interesting questions and observations around S, mostly referring to termination and word problems. Our paper collects known facts, but poses in addition several new questions. For some of these we provide solutions, but several tough open questions remain. 
07.11.21627 Michał Zwonek 
Optymalizacja Kombinatoryczna 3flow conjecture 
3flowconjecture Grötzsch proved that every triangle free (and loopless) planar graph is 3colorable. By flow/coloring duality, this is equivalent to the statement that every 4edgeconnected planar graph has a nowherezero 3flow. The 3flow conjecture asserts that this is still true without the assumption of planarity. Jaeger proved that 4edgeconnected graphs have nowherezero 4flows. The following weak version of the 3flow conjecture used to remain open until 2010, but the original 3flow conjecture remains wide open. C̶o̶n̶j̶e̶c̶t̶u̶r̶e̶ (The weak 3flow conjecture (Jaeger)) These problems and the surrounding results will be presented during the seminar.
(the seminar will only be online) 
05.06.18780 Bartłomiej Puget 
Podstawy Informatyki Evidence Normalization in System FC by Dimitrios Vytiniotis and Simon Peyton Jones 
System FC is an explicitly typed language that serves as the target language for Haskell source programs. System FC is based on System F with the addition of erasable but explicit type equality proof witnesses. Equality proof witnesses are generated from type inference performed on source Haskell programs. Such witnesses may be very large objects, which causes performance degradation in later stages of compilation, and makes it hard to debug the results of type inference and subsequent program transformations. In this paper, we present an equality proof simplification algorithm, implemented in GHC, which greatly reduces the size of the target System FC programs. 
26.11.84622 Mateusz Kaczmarek 
Optymalizacja Kombinatoryczna χboundedness 
If a graph has bounded clique number and sufficiently large chromatic number, what can we say about its induced subgraphs? To answer that question Paul Seymour and Alex Scott took a closer look at recent progress in this field in their χboundedness survey. Based on their work I will present some results on forests and holes and few open problems like GyárfásSumner conjecture or χboundedness connection to ErdősHajnal conjecture.
(the seminar will only be online) 
18.08.84599 Kornel Dulęba 
Optymalizacja Kombinatoryczna Odd Perfect numbers 
A number is perfect if it is equal to the sum of its divisors. So far only even perfect numbers have been found. For example, it was proven that squares of Mersenne’s numbers are perfect. However, no one has been able to prove that odd perfect numbers don’t exist. I’m going to start by presenting a summary of known facts about odd prime numbers. Then I’ll prove that an odd perfect number with at least eight distinct prime factors has to be divisible by 5.
(the seminar will only be online) 
16.03.81752 Jakub Dyczek 
Podstawy Informatyki On probabilistic term rewriting by Martin Avanzinia,Ugo Dal Lago and Akihisa Yamadac 
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite systems are considered. Two instances of the interpretation method polynomial and matrix interpretations are analyzed and shown to capture interesting and nontrivial examples when automated. We capture probabilistic computation in a novel way by means of multidistribution reduction sequences, thus accounting for both the nondeterminism in the choice of the redex and the probabilism intrinsic in firing each rule. 
21.07.65457 Bartłomiej Jachowicz 
Optymalizacja Kombinatoryczna Lonely runner conjecture 
One of number theory open problem is the Lonely Runner Conjecture. It is interesting for several reasons. First the conjecture is relatively intuitive to grasp and easy to state. This conjecture can be find in two different contexts: as a problem in Diophantine’s approximation and as a geometric view obstruction problem. What is more, the difficulty of proving the Lonely Runner Conjecture may seem to increase exponentially with the number of runners. I present statement of the conjecture and known partial results.
(the seminar will only be online) 
13.04.65434 Filip Bartodziej 
Optymalizacja Kombinatoryczna Meyniel’s conjecture on the cop number 
A cops and robbers problem determines if the number of cops is sufficient to always catch a robber in a game with defined rules played on an undirected graph. Cop number of a graph is the minimal number of cops necessary for cops to win in that game on the specific graph. Mayniel’s conjuncture remains an open problem and states that cop number for graphs of order n is sqrt(n). I’ll present a survey of results achieved that are related to this conjecture.
(the seminar will only be online) 
09.11.62586 Jan Kościsz 
Podstawy Informatyki Fast Synchronization of Random Automata by Cyril Nicaud 
A synchronizing word for an automaton is a word that brings that automaton into one and the same state, regardless of the starting position. Cerný conjectured in 1964 that if a nstate deterministic automaton has a synchronizing word, then it has a synchronizing word of length at most (n − 1)^2. Berlinkov recently made a breakthrough in the probabilistic analysis of synchronization: he proved that, for the uniform distribution on deterministic automata with n states, an automaton admits a synchronizing word with high probability. In this article, we are interested in the typical length of the smallest synchronizing word, when such a word exists: we prove that a random automaton admits a synchronizing word of length O(n log^3 n) with high probability. As a consequence, this proves that most automata satisfy the Cerný conjecture. 
15.03.46292 Mateusz Pabian 
Optymalizacja Kombinatoryczna Synchronizing Automata and the Černý Conjecture 
I present many results and finally open problem related to synchronizing automata and synchronizing word sends any state of the DFA to one and the same state. This leads to the some natural problems such as: how can we restore control over such a device if we don't know its current state but can observe outputs produced by the device under various actions? I prove some uperbounds for length of this kind of word and in particular I will make a statement of Cerny conjecture.
(the seminar will only be online) 
06.12.46268 Adrian Siwiec 
Optymalizacja Kombinatoryczna Online Computation with Untrusted Advice 
The advice model of online computation captures the setting in which the online algorithm is given some partial information concerning the request sequence. We study online computation in a setting in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms that are robust and perform well even when the advice is generated in a malicious, adversarial manner.To this end, we focus on wellstudied online problems such as ski rental, online bidding, bin packing, and list update.
(the seminar will only be online) 
05.07.43421 Magdalena Proszewska 
Podstawy Informatyki Singular value automata and approximate minimization by Borja Balle, Prakash Panangaden and Doina Precup 
The present paper uses spectral theory of linear operators to construct approximately minimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the singular value decomposition (SVD) decomposition of finiterank infinite Hankel matrices based on their representation in terms of weighted automata, (ii) a new canonical form for weighted automata arising from the SVD of its corresponding Hankelmatrix, and (iii) an algorithm to construct approximate minimizations of given weighted automata by truncating the canonical form. We give bounds on the quality of our approximation. 
09.11.27126 Wojciech Buczek 
Optymalizacja Kombinatoryczna Seymour's Second Neighbourhood Conjecture 
Seymour's Second Neighbourhood Conjecture tells us, that any oriented graph has a vertex whose outdegree is at most its second outdegree, which is also known as Second neighborhood problem. Intuitively, it suggests that in a social network described by such a graph, someone will have at least as many friendsoffriends as friends. We will say about ChenShenYuster prove, that for any digraph D, there exists a vertex v such that N^{++}(v)≥γN^{+}(v), where γ=0.67815. We will consider graphs, in which we know, that such vertex exists. We will also say about unsuccessful attempts at proving this conjecture.
(the seminar will only be online) 
02.08.27103 Mikołaj Twaróg 
Optymalizacja Kombinatoryczna Collatz conjecture 
The Collatz conjecture, also known as 3n + 1 conjecture considers a function, which returns n/2 if n is even and 3n + 1 if n is odd. The conjecture states that for every n we can repeatedly apply this function to eventually reach 1. I will talk about different approaches to proving this conjecture. (the seminar will only be online) 
28.02.24256 Jacek Kurek 
Podstawy Informatyki Complexity of translations from resolution to sequent calculus by GISELLE REIS and BRUNO PALEO 
Resolution and sequent calculus are two wellknown formal proof systems. Their differences make them suitable for distinct tasks. Resolution and its variants are very efficient for automated reasoning and are in fact the theoretical basis of many theorem provers. However, being intentionally machine oriented, the resolution calculus is not as natural for human beings and the input problem needs to be preprocessed to clause normal form. Sequent calculus, on the other hand, is a modular formalism that is useful for analysing metaproperties of various logics and is, therefore, popular among proof theorists. The input problem does not need to be preprocessed, and proofs are more detailed. However, proofs also tend to be larger and more verbose. When the worlds of proof theory and automated theorem proving meet, translations between resolution and sequent calculus are often necessary. In this paper, we compare three translation methods and analyse their complexity. 
04.07.7961 Adam Pardyl 
Optymalizacja Kombinatoryczna Undirected edge geography 
The game of edge geography is played by two players who alternately move a token on a graph from one vertex to an adjacent vertex, erasing the edge in between. The player who first has no legal move loses the game. We analyze the space complexity of the decision problem of determining whether a start position in this game is a win for the first player. We also show a polynomial time algorithm for finding winning moves for bipartite graphs.
(the seminar will only be online) 
27.03.7938 Piotr Mikołajczyk 
Optymalizacja Kombinatoryczna ARRIVAL game 
Consider a directed graph such that every vertex has at most 2 outgoing edges  one of them is labeled as 'open' (we can traverse it) and the second one is labeled as 'closed' (we cannot traverse it). Every time we go somewhere from the vertex v, labels at its two edges are swapped, so the next time we visit v, we will take another direction. Given designated two vertices: origin and destination, we need to decide, whether eventually we will reach destination starting in the origin. This problem lies in both NP and coNP, but it is still an open question whether it belongs to P.
(the seminar will only be online) 
23.10.5090 Rafał Byczek 
Podstawy Informatyki Bijection between oriented maps and weighted nonoriented maps by Agnieszka CzyzewskaJankowska and Piotr Śniady 
We consider bicolored maps, i.e. graphs which are drawn on surfaces, and construct a bijection between (i) oriented maps with arbitrary face structure, and (ii) (weighted) nonoriented maps with exactly one face. Above, each non oriented map is counted with a multiplicity which is based on the concept of the orientability generating series and the measure of orientability of a map. This bijection has the remarkable property of preserving the underlying bicolored graph. Our bijection shows equivalence between two explicit formulas for the topdegree of Jack characters, i.e. (suitably normalized) coefficients in the expansion of Jack symmetric functions in the basis of powersum symmetric functions. 
01.12.73647 Vladyslav Rachek 
Optymalizacja Kombinatoryczna Small weak epsilonnets 
Let P be a set of n points in R^{2}. A point q (not necessarily in P) is called a centerpoint of P if each closed halfplane containing q at least ⌈n/3⌉ points of P, or, equivalently, any convex set that contains more than ^{2}/_{3 }n points of P must also contain q. It is a wellknown fact that a centerpoint always exists and the constant ^{2}/_{3} is the best possible. Can we improve this constant by using, say, two points, or some other small number of points? In the presentation we'll try to answer those questions. Vladyslav Rachek. Small weak epsilonnets. slides. 2020. (the seminar will only be online) 
29.06.70800 Michał Zwonek 
Podstawy Informatyki FUNCTIONAL PEARL How to find a fake coin by RICHARD BIRD 
The aim of this pearl is to solve the following wellknown problem that appears in many puzzle books, for example Levitin & Levitin (2011) and Bellos (2016), usually for the particular case n=12.

03.11.54505 Kamil Rajtar 
Optymalizacja Kombinatoryczna How voting can be manipulated during selecting voting places 
During today presentation we will learn how we can use graph theory to proof hardness of general problem of manipulating poll outcome. Based on paper: "Selecting Voting Locations for Fun and Profit" written by Zack Fitzsimmons and Omer Lev. Zack Fitzsimmons, Omer Lev. Selecting Voting Locations for Fun and Profit. arXiv:2003.06879. 2020. (the seminar will only be online) 
26.07.54482 Mateusz Tokarz 
Optymalizacja Kombinatoryczna The HadwigerNelson problem 
We will focus on HadwigerNelson problem  an open question from geometric graph theory that asks for the minimum number of colors required to color the plane such that no two points at distance 1 from each other have the same color. There are a few interesting theorems related to the problem and results which we will go through. We will focus in particular on the most recent result of Aubrey de Grey who showed that the desired chromatic number is at least 5.
(the seminar will only be online) 
22.02.51635 Mateusz Tokarz, wyniki własne, kontynuacja 
Podstawy Informatyki The largest fixed point in iterative programs 
We study the smallest ordinal number α such that every Prologue program will reach its greatest fixed point after α downward iterations. Firstly, we show that the continuity of Prologue’s resolution function does not help with this matter. Then, due to the embedding of the recursive functions in Prologue, we get that α is at least ChurchKleene Omega. Using recursive linear order presented in “On the Forms of the Predicates in the Theory of Constructive Ordinals“ (Kleene, 1944) we construct a Prologue’s program requiring at least CK Omega steps to achieve its greatest fixed point. To get the upper bound on α we use clockable ordinals introduced in “Infinite Time Turing Machines” (Joel David Hamkins, Andy Lewis, 1998). 
17.10.32469 Mateusz Tokarz wyniki własne 
Podstawy Informatyki The largest fixed point in iterative programs 
We study the smallest ordinal number α such that every Prologue program will reach its greatest fixed point after α downward iterations. Firstly, we show that the continuity of Prologue’s resolution function does not help with this matter. Then, due to the embedding of the recursive functions in Prologue, we get that α is at least ChurchKleene Omega. Using recursive linear order presented in “On the Forms of the Predicates in the Theory of Constructive Ordinals“ (Kleene, 1944) we construct a Prologue’s program requiring at least CK Omega steps to achieve its greatest fixed point. To get the upper bound on α we use clockable ordinals introduced in “Infinite Time Turing Machines” (Joel David Hamkins, Andy Lewis, 1998). 
12.01.65434 Jan Gwinner 
Optymalizacja Kombinatoryczna Spectrally Robust Graph Isomorphism 
In the paper authors consider certain variants of Graph Isomorphism problem. They focus on properties of graph spectra and eigenspaces  namely if Laplacian of one of the graphs is greater or equal to another in Loewner ordering. In the first part of the paper they prove that one of the problems named Spectral Graph Dominance is NPC. The rest of the paper is devoted to an approximation algorithm for special case of the problem called Spectrally Robust Graph Isomorphism. 
10.08.62586 Weronika Grzybowska i Mateusz Tokarz 
Podstawy Informatyki On two subclasses of Motzkin paths and their relation to ternary trees by Helmut Prodinger, Sarah J. Selkirk and Stephan Wagner 
Two subclasses of Motzkin paths, SMotzkin and TMotzkin paths, are introduced. We provide bijections between SMotzkin paths and ternary trees, SMotzkin paths and noncrossing trees, and TMotzkin paths and ordered pairs of ternary trees. Symbolic equations for both paths, and thus generating functions for the paths, are provided. Using these, various parameters involving the two paths are analyzed. 
15.12.46291 Gabriela Czarska 
Optymalizacja Kombinatoryczna Driver surge pricing 
Authors study Uber's pricing mechanisms from the perspective of drivers, presenting the theoretical foundation that has informed the design of Uber’s new additive driver surge mechanism. They present a dynamic stochastic model to capture the impact of surge pricing on driver earnings and their strategies to maximize such earnings. Nikhil Garg, Hamid Nazerzadeh. Driver Surge Pricing. arXiv. 2019. 
06.09.46268 Bartosz Podkanowicz 
Optymalizacja Kombinatoryczna Planar graphs have bounded queuenumber 
The paper presents proof that the queue number of planar graphs is bounded. It also mentions generalizations of the result and other theorems that have similar proofs. 
04.12.46213 Katarzyna Król, Paweł Mader 
On the Complexity of Lattice Puzzles [Kobayashi et al.] 
Autorzy pracy badają złożoność obliczeniową tradycyjnej łamigłówki zwaną dalej układanką kratową. Celem układanki jest złożenie kraty o wymiarach n×n z 2n płytek z szczelinami. Łamigówka ta jest powszechnie znanym problemem, niemniej jednak do tej pory nie była ona badana przez informatykę teoretyczną. Autorzy pracy pokazują, że naturalne warianty tej układanki redukują się do podklas w klasie złożoności NP. Jedną z takich podklas jest klasa problemu izomorfizmów grafów GI. O ile wiadomo autorom pracy, jest to pierwszy nietrywialny GIzupełny problem scharakteryzowany przez klasyczną łamigłówkę. 
11.10.43530 Michał Seweryn 
Informatyka Teoretyczna ErdösHajnal properties for powers of sparse graphs 
The notion of nowhere dense classes of graphs attracted much attention in recent years and found many applications in structural graph theory and algorithmics. The powers of nowhere dense graphs do not need to be sparse, for instance the second power of star graphs are complete graphs. However, it is believed that powers of sparse graphs inherit somewhat simple structure. In this spirit, we show that for a fixed nowhere dense class of graphs, a positive real ε and a positive integer d, in any nvertex graph G in the class, there are disjoint vertex subsets A and B with A=Ω(n) and B=Ω(n^{1ε}) such that in the dth power of G, either there is no edge between A and B, or there are all possible edges between A and B.
Joint work with Marcin Briański, Piotr Micek and Michał Pilipczuk 
05.04.43421 Wojciech Grabis 
Podstawy Informatyki Ant colony optimization theory: A survey by Marco Dorigoa and Christian Blumb 
Research on a new metaheuristic for optimization is often initially focused on proofofconcept applications. It is only after experimental work has shown the practical interest of the method that researchers try to deepen their understanding of the method’s functioning not only through more and more sophisticated experiments but also by means of an effort to build a theory. Tackling questions such as “how and why the method works’’ is important, because finding an answer may help in improving its applicability. Ant colony optimization, which was introduced in the early 1990s as a novel technique for solving hard combinatorial optimization problems, finds itself currently at this point of its life cycle. With this article we provide a survey on theoretical results on ant colony optimization. First, we reviewsome convergence results. Then we discuss relations between ant colony optimization algorithms and other approximate methods for optimization. Finally, we focus on some research efforts directed at gaining a deeper understanding of the behavior of ant colony optimization algorithms. Throughout the paper we identify some open questions with a certain interest of being solved in the near future. 
10.08.27126 Wojtek Grabis 
Optymalizacja Kombinatoryczna Algorithms for Destructive Shift Bribery. 
Destructive Shift Bribery is a problem in which we are given an election with a set of candidates and a set of voters, a budget , a despised candidate and price for shifting the despised candidate in the voters rankings. Our objective is to ensure that selected candidate cannot win the election. We're going to study the complexity of this problem under diffrent election methods. Andrzej Kaczmarczyk, Piotr Faliszewski. Algorithms for Destructive Shift Bribery. arXiv. 2018. 
03.05.27103 Dominik Gryboś 
Optymalizacja Kombinatoryczna Imperfect Forward Secrecy: How DiffieHellman Fails in Practice 
The paper shows that the DiffieHellman protocol is not as secure as we thought. The authors present the Logjam attack, which consists in quickly calculating discrete logarithms based on previously performed calculations. This can be done because many websites use the same prime numbers in the message encryption process. 
29.11.24255 Piotr Gaiński 
Podstawy Informatyki How Similar Are Two Elections by Piotr Faliszewski, Piotr Skowron, Arkadii Slinko, Stanisław Szufa and Nimrod Talmon 
We introduce the ELECTION ISOMORPHISM problem and a family of its approximate variants, which we refer to as dISOMORPHISM DISTANCE (dID) problems (where d is a metric between preference orders). We show that ELECTION ISOMORPHISM is polynomialtime solvable, and that the dISOMORPHISM DISTANCE problems generalize various classic rankaggregation methods (e.g., those of Kemeny and Litvak). We establish the complexity of our problems (including their inapproximability) and provide initial experiments regarding the ability to solve them in practice. 
04.08.54505 Kamil Kropiewnicki 
Optymalizacja Kombinatoryczna Impossibility of Distributed Consensus with One Faulty Proces 
he consensus problem involves an asynchronous system of processes, some of which may be unreliable. The problem is for reliable processes to agree on a binary value. In this paper, it is shown that every protocol for this problem has the possibility of nontermination, even with only one faulty process. By way of contrast, solutions are known for the synchronous case, the “Byzantine Generals” problem. Authors of the paper were awarded a Dijkstra Prize for this work  given to the most influential papers in distributed computing. 
26.04.54482 Filip Bartodziej 
Optymalizacja Kombinatoryczna How to eat 4/9 of a pizza 
Unevenly cut pizza is a frustrating occurrence. How can we then make sure that a friend is not trying to reduce our portion of the delicious meal? We will present a strategy which guarantees that one will leave the table satisfied, assuming that they started eating first. Kolja Knauer, Piotr Micek, Torsten Ueckerdt. How to eat 4/9 of a pizza. arXiv. 2008. 
23.11.51634 Bartosz Podkanowicz 
Podstawy Informatyki Riordan arrays and combinatorial sums by Renzo Sprugnoli 
The concept of a Riordan array is used in a constructive way to find the generating function of many combinatorial sums. The generating function can then help us to obtain the closed form of the sum or its asymptotic value. Some examples of sums involving binomial coefficients and Stirling numbers are examined, together with an application of Riordan arrays to some walk problems. 
29.03.35340 Krzysztof Michalik 
Optymalizacja Kombinatoryczna Coloring planar graphs with 3 colors and no large monochromatic components 
I will present a proof that there exists a function f(d), such that there exists a 3coloring of any planar graph G in which each monochromatic subgraph has at most f(d) vertices, where d is the degree of the highestdegree vertex in G. 
20.12.35316 Mateusz Kaczmarek 
Optymalizacja Kombinatoryczna Hadwiger’s conjecture 
Survey of Hadwiger's Conjecture from 1943, that for all t ≥ 0, every graph is either tcolorable or has a subgraph that can be contracted to the complete t+1 vertices graph. This conjecture is the tremendous strengthening of the fourcolor problem also known as map coloring problem. 
18.03.35262 Krzysztof Pióro, Krzysztof Potępa 
LinearSpace Data Structures for Range Mode Query in Arrays [Chan, Durocher, Larsen, Morrison, Wilkinson] 
Modą multizbioru S nazywamy element, który występuje w S najczęściej, tzn. występuje w S co najmniej tyle razy co każdy inny element S. Mając daną nelementową tablicę A[1:n] rozważamy prosty problem: konstrukcję statycznej struktury danych pozwalającej szybko odpowiadać na zapytania o modę na przedziale A. Każde zapytanie składa się z pary (i,j), dla której odpowiedzią jest moda A[i:j]. Autorzy pracy prezentują strukturę danych z liniową pamięcią odpowiadającą na zapytania w czasie O(sqrt(n / log n)). Dodatkowo pokazują silną przesłankę, że czas zapytania zdecydowanie niższy od sqrt(n) nie może być uzyskany przy użyciu czysto kombinatorycznych technik  mnożenie macierzy logicznych rozmiaru sqrt(n) x sqrt(n) redukuje się do n zapytań o modę na przedziale w tablicy rozmiaru O(n). Autorzy prezentują też struktury danych dla ortogonalnych zapytań w wyższych wymiarach (zapytania w czasie bliskim O(n^{11/2d})) oraz zapytań o półprzestrzenie (zapytania w czasie O(n^{11/d^2})). 
23.01.32579 Adam Polak 
Informatyka Teoretyczna Monochromatic triangles, intermediate matrix products, and convolutions 
The most studied linear algebraic operation, matrix multiplication, has surprisingly fast O(n^{ω}) time algorithms, for ω<2.373. On the other hand, the (min,+)product, which is at the heart of APSP, is widely conjectured to require cubic time. There is a plethora of matrix products and graph problems whose complexity seems to lie in the middle of these two problems, e.g. the (min,max)product, the minwitness product, APSP in directed unweighted graphs. The best runtimes for these "intermediate" problems are all O(n^{(3+ω)/2}). A similar phenomenon occurs for convolution problems.

18.07.32469 Mateusz Górski 
Podstawy Informatyki A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic by Paul Wild, Lutz Schroder, Dirk Pattinson and Barbara Konig. 
The fuzzy modality probably is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is nonexpansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem theorem, which states that modal logic is precisely the bisimulationinvariant fragment of firstorder logic. Specifically, we show that every formula in probabilistic fuzzy firstorder logic that is nonexpansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic. 
15.08.16151 Kornel Dulęba 
Optymalizacja Kombinatoryczna The Return of Coppersmith’s Atack: Practical Factorization of Widely Used RSA Moduli 
During the seminar I will discuss a clever attack on RSA library used in Infineon chips. Researchers discovered that the prime factors used for constructing private keys have a peculiar form. This allowed them to use a modified version of Coppersmith algorithm to recover private key basing on their public counterpart in a reasonable time for keys up to 2048 bit long. 
13.03.13304 Michał Zwonek 
Podstawy Informatyki Probably Half True: Probabilistic Satisfability over Lukasiewicz Infnitelyvalued Logic by Marcelo Finger and Sandro Preto 
We study probabilisticlogic reasoning in a context that allows for "partial truths", focusing on computational and algorithmic properties of nonclassical Lukasiewicz In nitelyvalued Probabilistic Logic. In particular, we study the satis ability of joint probabilistic assignments, which we call LIPSAT. Although the search space is initially in nite, we provide linear algebraic methods that guarantee polynomial size witnesses, placing LIPSAT complexity in the NPcomplete class. An exact satis ability decision algorithm is presented which employs, as a subroutine, the decision problem for Lukasiewicz In nitelyvalued (non probabilistic) logic, that is also an NPcomplete problem. We develop implementations of the algorithms described and discuss the empirical presence of a phase transition behavior for those implementations. 
27.05.79123 Mikołaj Twaróg 
Optymalizacja Kombinatoryczna A Short Guide to Hackenbush 
Hackenbush is a two player game played on a graph with a few marked vertices. Players alternate turns. Each turn consists of removing one edge from the graph and all vertices that lost their connection to all marked ones. Player, that can't make a move, loses. I will present three different variants of Hackenbush(RedBlue Hackenbush, Green Hackenbush and RGB Hackenbush) with methods to determine, which player has a winning strategy. Padraic Bartlett. A Short Guide to Hackenbush. VIGRE REU 2006. 
22.08.79068 Katarzyna Bułat, Dawid Tracz 
Parity Games: Zielonka’s Algorithm in QuasiPolynomial Time [P. Parys] 
Gry parzystości to gry pomiędzy dwoma graczami (zwyczajowo Even oraz Odd) na grafie skierowanym G = (V, E). Gracze przesuwają między wierzchołkami wirtualny token, tworząc ścieżkę. Wierzchołki grafu są etykietowane liczbami naturalnymi i każdy z nich jest przypisany do jednego gracza, który decyduje w jakim kierunku zostanie wykonany ruch z tego wierzchołka. Celem każdego z graczy jest wybranie takiej strategii, że przy nieskończonej grze (ścieżce), najwyższa nieskończenie wiele razy powtarzająca się etykieta będzie odpowiednio parzysta bądź nieparzysta. Problem gry parzystości jest deterministyczny, to znaczy dla każdego wierzchołka jeden z graczy posiada strategię wygrywającą. Rekurencyjny algorytm Zielonki rozwiązuje grę parzystości w czasie wykładniczym. Istnieje jednak algorytm działający w czasie quasiwielomianowym, czyli 2^{O((log(n))^c)} dla pewnego, ustalonego c. W trakcie prezentacji omówiony zostanie schemat nowej wersji algorytmu, przeprowadzona analiza jego złożoności oraz przedstawiony dowód poprawności zwracanego przez niego wyniku. 
29.06.76385 22.02.57220 Patryk Mikos 
Informatyka Teoretyczna Efficient enumeration of nonisomorphic interval graphs 
Recently, Yamazaki et al. provided an algorithm that enumerates all nonisomorphic interval graphs on n vertices with an O(n^{4}) time delay between the output of two consecutive graphs. We improve their algorithm and achieve O(n^{3} log n) time delay. We also extend the catalog of these graphs providing a list of all nonisomorphic interval graphs for all n up to 15 (previous best was 12). 
23.12.76275 Piotr Mikołajczyk 
Podstawy Informatyki Satisfiability in Strategy Logic can be Easier than Model Checking by Erman Acar, Massimo Benerecetti and Fabio Mogavero. 
In the design of complex systems, modelchecking and satisfiability arise as two prominent decision problems. While The SL fragment we consider is obtained by preventing strategic quantifications within the scope of temporal operators. The resulting logic is quite powerful, still allowing to express important gametheoretic properties of multiagent systems, such as existence of Nash and immune equilibria, as well as to formalize the rational synthesis problem. We show that satisfiability for such a fragment is PSPACECOMPLETE, while its modelchecking complexity is 2EXPTIMEHARD. The result is obtained by means of an elegant encoding of the problem into the satisfiability of conjunctivebinding firstorder logic, a recently discovered decidable fragment of firstorder logic. 
28.04.59981 Adrian Siwiec 
Optymalizacja Kombinatoryczna Edge Coloring Signed Graphs 
We define a method for edge coloring signed graphs and what it means for such a coloring to be proper. It then turns out that Vizing's Theorem is a special case of the more difficult theorem concerning signed graphs. 
19.01.59958 Paweł Palenica 
Optymalizacja Kombinatoryczna Guess the Larger Number 
We will discuss variations of a zero sum game where one player writes down two numbers on cards. The second player learns one of the numbers to make a guess which of the numbers is larger. We will show variations of the game where the second player has a greater chance of winning than 1/2. 
18.04.59903 Jędrzej Kula, Przemysław Simajchel 
Subtree Isomorphism Revisited [A. Abboud et al.] 
Problem Izomorfizmu Poddrzew zadaje pytanie, czy dane drzewo zawarte jest w innym danym drzewie. Ten problem o zasadniczym znaczeniu dla algorytmiki jest badany już od lat 60. ubiegłego wieku. Podkwadratowe algorytmy znane są dla niektórych wariantów, np. drzew uporządkowanych, ale nie w ogólnym przypadku. Poprzez redukcję z problemu Wektorów Ortogonalnych pokażemy, że prawdziwie podkwadratowy algorytm dla Izomorfizmu Poddrzew przeczy SETH. Dodatkowo pokażemy, że to samo ograniczenie dolne utrzymuje się również w przypadku ukorzenionych drzew o logarytmicznej wysokości. W opozycji do niego zaprezentujemy również podkwadratowy algorytm randomizowany dla drzew o stałym stopniu i logarytmicznej wysokości. Redukcja korzysta z nowych "gadżetów drzewowych", które prawdopodobnie przydadzą się w przyszłości w wyznaczaniu ograniczeń dolnych opartych na SETH dla problemów na drzewach. Algorytmy opierają się na znanych wynikach o złożoności randomizowanych drzew decyzyjnych. 
18.08.57110 Edyta Garbarz 
Podstawy Informatyki Unifying Logical and Statistical AI Pedro by Domingos, Daniel Lowd, Stanley Kok, Aniruddh Nath, Hoifung Poon Matthew Richardson and Parag Singla 
Intelligent agents must be able to handle the complexity and uncertainty of the real world. Logical AI has focused mainly on the former, and statistical AI on the latter. Markov logic combines the two by attaching weights to firstorder formulas and viewing them as templates for features of Markov networks. Inference algorithms for Markov logic draw on ideas from satisfiability, Markov chain Monte Carlo and knowledgebased model construction. Learning algorithms are based on the voted perceptron, pseudolikelihood and inductive logic programming. Markov logic has been successfully applied to a wide variety of problems in natural language understanding, vision, computational biology, social networks and others, and is the basis of the opensource Alchemy system. 
17.10.38054 Grzegorz Guśpiel 
Informatyka Teoretyczna Smaller Universal Targets for Homomorphisms of EdgeColored Graphs 
The density D(G) of a graph G is the maximum ratio of the number of edges to the number of vertices ranging over all subgraphs of G. For a class F of graphs, the value D(F) is the supremum of densities of graphs in F. A kedgecolored graph is a finite, simple graph with edges labeled by numbers 1,...,k. A function from the vertex set of one kedgecolored graph to another is a homomorphism if the endpoints of any edge are mapped to two different vertices connected by an edge of the same color. Given a class F of graphs, a kedgecolored graph H (not necessarily with the underlying graph in F) is kuniversal for F when any kedgecolored graph with the underlying graph in F admits a homomorphism to H. Such graphs are known to exist exactly for classes F of graphs with acyclic chromatic number bounded by a constant. The minimum number of vertices in a kuniform graph for a class F is known to be Ω(k^{D(F)}) and O(k^{d}), where d is the ceiling of D(F) (result obtained in 2015 with Gutowski), and has been conjectured to be ϴ(k^{D(F)}). In this talk, I will present a construction of a kuniversal graph on O(k^{d}) vertices for any rational bound d on the density D(F). It follows that if D(F) is rational, the minimum number of vertices in a kuniversal graph for F is indeed ϴ(k^{D(F)}). 
12.04.37945 Jan Kościsz 
Podstawy Informatyki Bohm's Theorem, Church's Delta, Numeral Systems, and Ershov Morphisms by Richard Statman and Henk Barendregt 
In this note we work with untyped lambda terms under betaconversion and consider the possibility of extending Bohm's theorem to infnite RE (recursively enumerable) sets. Bohm's theorem fails in general for such sets V even if it holds for all fnite subsets of it. It turns out that generalizing Bohm's theorem to infnite sets involves three other superfcially unrelated notions; namely, Church's delta, numeral systems, and Ershov morphisms. Our principal result is that Bohm's theorem holds for an infnite RE set V closed under beta conversion iff V can be endowed with the structure of a numeral system with predecessor iff there is a Church delta (conditional) for V iff every Ershov morphism with domain V can be represented by a lambda term 
09.05.21627 Kamil Rajtar 
Optymalizacja Kombinatoryczna A PriceBased Iterative Double Auction for Charger Sharing Markets 
05.08.21572 Nicoll Bryła, Mateusz Pabian 
Faster Algorithms for All Pairs NonDecreasing Paths Problem [Duan, Jin, Wu] 
W tej pracy autorzy prezentują poprawiony algorytm dla problemu wszystkich par ścieżek niemalejących (APNP) dla grafów prostych, skierowanych i ważonych o czasie działania Õ(n^((3+ω)/2)) = Õ(n^2,686), gdzie n jest liczbą wierchołków, a ω jest wykładnikiem złożoności algorytmu szybkiego mnożenia macierzy z pracy [Williams 2012, Le Gall 2014]. To odpowiada najlepszemu, obecnemu górnemu ograniczeniu dla (max, min)iloczynu macierzy, który można zredukować do APNP. Następne usprawnienia dla APNP implikują szybszy algorytm dla (max, min)iloczynu macierzy. Poprzednie najlepsze oszacowanie górne dla ważonych, skierowanych grafów było Õ(n^(1/2(3+(3ω)/(ω+1) + ω))) = Õ(n^2,78) [Duan, Gu, Zhang 2018]. Autorzy pokazują również algorytm Õ(n^2) dla APNP w nieskierowanych, prostych grafach, który również osiąga optimum z czynnikiem logarytmicznym. 
06.12.18779 Rafał Burczyński 
Podstawy Informatyki Compaction of Church Numerals by Isamu Furuya and Takuya Kida 
In this study, we address the problem of compaction of Church numerals. Church numerals are unary representations of natural numbers on the scheme of lambda terms. We propose a novel decomposition scheme from a given natural number into an arithmetic expression using tetration, which enables us to obtain a compact representation of lambda terms that leads to the Church numeral of the natural number. For natural number n, we prove that the size of the lambda term obtained by the proposed method is O((s log2n)^(log n/ (log log n))). Moreover, we experimentally confirmed that the proposed method outperforms binary representation of Church numerals on average, when n is less than approximately 10,000 . 
16.02.84599 Bartosz Walczak 
Informatyka Teoretyczna Coloring and Maximum Weight Independent Set of rectangles 
We prove that every intersection graph of axisparallel rectangles in the plane with clique number ω has chromatic number Joint work with Parinya Chalermsook. 
11.08.84489 Jan Mełech 
Podstawy Informatyki On compressing and indexing repetitive sequences by Sebastian Kreft and Gonzalo Navarro 
We introduce LZEnd, a new member of the Lempel–Ziv family of text compressors, which achieves compression ratios close to those of LZ77 but is much faster at extracting arbitrary text substrings. We then build the first selfindex based on LZ77 (or LZEnd) compression, which in addition to text extraction offers fast indexed searches on the compressed text. This selfindex is particularly effective for representing highly repetitive sequence collections, which arise for example when storing versioned documents, software repositories, periodic publications, and biological sequence databases. 
08.09.68171 Vladyslav Rachek 
Optymalizacja Kombinatoryczna On Chromatic Number of Exact Distance Graphs 
For any graph G and positive integer p we can consider "exact distance graph" G in which vertices x and y are connected if and only if their distance in G is exactly p. We can bound chromatic number of such graphs using notion of weak coloring numbers. Proof becomes particularly valuable for odd p and planar graphs G. 
12.10.65433 Gwenaël Joret Université Libre de Bruxelles 
Informatyka Teoretyczna A new proof of the ErdősPósa theorem with applications 
A classic result of Erdős and Pósa (1965) states that for every graph G and every integer k, either G has k vertexdisjoint cycles, or G has a set of Joint work with Henning Bruhn, Wouter Cames van Batenburg, and Arthur Ulmer. 
06.04.65324 Rafał Byczek 
Podstawy Informatyki Suffix array and Lyndon factorization of a text by Sabrina Mantaci, Antonio Restivo, Giovanna Rosone and Marinella Sciortino 
The main goal ofthis paper is to highlight the relationship between the suffix array of a text and its Lyndon factorization. It is proved in [15]that one can obtain the Lyndon factorization of a text from its suffix array. Conversely, here we show a new method for constructing the suffix array of a text that takes advantage of its Lyndon factorization. The surprising consequence of our results is that, in order to construct the suffix array, the local suffixes inside each Lyndon factor can be separately processed, allowing different implementative scenarios, such as online, external and internal memory, or parallel implementations. Based on our results, the algorithm that we propose sorts the suffixes by starting from the leftmost Lyndon factors, even if the whole text or the complete Lyndon factorization are not yet available. 
04.05.49006 Vladyslav Rachek 
Optymalizacja Kombinatoryczna Steinberg's conjecture is false 
It's commonly known that planar graphs are at most 4colorable. One possible direction towards determining when planar graphs can be 3colorable is to narrow to particular planar graphs with enforced structure. For example, one can forbid cycles of length 4,5,...,k where k>=4. There is a conjecture of Steinberg from 1976, that planar graphs without cycles of length 4 and 5 (as subgraphs) are 3colorable. It has been open problem till 2016, when it was disproved in joint paper of Vincent CohenAddad, Michael Hebdige, Daniel Kral, Zhentao Li, Esteban Salgado, and we present proof from that paper. 
31.07.48951 Piotr Helm, Krzysztof Zysiak 
Optimal Sorting with Persistent Comparison Errors [B. Geissmann et al.] 
Rozważamy problem sortowania n elementów w przypadku stałego błędu porównań. W tym problemie, każde porównanie między dwoma elementami może się pomylić ze stałym (małym) prawdopodobieństwem, i porównania nie mogą zostać powtórzone. Perfekcyjne posortowanie w tym modelu jest niemożliwe i celem jest zminimalizowanie dyslokacji każdego z elementów w zwróconym ciągu, czyli odległość od jego poprawnej pozycji. Istniejące ograniczenia dolne dla tego problemu pokazują, że żaden algorytm nie zagwarantuje z wysokim prawdopodobieństwem maksymalnej i sumarycznej dyslokacji lepszej niż Ω(logn) i Ω(n), odpowiednio, bez względu na czas działania. W tej pracy, prezentujemy pierwszy sortujący algorytm o złożoności O(n log n), który gwarantuje zarówno maksymalna dyslokację O(log n), jak i sumaryczną dyslokację O(n) z wysokim prawdopodobieństwem. To rozstrzyga złożoność czasową tego problemu i pokazuje, że błędy porównań nie zwiększają jego złożoności czasowej: ciąg z najlepszą możliwą dyslokacją może zostać uzyskany w czasie O(n logn), i nawet bez błędów porównań czas Ω(n log n) jest konieczny, by zagwarantować takie ograniczenia dyslokacji. Aby osiągnąć ten optymalny wynik, rozwiązujemy dwa podproblemy, za pomocą metod, które mogą mieć dalsze, osobne zastosowania. Jednym z nich jest zlokalizowanie pozycji, na którą należy wstawić element do prawie posortowanego ciągu o dyslokacji O(log n) w taki sposób, aby dyslokacja zwracanego ciągu wciąż była O(logn). Drugi problem  jak równocześnie wstawić m elementów w prawie posortowany ciąg innych m elementów, tak aby zwracany ciąg 2m elementów pozostał prawie posortowany. 
06.06.46268 Mikkel Abrahamsen Københavns Universitet 
Informatyka Teoretyczna Geometric Multicut 
We study the following separation problem: Given a collection of colored objects in the plane, compute a shortest "fence" F, i.e., a union of curves of minimum total length, that separates every two objects of different colors. Two objects are separated if F contains a simple closed curve that has one object in the interior and the other in the exterior. We refer to the problem as Geometric kCut, where k is the number of different colors, as it can be seen as a geometric analogue to the wellstudied multicut problem on graphs. We first give an Joint work with Panos Giannopoulos, Maarten Löffler, and Günter Rote. Presented at ICALP 2019. 
20.10.46158 Maciej Nemś 
Podstawy Informatyki Generating Random WellTyped Featherweight Java Programs Using Quick Check by Samuel da Silva Feitosaa, Rodrigo Geraldo Ribeirob and Andre Rauber Du Bois 
Currently, Java is one of the most used programming language, being adopted in many large projects, where applications reach a level of complexity for which manual testing and human inspection are not enough to guarantee quality in software development. Even when using automated unit tests, such tests rarely cover all interesting cases of code, which means that a bug could never be discovered, once the code is tested against the same set of rules over and over again. This paper addresses the problem of generating random welltyped programs in the context of Featherweight Java, a wellknown objectoriented calculus, using QuickCheck, a Haskell library for propertybased testing. 
25.03.29786 Bartłomiej Jachowicz, Mateusz Kaczmarek 
Separating strings with small automata [J.M.Robson] 
Tematem pracy jest problem znalezienia automatu skończonego rozróżniającego dwa łańcuchy o możliwie najmniejszej liczbie stanów. Autorzy pokazują, że dla łańcuchów ograniczonych przez długość n istnieje automat akceptujący tylko jeden z łańcuchów o O(n^{2/5} * log^{3/5}n) stanach, co dla przypadku, gdy łańcuchy na wejściu są równej długości jest najlepszym znanym ograniczeniem.

25.07.26993 Jacek Kurek 
Podstawy Informatyki GENERIC ALGORITHMS FOR HALTING PROBLEM AND OPTIMAL MACHINES REVISITED 
The halting problem is undecidable but can it be solved for "most" inputs? This natural question was considered in a number of papers, in diferent settings. We revisit their results and show that most of them can be easily proven in a natural framework of optimal machines (considered in algorithmic information theory) using the notion of Kolmogorov complexity. We also consider some related questions about this framework and about asymptotic properties of the halting problem. In particular, we show that the fraction of terminating programs cannot have a limit, and all limit points are MartinLof random reals. We then consider mass problems of finding an approximate solution of halting problem and probabilistic algorithms for them, proving both positive and negative results. We consider the fraction of terminating programs that require a long time for termination, and describe this fraction using the busy beaver function. We also consider approximate versions of separation problems, and revisit Schnorr's results about optimal numberings showing how they can be generalized. 
22.08.10675 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna Choosability number of planar graphs 
During the seminar, we will discuss some open problems regarding the choosability number of planar graphs and related problems. 
25.10.54481 Bartłomiej Kielak 
Informatyka Teoretyczna Generalized Turán densities and counting cycles in graphs 
The Turán number In this talk, we will show an elementary proof that Joint work with Andrzej Grzesik. 
24.08.38077 Bruno Pitrus 
Optymalizacja Kombinatoryczna A Borsuk–Ulam Equivalent that Directly Implies Sperner’s Lemma 
It is a known fact that Sperner's purely combinatorial lemma of triangulation is equivalent to theorems in the field of topology: Brouwer with a fixed point and KnastraKuratowskiMazurkiewicz on covering the symplex. Both of these topological theorems have stronger versions (BorsukUlam and LusternikSchnirelmann theorems on antiinflammatory points). In the paper, the authors show a combinatorial analogue of BorsukUlam theorem and use it to directly prove the Sperner lemma, closing the stronger trinity of theorems. 
17.05.38054 Paweł Palenica 
Optymalizacja Kombinatoryczna Three famous theorems on finite sets 
During the seminar I will present three statements about finite sets with evidence. Two of them are classic theorems of combinatorial power theory  theorems of Sperner and ErdősKoRado. The third of these is one of the most important theorems in finite set theory  the Hall theorem. 
20.06.35316 Bartosz Walczak 
Informatyka Teoretyczna Subexponential algorithms for finding large induced sparse subgraphs 
Let 𝒞 and 𝒟 be hereditary graph classes. Consider the following problem: given a graph
This leads, for example, to the following corollaries for specific classes 𝒞 and 𝒟:
Joint work with Jana Novotná, Karolina Okrasa, Michał Pilipczuk, Paweł Rzążewski, and Erik Jan van Leeuwen. 
09.01.18889 Dominika Salawa 
Optymalizacja Kombinatoryczna The Hardness of the Lemmings Game, or Oh no, more NPCompleteness Proofs 
In computer game 'Lemmings', lemmings are placed in a level walking towards certain direction. When they encounter a wall, they turn and walk back in the direction they came from and when they encounter a hole, they fall. If a lemming falls beyond a certain distance, it dies. The goal is to guide lemmings to the exit by assigning them skills and modifying their behavior. I will show by polynomialtime reduction from 3SAT that deciding whether particular level is solvable is an NPComplete problem. This holds even if there is only one lemming in the level to save. Graham Cormode. The Hardness of the Lemmings Game, or Oh no, more NPCompleteness Proofs. 
28.06.16041 Szymon Stankiewicz 
Podstawy Informatyki Bohm's Theorem, Church's Delta, Numeral Systems, and Ershov Morphisms by Richard Statman and Henk Barendregt 
In this note we work with untyped lambda terms under betaconversion and consider the possibility of extending Bohm's theorem to in¯nite RE (recursively enumerable) sets. Bohm's theorem fails in general for such sets V even if it holds for all finite subsets of it. It turns out that generalizing Bohm's theorem to infnite sets involves three other superfcially unrelated notions; namely, Church's delta, numeral systems, and Ershov morphisms. Our principal result is that Bohm's theorem holds for an infnite RE set V closed under beta conversion iff V can be endowed with the structure of a numeral system withc predecessor iff there is a Church delta (conditional) for V iff every Ershov morphism with domain V can be represented by a lambda term. 
19.03.13413 Jarosław Grytczuk Politechnika Warszawska 
Algorytmy Randomizowane i Aproksymacyjne Graph polynomials and choosability 
A result of Thomassen asserts that every planar graph is 5choosable (colorable from arbitrary lists of size 5 preassigned to the vertices of a graph). We prove that every planar graph has a matching whose deletion gives a 4choosable graph. The proof is based on Combinatorial Nullstellensatz  a famous algebraic result of Alon involving multivariable polynomials. We also discuss possible applications of this method to other graph coloring problems, like the four color problem or the empire coloring problem, for instance.
Joint work with Xuding Zhu. 
05.03.81751 Bartłomiej Puget 
Podstawy Informatyki Solving the Rubik’s Cube Optimally is NPcomplete by Erik D. Demaine and Sarah Eisenstat 
In this paper, we prove that optimally solving an n × n × n Rubik’s Cube is NPcomplete by reducing from the Hamiltonian Cycle problem in square grid graphs. This improves the previous result that optimally solving an n×n×n Rubik’s Cube with missing stickers is NPcomplete. We prove this result first for the simpler case of the Rubik’s Square – an n × n × 1 generalization of the Rubik’s Cube – and then proceed with a similar but more complicated proof for the Rubik’s Cube case. Our results hold both when the goal is make the sides monochromatic and when the goal is to put each sticker into a specific location. 
28.10.62585 Maciej Czerwiński 
Podstawy Informatyki Automata Theoretic Account of Proof Search by Aleksy Schubert, Wil Dekkers and Henk P. Barendregt 
Techniques from automata theory are developed that handle search for inhabitants in the simply typed lambda calculus. The resulting method for inhabitant search, which can be viewed as proof search by the CurryHoward isomorphism, is proven to be adequate by a reduction of the inhabitant existence problem to the emptiness problem for appropriately defined automata. To strengthen the claim, it is demonstrated that the latter has the same complexity as the former. We also discuss the basic closure properties of the automata. 
05.01.46268 Krzysztof Maziarz 
Optymalizacja Kombinatoryczna Exact Algorithms via Monotone Local Search 
Parameterized algorithms can solve some optimization problems quickly, assuming a certain parameter is bounded: for example, when we aim to satisfy a SAT formula by setting at most k (out of n) variables to true. However, the same algorithms directly applied to the unbounded case (k = n) usually yield poor results. Here I will discuss a bridge between parameterized algorithms and general exact exponentialtime algorithms. I will show a remarkably simple approach to obtaining a good exact exponentialtime algorithm, given a good parameterized algorithm. The resulting algorithm will be randomized, but it is also possible to derandomize it with subexponential additional cost in the complexity. This approach, at the time of publishing, pushed the stateoftheart for many optimization problems. 
08.02.43530 Krzysztof Kleiner 
Informatyka Teoretyczna Range queries and counting triangles 
Listing and counting triangles in sparse graphs are wellstudied problems. For a graph with m edges, Björklund et al. gave an O(m^{1.408}) algorithm which can list up to m triangles. The exact exponent depends on the exponent omega in matrix multiplication, and becomes 4/3 if omega=2. Pătraşcu proved that an algorithm faster than O(m^{4/3}) would imply a subquadratic algorithm for 3SUM, which is considered unlikely. In our work we consider a variant of triangle problem asking to determine for every edge the number of triangles which contains that edge. We prove that this problem is no easier than listing up to m triangles, although it still admits an algorithm of the same O(m^{1.408}) complexity. We also propose a natural class of range query problems, including for example the following problem: given a family of ranges in an array, compute the number of inversions in each of them. We prove that all the problems in this class are equivalent, under onetopolylog reductions, to counting triangles for each edge. In particular the time complexities of these problems are the same up to polylogarithmic factors. This is joint work of Lech Duraj, Krzysztof Kleiner, Adam Polak and Virginia VassilevskaWilliams. 
23.06.43420 Przemysław Rutka (Lublin) 
Podstawy Informatyki Wybrane algorytmiczne zastosowania klasycznych wielomianów ortogonalnych 
Klasyczne wielomiany ortogonalne, odpowiadające im klasyczne funkcje wagowe oraz ich własności znajdują wiele zastosowań w takich chociażby obszarach jak tomografia, mechanika kwantowa, kombinatoryka, przetwarzanie obrazów i sygnałów, kompresja danych oraz zwiększanie wydajności algorytmów. W tym ostatnim zakresie cały czas uzyskuje się wiele ciekawych wyników, pozwalających na efektywne numeryczne rozwiązywanie różnych problemów. Można do tych problemów w szczególności zaliczyć barycentryczne interpolacje Fejéra, Hermite'a i Lagrange'a oraz problemy ekstremalne typu Szegő i MarkowaBernsteina. W pierwszym przypadku, gdy interpolowanych jest n wartości w węzłach, będących zerami klasycznych wielomianów ortogonalnych, możliwa jest poprawa złożoności obliczeniowej algorytmów, obliczających wartości wielomianów interpolacyjnych w oparciu o wzory barycentryczne, z O(n^2) do O(n). Wymagane jest w tym celu zastosowanie odpowiednich jawnych wzorów na wagi barycentryczne lub wzorów wiążących wagi barycentryczne z wagami i węzłami kwadratur Gaussa. Z kolei w drugim przypadku, jak się okazuje powiązanym z pierwszym, daje się sformułować wzory, pozwalające bezpośrednio obliczać na komputerze najlepsze stałe, występujące w nierównościach typu Szegő i MarkowaBernsteina oraz wartości wielomianów ekstremalnych, dla których te nierówności stają się równościami. Nierówności te związane są z iterowanymi klasycznymi funkcjami wagowymi i można je wykorzystać do szacowania wartości lub norm pochodnych D^{k}p lub różnic progresywnych Δ^{k}p wielomianów p(x), odpowiednio w przypadku ciągłym lub dyskretnym.
Inne tego typu rezultaty, korzystające z klasycznych wag i/lub klasycznych wielomianów ortogonalnych, można otrzymać także dla problemu typu izoperymetrycznego w klasie płaskich, zamkniętych krzywych wielomianowych, problemu równowagi elektrostatycznej układu ładunków, problemu efektywnej, stabilnej i najbardziej ekonomicznej interpolacji oraz problemu dwustronnych oszacowań aproksymacyjnych a priori typu Chernoffa. 
08.12.27125 Anita Badyl 
Optymalizacja Kombinatoryczna A Simplification of the MV Matching Algorithm and its Proof 
Simple and effective algorithms solving the problem of finding maximum matchings in bipartite graphs had been known for years before a lowcomplexity algorithm for nonbipartite graphs was published for the first time. That algorithm is known as the MicaliVazirani algorithm, and it constitutes an intricate combination of the HopcroftKarp algorithm for bipartite graphs and the Blossom algorithm for general graphs. It achieves the complexity of O(m√n), which demonstrates that matchings in general graphs are not harder to find than matchings in bipartite ones. We present an intuitive introduction to the algorithm, explaining its main definitions and procedures. Vijay V. Vazirani. A Simplification of the MV Matching Algorithm and its Proof. arXiv. 2012. 
31.08.27102 Kamil Rajtar 
Optymalizacja Kombinatoryczna Rectangular tiling 
During the seminar will be presented proofs of the seemingly geometrical problem of tiling a rectangle with tiles with at least one side of total length. 
16.02.24255 Weronika Grzybowska 
Podstawy Informatyki A Mesh of Automata by Sabine Broda, Markus Holzer, Eva Maia, Nelma Moreira, Rogerio Reis 
We contribute new relations to the taxonomy of di erent conversions from regular expressions to equivalent nite automata. In particular, we are interested in transformations that construct automata such as, the follow automaton, the partial derivative automaton, the prefix automaton, the automata based on pointed expressions recently introduced and studied, and last but not least the position, or Glushkov automaton (A_POS), and their double reversed construction counterparts. We deepen the understanding of these constructions and show that with the artefacts used to construct the Glushkov automaton one is able to capture most of them. As a byproduct we define a dual version of the position automaton which plays a similar role as A_POS but now for the reverse expression. Moreover, it turns out that the prefix automaton A_Pre is central to reverse expressions, because the determinisation of the double reversal of A_Pre (first reverse the expression, construct the automaton A_Pre, and then reverse the automaton) can be represented as a quotient of any of the considered deterministic automata that we consider in this investigation. This shows that although the conversion of regular expressions and reversal of regular expressions to nite automata seems quite similar, there are signifcant differences. 
13.05.70932 Michał Stobierski 
Optymalizacja Kombinatoryczna How 'hard' a video game can be? 
Computer games are a wellstudied branch of the theory of complexity. Many of them fit into a similar scheme, lying in the NP (and even NPhard) and, thanks to Savitch's Theorem, in PSPACE (hard). It turns out, however, that some of them, thanks to their unique mechanics, are able to simulate the operation of the Turing Machine and thus pose undecidable problems! An interesting example of such a game is Braid, on which this presentation is based. We will start by showing differences and similarities with other games, then we will show how to simulate the operation of the abstract 'counter machine' and talk about a particularly interesting variant of the game, which introduces an TM model that, when it writes to the tape, deletes all data on the tape to the right of the head. And despite the fact that it looks like simplified variant, it lies in EXPSPACE, making Braid a totally 'nonschematic' game. 
03.02.70909 Rafał Byczek 
Optymalizacja Kombinatoryczna The chromatic number of Kneser graphs 
In 1955 the number theorist Martin Kneser posed a seemingly innocuous problem that became one of the great challenges in graph theory until a brilliant and totally unexpected solution, using the “Borsuk–Ulam theorem” from topology, was found by László Lovász twentythree years later. It happens often in mathematics that once a proof for a longstanding problem is found, a shorter one quickly follows, and so it was in this case. Within weeks Imre Bárány showed how to combine the Borsuk–Ulam theorem with another known result to elegantly settle Kneser’s conjecture. Then in 2002 Joshua Greene, an undergraduate student, simplified Bárány’s argument even further, and it is his version of the proof that I present here. 
09.03.68171 Bartłomiej Bosek 
Informatyka Teoretyczna Algorithms for posets and graphs games – coloring and matching 
Graph colorings and online algorithms on graphs constitute the key fragments of the algorithmic graph theory. Specifically, the subject of this study will be a presentation of the results concerning
The first part of the talk will concern different aspects of the coloring problem as well as different evidential techniques. The presented results concern majority choosability of digraphs, harmonious coloring of hypergraphs and semiuni conjecture of product of two posets. The next part of presentation will concern online chain partitioning of posets. There will be presented a full characterization of the class of posets, for which the number of colors (chains) used by firstfit is a function of width, i.e. best offline solution. This part will also present two different subexponential online algorithm for the online chain partitioning problem. The last part will concern the incremental matching problem in bipartite graphs. There will be presented an incremental algorithm that maintains the maximum size matching in total time equal the running time of one of the fastest offline maximum matching algorithm that was given by Hopcroft and Karp. Moreover, I will show an analysis of the shortest augmenting path algorithm. This is joint work with Marcin Anholcer, Jarosław Grytczuk, Sebastian Czerwiński, Paweł Rzążewski, Stefan Felsner, Kolja Knauer, Grzegorz Matecki, Tomasz Krawczyk, H. A. Kierstead, Matthew Smith, Dariusz Leniowski, Piotr Sankowski, Anna ZychPawlewicz. 
27.04.68112 Bartłomiej Jachowicz, Mateusz Kaczmarek 
On the Complexity of Exact Pattern Matching in Graphs: Binary Strings and Bounded Degree (M. Equi et al.) 
Szukanie dokładnego wzorca w grafie etykietowanym to problem polegający na szukaniu ścieżek w grafie G = (V, E), których etykiety tworzą napis taki sam jak wzorzec P[1…m]. Ten problem można rozwiązać za pomocą algorytmu działającego w kwadratowym czasie O(Em). Jednakże w tej pracy, autorzy podają warunkowe ograniczenie dolne na czas działania algorytmu. Przy założeniu Strong Exponential Time Hypothesis (SETH) nie istnieje algorytm działający w czasie O(m E^{1e}) lub O(E m^{1e}) dla dowolnej stałej e > 0. 
02.11.49005 27.06.29840 Tomasz Krawczyk 
Informatyka Teoretyczna Testing isomorphism of circulararc graphs  Hsu's approach revisited 
Circulararc graphs are intersection graphs of arcs on the circle. The aim of our work is to present a polynomial time algorithm testing whether two circulararc graphs are isomorphic. To accomplish our task we construct decomposition trees, which are the structures representing all normalized intersection models of circulararc graphs. Normalized models reflect the neighbourhood relation in a circulararc graph and can be seen as its canonical representations; in particular, every intersection model can be easily transformed into a normalized one.
Our work adapts and appropriately extends the previous work on similar topic done by Hsu [SIAM J. Comput. 24(3), 411439, (1995)]. In his work Hsu developed decomposition trees representing the structure of all normalized models of circulararc graphs. However, due to the counterexample given in [Discrete Math. Theor. Comput. Sci., 15(1), 157182, 2013] his decomposition trees can not be used by the algorithm testing isomorphism of circulararc graphs. 
21.12.48946 Rafał Kaszuba, Michał Zwonek 
A simpler implementation and analysis of Chazelle’s Soft Heaps (H. Kaplan, U. Zwick) 
W 2000 roku Chazelle wymyślił nową strukturę danych: aproksymacyjne priorytetowe kolejki złączalne (Soft Heaps) i użył jej aby uzyskać najszybszy znany deterministyczny algorytm oparty na porównaniach do obliczenia minimalnego drzewa rozpinającego, jak również nowe algorytmy do znajdowania ktej najmniejszej liczby na liście i przybliżonego sortowania. Jeśli wstawimy do kolekcji miękkich kopców n elementów to co najwyżej εn ze wszystkich elementów będących aktualnie w kopcach dla danego parametru ε może być uszkodzonych, to znaczy ich klucze zostały sztucznie podwyższone. Dzięki pozwoleniu na uszkodzenia każda operacja na miękkim kopcu jest wykonywana w O(log 1/ε) amortyzowanym czasie. Chazelle uzyskał miękkie kopce przy pomocy kopców dwumianowych, gdzie każda kolejka priorytetowa to kolekcja drzew dwumianowych. W tej pracy autorzy opisują prostszą i bardziej bezpośrednią implementację miękkich kopców, gdzie każda kolejka priorytetowa jest złożona z kolekcji standardowych drzew binarnych. Ta implementacja ma przewagę nad wcześniejszą, bo nie trzeba wykonywać operacji sprzątania, której używał Chazelle w swojej. W pracy przedstawiona jest również zwięzła analiza amortyzowana nowej implementacji. 
16.03.48896 Dawid Tracz 
Podstawy Informatyki Regular Matching and Inclusion on Compressed Tree Patterns with Context Variables by Iovka Boneva, Joachim Niehren, and Momar Sakho 
We study the complexity of regular matching and inclusion for compressed tree patterns extended by context variables. The addition of context variables to tree patterns permits us to properly capture compressed string patterns but also compressed patterns for unranked trees with tree and hedge variables. Regular inclusion for the latter is relevant to certain query answering on Xml streams with references. 
01.09.32601 Filip Bartodziej 
Optymalizacja Kombinatoryczna Turán’s graph theorem 
We’ll cover the Turan theorem from 1941, which provides a restriction on the number of edges in a graph that doesn’t contain an induced kclique, depending on parameter k. 
24.05.32578 Mateusz Pabian 
Optymalizacja Kombinatoryczna Gaming is a hard job, but someone has to do it! 
General schemes relating the computational complexity of a video game to the presence of certain common elements or mechanics, such as destroyable paths, collectible items, doors opened by keys or activated by buttons or pressure plates, etc. Proofs of complexity of several video games, including PacMan, Tron, Lode Runner, Boulder Dash, Deflektor, Mindbender, Pipe Mania, Skweek, Prince of Persia, Lemmings, Doom, Puzzle Bobble 3, and Starcraft. Giovanni Viglietta. Gaming is a hard job, but someone has to do it! arXiv. 2013. 
10.11.29730 Jan Derbisz 
Podstawy Informatyki What Percentage of Programs Halt? by Laurent Laurent Bienvenu, Damien Desfontaines and Alexander Shen 
Fix an optimal Turing machine U and for each n consider the ratio \rho^U_n of the number of halting programs of length at most n by the total number of such programs. Does this quantity have a limit value? In this paper, we show that it is not the case, and further characterise the reals which can be the limsup of such a sequence \rho^U_n . We also study, for a given optimal machine U, how hard it is to approximate the domain of U from the point of view of coarse and generic computability. 
26.04.13436 Marcin Briański 
Optymalizacja Kombinatoryczna A short story of graphs that count 
In 1978 Thomason provided a simple, constructive proof of Smith’s theorem; in particular this proof provides a simple algorithm enables one to find a second Hamiltonian cycle whenever one is given a cubic graph and a Hamiltonian cycle in it. For a couple of years, the runtime of the algorithm remained unknown, with worst known cases being cubic (in the number of vertices), however in 1999 Krawczyk found an example of a graph family, such that Thomason’s algorithm takes time Ω(2^{n/8}) where is the number of vertices in the input graph from the family. In this talk, I will present a family of cubic, planar, and 3connected graphs, such that Thomason’s algorithm takes time Θ(1.1812^{n}) on the graphs in this family. This scaling is currently the best known. 
01.01.79146 Vladyslav Hlembotskyi 
Optymalizacja Kombinatoryczna The Angel of power 2 wins 
Let's consider the following game: we have two players (they are called the angel and the devil) and an infinite chessboard. The angel is located in some cell on the board. Players make moves alternatively. The devil chooses any cell that is not occupied by the angle and blocks it. The angel can jump to any other cell which is at distance at most p (p is fixed) from its present location and is not blocked. The devil wins if the angel cannot jump to any other cell. The angel wins if it can avoid being captured forever. We will show that the angel of power 2 has a winning strategy. 
24.09.79122 Katarzyna Bułat 
Optymalizacja Kombinatoryczna Distributed tracing 
The presentation will cover the topic of distributed tracing, which is an important issue in the field of distributed systems. Services are nowadays implemented as complex networks of related subsystems and it is often hard to determine the source of performance problem in such complex structures. We will take a look at Dapper, a largescale distributed systems tracing infrastructure, and discuss the challenges its designers had to face, as well as the opportunities the tool gives to programmers. We will discuss the core goals of effective instrumentation, analyze the problem of handling huge amount of tracing data and focus on security concerns. 
19.05.59957 Adrian Siwiec 
Optymalizacja Kombinatoryczna Online Maximum Matching with Recourse 
Online maximum matching problem has a recourse of k, when the decision whether to accept an edge to a matching can be changed k times, where k is typically a small constant. First, we consider the model in which arriving edge never disapears. We show that greedy algorithm has competitive ratio of 3/2 for even k and 2 for odd k. Then we show an improvement for typical values of k and proceed to show a lower bound of 1+1/(k1). Later, we discuss a model where edges can appear and disappear at any time and show generalized algorithms. 
05.11.57109 Rafał Byczek 
Podstawy Informatyki Improving the Upper Bound on the Length of the Shortest Reset Words by Marek Szykula 
We improve the best known upper bound on the length of the shortest reset words of synchronizing automata. The new bound is slightly better than 114n^3 / 685+O(n^2). The Cerny conjecture states that (n−1)^2 is an upper bound. So far, the best general upper bound was (n^3−n)/6−1 obtained by J.E. Pin and P. Frankl in 1982. Despite a number of efforts, it remained unchanged for about 35 years. To obtain the new upper bound we utilize avoiding words. A word is avoiding for a state q if after reading the word the automaton cannot be in q. We obtain upper bounds on the length of the shortest avoiding words, and using the approach of Trahtman from 2011 combined with the wellknown Frankl theorem from 1982, we improve the general upper bound on the length of the shortest reset words. For all the bounds, there exist polynomial algorithms finding a word of length not exceeding the bound. 
12.01.40792 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna Open problem session 
At the seminar were presented some interesting open problems in the field of graph theory. 
14.05.37999 Kornel Dulęba, Jan Mełech 
A Randomized MaximumFlow Algorithm (Cheriyan & Hagerup) 
Praca przedstawia randomizowany algorytm obliczający maksymalny przepływ. Dla sieci przepływowej o n wierzchołkach i m krawędziach, czas wykonania jest O(nm + n^{2}(log n)^{2}) z prawdpodobieństwem co najmniej 1  2^{sqrt(nm)}. Algorytm jest zawsze poprawny i w najgorszym przypadku działa w czasie O(nm log n). Czynnik randomizujący składa się tylko z zastosowania losowych permutacji do list sąsiedztwa wierzchołków na początku algorytmu. 
30.06.37944 Vladyslav Hlembotskyi 
Podstawy Informatyki Upper Bounds for Standardizations and an Application by Hongwei Xi 
We present a new proof for the standardization theorem in lambdacalculus, which is largely built upon a structural induction on lambdaterms. We then extract some bounds for the number of betareduction steps in the standard betareduction sequence obtained from transforming a given betareduction sequence, sharpening the standardization theorem. As an application, we establish a super exponential bound for the lengths of betareduction sequences from any given simply typed A 
06.09.21626 Kamil Kropiewnicki 
Optymalizacja Kombinatoryczna Identities versus bijections 
In 1740 Leonhard Euler began to work on counting partitions. It resulted in two fundamental papers in the field. Integer partitions have been an active field of study ever since, tackled by many including Srinivasa Ramanujan, Paul Erdős and Donald Knuth. We present a few beautiful proofs of identities using only basic generating functions and simple bijections. 
09.10.18888 Zoltán Lóránt Nagy Eötvös University & Alfréd Rényi Institute of Mathematics 
Informatyka Teoretyczna Triangles in line arrangements 
A widely investigated subject in combinatorial geometry, originating from Erdős, is the following: given a point set P of cardinality n in the plane, how can we describe the distribution of the determined distances, e.g., determine the maximum number of unit distances, the maximum number of minimum/maximum distances, the minimum number of distinct distances? This has been generalized in many directions by taking point sets in a certain (not necessarily Euclidean) metric space and studying the distribution of certain configurations — and a whole theory emerged. In this talk I propose the following problem variant: consider planar line arrangements of n lines, and determine the maximum number of unit/maximum/minimum area determined by these lines. We prove that the order of magnitude for the maximum occurrence of unit area lies between Joint work with Gábor Damásdi, Leo MartínezSandoval and Dániel T. Nagy. 
23.02.18779 Jan Derbisz, Pola Kyzioł, Krzysztof Maziarz, Jakub Nowak, Grzegorz Juzrdziński 
Podstawy Informatyki Prezentacje prac magisterskich 
Jan Derbisz, Promotor: dr hab. Tomasz Krawczyk Pola Kyzioł, Promotor: dr hab. Tomasz Krawczyk Krzysztof Maziarz, Promotor: prof. dr hab. Jacek Tabor Jakub Nowak, Promotor: prof. dr hab. Jacek Tabor Grzegorz Jurdziński, Promotor: dr Piotr Micek 
29.09.76384 Michał Wrona 
Informatyka Teoretyczna Relational Width of FirstOrder Expansions of Homogeneous Graphs with Bounded Strict Width 
We study the amount of consistency (measured by relational width) needed to solve the CSP parametrized by firstorder expansions of countably infinite homogeneous graphs, that are, the structures firstorderdefinable in a homogeneous graph containing the edge relation E, the relation N that holds between different vertices not connected by an edge and the equality. We study our problem for structures that additionally have bounded strict width, i.e., establishing local consistency of an instances of the CSP not only decides if there is a solution but also ensures that every solution may be obtained from a locally consistent instance by greedily assigning values to variables, without backtracking. It is known that with every countably infinite homogeneous graph G the finite unique minimal set S of finite graphs is associated such that some finite H is an induced substructure of G if and only if there is no H' in S such that H' embeds into H. 
02.11.73646 Marcin Briański 
Algorytmy Randomizowane i Aproksymacyjne Measuring sparsity (based on the lecture by M. Pilipczuk and S. Siebertz) 
09.12.68170 Rafał Burczyński 
Optymalizacja Kombinatoryczna Basic properties of 3CCP graphs 
We will introduce a class of graphs called 3CCP, which contains graphs that are 3connected, cubic (3regular) and planar. It was shown by Tarjan that finding Hamiltonian cycle in a graph assuming these properties remains NPcomplete  we will show the reduction from 3SAT problem. After that we will present Smith's theorem about parity of number of Hamiltonian cycles containing given edge in cubic graphs and show elegant constructive proof using Thomason's lollipop method. After that we will show a class of graphs for which previous algorithm for finding second Hamiltonian cycle takes exponential number of steps. 
28.01.68112 Jan Derbisz, Franciszek Stokowacki 
An Equivalence Class for Orthogonal Vectors (L.Chen, R.Williams) 
Problem sprawdzania, czy pośród n wektorów istnieje para wektorów ortogonalnych umiemy łatwo rozwiązać w czasie O(n^{2} log n), jednak nie jest znany algorytm szybszy niż n^{2}. Autorzy pracy dowodzą, że istnienie algorytmu podkwadratowego jest równoważne istnieniu takich algorytmów dla kilku innych problemów, między innymi ApxMinIP  znajdowania pary wektorów będących kaproksymacją maksymalnego iloczynu skalarnego oraz Approximate Bichrom.ℓpClosestPair  problemu znajdowania aproksymowanej najbliższej dwukolorowej pary punktów. Powyższe równoważności są zachowane w sytuacji, w której zamiast odpowiadać offline mamy strukturę danych i odpowiadamy na zapytania online. Dodatkowo w pracy przedstawione są nowe algorytmy aproksymowane dla ApxMinIP oraz rozwiązywania pewnych instancji MAXSAT. 
12.01.65433 Lech Duraj 
Informatyka Teoretyczna A subquadratic algorithm for Longest Common Increasing Subsequence 
The Longest Common Increasing Subsequence problem (LCIS) is a natural variant of the celebrated longest common subsequence (LCS). For LCIS, as well as for LCS, there is an O(n^{2}) algorithm and a SETHbased quadratic lower bound. Both the algorithm and the proof of the bound are, however, quite different for LCIS. For LCS, there is also the MasekPaterson O(n^{2}/log n) algorithm. Its technique (the 'four Russians trick') does not seem to work for LCIS in any obvious way, so a natural question arises: does any subquadratic algorithm exist for Longest Common Increasing Subsequence problem? We answer this question positively, presenting a O(n^{2}/log^{a}n) algorithm for some a>0. The algorithm is not based on memorizing small inputs (often used for logarithmic speedups, including LCS), but rather utilizes a new technique, bounding the number of significant symbol matches between the two sequences. 
04.08.49005 Adrian Siwiec 
Optymalizacja Kombinatoryczna List coloring of Latin Squares 
For each cell (i, j) of NxN square there is given a list C(i, j) of N colors. Can we choose a color for each cell in such a way that colors in each row and each column are distinct? 
22.09.48946 Katarzyna Bułat, Kamil Rajtar 
Correctness of constructing optimal alphabetic trees reviseted 
Prezentowana przez nas praca przedstawia nowe obserwacje, które pozwoliły autorom dowieść poprawności dwóch znanych algorytmów (HuTuckera i GarsiWachs) na konstrukcję optymalnych drzew utrzymujących porządek leksykograficzny. Omówimy uogólnioną wersję algorytmu GarsiWachs wraz z przejrzystym i łatwym do zilustrowania dowodem, który pomaga również w zrozumieniu podejścia HuTuckera. 
07.09.46267 Grzegorz Gutowski 
Informatyka Teoretyczna Entropy Compression for Acylic EdgeColorings 
Let G be a graph with maximum degree d. We show a randomized procedure that colors the edges of G so that:
Such a coloring is called an acylic edgecoloring of G. The minimum number of colors in an acyclic edge coloring of G is called the acylic index of G. It is conjectured that acylic index of G is at most d+2. We are able to prove that our coloring procedure succeeds for roughly 3.97d colors (improving on a previous result that used 4d colors). This is joint work with Jakub Kozik and Xuding Zhu. 
22.11.46157 Rafał Byczek i Paweł Mader 
Podstawy Informatyki A theory of linear typings as flows on 3valent graphs by Noam Zeilberger 
Building on recently established enumerative connections between lambda calculus and the theory of embedded graphs (or “maps”), this paper develops an analogy between typing (of lambda terms) and coloring (of maps). Our starting point is the classical notion of an abelian groupvalued “flow” on an abstract graph (Tutte, 1954). Typing a linear lambda term may be naturally seen as constructing a flow (on an embedded 3valent graph with boundary) valued in a more general algebraic structure consisting of a preordered set equipped with an “implication” operation and unit satisfying composition, identity, and unit laws. Interesting questions and results from the theory of flows (such as the existence of nowherezero flows) may then be reexamined from the standpoint of lambda calculus and logic. For example, we give a characterization of when the local flow relations (across vertices) may be categorically lifted to a global flow relation (across the boundary), proving that this holds just in case the underlying map has the orientation of a lambda term. We also develop a basic theory of rewriting of flows that suggests topological meanings for classical completeness results in combinatory logic, and introduce a polarized notion of flow, which draws connections to the theory of proofnets in linear logic and to bidirectional typing. 
11.10.43529 Marcin Briański 
Algorytmy Randomizowane i Aproksymacyjne Measuring sparsity (based on the lecture by M. Pilipczuk and S. Siebertz) 
29.03.29840 Kamil Kropiewnicki 
Optymalizacja Kombinatoryczna Shuffling cards 
What do the birthday paradox, the coupon collector problem and shuffling cards have in common? What does it mean for a deck of cards to be "random" or "close to random"? How long does one have to shuffle a deck of cards until it is random? In practical use cases, the question is not about the asymptote  it is about the exact numbers. 
17.05.29781 Bartłomiej Jachowicz, Mateusz Kaczmarek 
SETHbased Lower Bounds for Subset Sum and Bicriteria Path 
Głównym rezultatem tego artykułu jest ścisła redukcja z kSAT do problemu Subset Sum na gęstych instancjach, co pokazuje że algorytm Bellmana z 1962 roku O*(T)  dla Subset Sum z n liczbami i celem równym T nie da się poprawić do czasu T^{1  e} * 2^{o(n)}, dla dowolnego e > 0, pod warunkiem prawdziwości SETH. Wnioskiem z tego jest twierdzenie "DirectOR" dla problemu Subset Sum pod warunkiem prawdziwości SETH, dające nowe możliwości udowadniania dolnych ograniczeń. Daje nam to możliwość założenia, że podjęcie decyzji o tym, czy jedna z N danych instancji problemu Subset Sum jest TAKinstancją wymaga (NT)^{1o(1)} czasu. Zastosowaniem danego rezultatu jest dolne ograniczenie dla problemu BICRITERIA s,tPATH pod warunkiem prawdziwośći SETH. 
17.07.26992 Krzysztof Turowski Purdue University, USA 
Podstawy Informatyki Compression of Dynamic Graphs Generated by a Duplication Model 
One of the important topics in the information theory of nonsequential random data structures such as trees, sets, and graphs is the question of entropy: how many bits on average are needed to describe the structure. Here we consider dynamic graphs generated by a duplication model in which a new vertex selects an existing vertex and copies all of its neighbors. We provide asymptotic formulas for entopies for both labeled and unlabeled versions of such graphs and construct compression algorithms matching these bounds up to two bits. Moreover, as a side result, we were able to derive asymptotic expansions of expected value of f(X) for functions of polynomial growth, when X has betabinomial distribution  which in turn allowed to obtain e.g. asymptotic formula the entropy for a Dirichletmultinomial distribution. 
05.06.24364 Bartosz Wodziński 
Algorytmy Randomizowane i Aproksymacyjne Algorithmic barriers from phase transitions (Dimitris Achlioptas, Amin CojaOghlan) 
22.11.10674 Kamil Rajtar 
Optymalizacja Kombinatoryczna Communication without errors 
Main aim of the lecture is the answer for Claude Shannon's question from 1956: "Suppose we want to transmit messages across a channel (where some symbols may be distorted) to a receiver. What is the maximum rate of transmission such that the receiver may recover the original message without errors?" 
11.01.10616 Rafał Kaszuba, Krzysztof Zysiak 
Fast Modular Subset Sum using Linear Sketching 
Dostając zbiór n dodatnich liczb całkowitych, problem Modular Subset Sum polega na sprawdzeniu czy istnieje podzbiór, który sumuje się do zadanego t modulo dana liczba całkowita m. Jest to naturalne uogólnienie problemu Subset Sum (m=+∞), który silnie łączy się z addytywną kombinatoryką i kryptografią. Niedawno zostały opracowane efektywne algorytmy dla przypadku niemodularnego, działające w czasie bliskoliniowym pseudowielomianowym. Jednak dla przypadku modularnego najlepszy znany algorytm (Koiliaris'a i Xu) działa w czasie Õ(m^{5/4}). W tej pracy prezentujemy algorytm działający w czasie Õ(m), który dopasowuje się do warunkowego ograniczenia dolnego opartego na SETH. W przeciwieństwie do większości poprzednich wyników związanych z problemem Subset Sum, nasz algorytm nie korzysta z FFT. Natomiast, jest zdolny zasymulować "podręcznikowe" programowanie dynamiczne znacznie szybciej, używając pomysłów ze Szkicowania Liniowego. Jest to jedna z pierwszych aplikacji technik bazujących na szkicowaniu, by osiągnąć szybki algorytm dla problemów kombinatorycznych w modelu offline. 
24.03.57219 Filip Bartodziej 
Optymalizacja Kombinatoryczna Cayley’s formula for the number of trees & How to guard a museum 
First, several proofs for the number of labeled trees, each using different approach (bijection, linear algebra, recursion, double counting) will be presented. Second part of the seminar will introduce an interesting graph problem first raised by Victor Klee in 1973. This problem can be represented as placing guards in a museum to guard it properly  that is area of the museum must be completely covered by the field of view of the guards. 
26.04.54481 Agnieszka Łupińska University of California, Davis 
Informatyka Teoretyczna Gunrock: GPU Graph Analytics 
Gunrock is a CUDA library for graphprocessing designed specifically for the GPU. It uses a highlevel, bulksynchronous, datacentric abstraction focused on operations on a vertex or edge frontier. Gunrock achieves a balance between performance and expressiveness by coupling high performance GPU computing primitives and optimization strategies with a highlevel programming model that allows programmers to quickly develop new graph primitives with small code size and minimal GPU programming knowledge. 
13.07.54371 Jakub Łabaj i Gabriela Czarska 
Podstawy Informatyki Programming Languages Capturing Complexity Classes by LARS KRISTIANSEN and PAUL J. VODA 
We investigate an imperative and a functional programming language. The computational power of fragments of these languages induce two hierarchies of complexity classes. Our first main theorem says that these hierarchies match, level by level, a complexitytheoretic alternating spacetime hierarchy known from the literature. Our second main theorems says that a slightly different complexitytheoretic hierarchy (the GoerdtSeidl hierarchy) also can be captured by hierarchies induced by fragments of the programming languages. Well known complexity classes like LOGSPACE, LINSPACE, P, PSPACE etc., occur in the hierarchies. 
31.05.51743 Maciej Czerwiński 
Algorytmy Randomizowane i Aproksymacyjne Lovasz meets Weisfeiler and Leman (by Dell, Grohe and Rattan) 
"In this paper, we relate a beautiful theory by Lovász with a popular heuristic algorithm for the graph isomorphism problem, namely the color refinement algorithm and its k dimensional generalization known as the WeisfeilerLeman algorithm." 
23.02.38077 Franciszek Stokowacki 
Optymalizacja Kombinatoryczna An Approximate Restatement of the FourColor Theorem 
Four color theorem was proven in 1976 with extensive computer help. Since then there is interest in finding a simpler proof that uses no computer computation. I will present relation between Four Color Theorem and edge 3coloring of planar, cubic graphs without bridges, and a new result proving that the existence of approximate coloring (with the fourth color used ‘rarely’) is enough to imply Four Color Theorem. 
16.11.38053 Vladyslav Hlembotskyi 
Optymalizacja Kombinatoryczna EERTREE: An Efficient Data Structure for Processing Palindromes in Strings 
A palindrome is a string which reads the same forward as backward, such as `Ada` or `lol`. We will present a data structure which stores information about all the different palindromic substrings of a given string and prove some basic facts about the data structure. We will show that it is useful and discuss some problems which can be solved with it. 
05.01.37995 Łukasz Miśkiewicz, Adam Pardyl 
SpaceEfficient Algorithms for Longest Increasing Subseqence 
Najdłuższy rosnący podciąg jest znanym problemem, który można rozwiązać w złożoności O(n*log(n)) używając O(n*log(n)) dodatkowych bitów. Autorzy pracy prezentują algorytmy korzystające z mniejszej ilości dodatkowej pamięci. Konkretniej, dla sqrt(n) <= s <= n, pokazują sposób obliczania długości najdłuższego rosnącego podciągu w O(1/s * n^{2} * log(n)) korzystając z O(s * log(n)) dodatkowych bitów oraz obliczanie tego podciągu w czasie O(1/s * n^{2} * log^{2}(n)) używając tyle samo dodatkowych bitów. Dodatkowo autorzy dowodzą, że dla danej złożoności pamięciowej złożoności czasowe w modelu dostępu sekwencyjnego są optymalne z dokładnością do czynników polilogarytmicznych. 
21.12.35315 Łukasz Lachowski 
Informatyka Teoretyczna Complexity of the quorum intersection property of the Federated Byzantine Agreement System 
A Federated Byzantine Agreement System is defined in the paper https://www.stellar.org/
as a pair (V,Q) consisting of a set of nodes V and a quorum function Q : V → P(P(V)) specifying for each node a nonempty family of subsets of nodes, called quorum slices. A subset of nodes is a quorum if and only if for each of its nodes it also contains at least one of its quorum slices. The Disjoint Quorums Problem answers the question whether a given instance of fbas contains two quorums that have no nodes in common. We show that this problem is NPcomplete. We also study the problem of finding a quorum of minimal size and show it is NPhard. Further, we consider the problem of checking whether a given subset of nodes contains a quorum for some selected node. We show this problem is Pcomplete and describe a method that solves it in linear time with respect to number of nodes and the total size of all quorum slices. Moreover, we analyze the complexity of some of these problems using the parametrized point of view.

05.05.35206 Dominik Gryboś 
Podstawy Informatyki Characterizing Polynomial and Exponential Complexity Classes in Elementary LambdaCalculus by Patrick Baillot, Erika De Benedetti, Simona Ronchi Della Rocca 
In this paper an implicit characterization of the complexity classes kEXP and kFEXP, for k \geq 0, is given, by a type assignment system for a stratified lambda  calculus, where types for programs are witnesses of the corresponding complexity class. Types are formulae of Elementary Linear Logic (ELL), and the hierarchy of complexity classes kEXP is characterized by a hierarchy of types. 
02.06.18884 Jakub Nowak 
Optymalizacja Kombinatoryczna Snowflake to Avalanche: A Novel Metastable Consensus Protocol Family for Cryptocurrencies 
Consensus is one of the most important goals to be achieved when many distributed computers share the same task and resources. There are two main families of algorithms solving this problem. Traditional consensus protocols require O(n^{2}) communication, while blockchains rely on proofofwork. In this talk we will introduce a new family of leaderless Byzantine fault tolerance protocols, built on a metastable mechanism. These protocols provide a strong probabilistic safety and are both quiescent and green. We will analyze some of their properties and guarantees. Finally we will see results of porting Bitcoin transactions to the introduced family of protocols. 
28.12.16040 Bartłomiej Puget 
Podstawy Informatyki THE SAFE LAMBDA CALCULUS by WILLIAM BLUM AND LUKE ONG 
Safety is a syntactic condition of higherorder grammars that constrains occurrences of variables in the production rules according to their typetheoretic order. In this paper, we introduce the safe lambda calculus, which is obtained by transposing (and generalizing) the safety condition to the setting of the simplytyped lambda calculus. In contrast to the original definition of safety, our calculus does not constrain types (to be homogeneous). We show that in the safe lambda calculus, there is no need to rename bound variables when performing substitution, as variable capture is guaranteed not to happen. We also propose an adequate notion of betareduction that preserves safety. In the same vein as Schwichtenberg’s 1976 characterization of the simplytyped lambda calculus, we show that the numeric functions representable in the safe lambda calculus are exactly the multivariate polynomials; thus conditional is not definable. We also give a characterization of representable word functions. We then study the complexity of deciding betaeta equality of two safe simplytyped terms and show that this problem is PSPACEhard. Finally we give a gamesemantic analysis of safety: We show that safe terms are denoted by Pincrementally justified strategies. Consequently pointers in the game semantics of safe lambda terms are only necessary from order 4 onwards. 
14.03.81856 Jan Derbisz 
Optymalizacja Kombinatoryczna Choosability of Planar Graphs 
Colorability and choosability of planar graphs have been heavily studied in the past. In 1994 Thomassen proved that every planar graph is 5choosable using concise induction. Recently Grytczuk and Zhu used similar ideas to prove that for every planar graph G we can find a matching M in it such that GM is 4choosable with the help of Combinatorial Nullstellensatz theorem. 
11.06.81801 Konrad Deka, Szymon Kapała 
Tighter Connections Between FormulaSAT and Shaving Logs 
W 2015, Abboud, Backurs i VassilevskaWilliams pokazali że algorytm dla LCS działający w czasie O(n^{2eps}) implikowałby szybki algorytm dla CNFSAT, i tym samym fałszywość SETH. W tej pracy, na podstawie innych hipotez dotyczących SAT, autorzy szukają dolnych ograniczeń postaci O(n^{2}/log^{c} n) dla LCS, a także problemu odległości Frecheta oraz problemu matchowania regexów. Głównym rezultatem jest redukcja z SATa na formule wielkości s, mającej n zmiennych, do LCS na ciągach długości 2^{n/2}s^{1+o(1)}. Wynika stąd, że algorytm dla LCS działający w O(n^{2}/log^{7+eps}n) implikowałby fałszywość pewnych hipotez o FormulaSAT, a algorytm działający w O(n2/log17+epsn)  znaczący postęp w teorii złożoności obwodów. 
27.05.79122 15.08.16150 Piotr Kawałek 
Informatyka Teoretyczna Computational approach to solving equations in finite realms 
Computational approach to the problem of solving equation, began with the question of David Hilbert. He asked, if there exists an algorithm, that decides wheather given Diophantine equation has a solution or not. Yuri Matiyasevich proved this problem to be undecidable. An analogy for decidability in finite realms is tractability. During the talk, we introduce the notion of PolSat problem for finite algebras and discuss the results for the wide class of algebraic structures. 
09.10.79012 Jacek Kurek i Bruno Pitrus 
Podstawy Informatyki COMPLEXITY PROBLEMS IN ENUMERATIVE COMBINATORICS by IGOR PA 
The subject of enumerative combinatorics is both classical and modern. It is classical, as the basic counting questions go back millennia; yet it is modern in the use of a large variety of the latest ideas and technical tools from across many areas of mathematics. The remarkable successes from the last few decades have been widely publicized; yet they come at a price, as one wonders if there is anything left to explore. In fact, are there enumerative problems that cannot be resolved with existing technology? In this paper we present many challenges in the field from the computational complexity point of view, and describe how recent results fit into the story. 
29.06.76384 18.09.13412 Dominika Salawa, Kamil Kropiewnicki 
Algorytmy Randomizowane i Aproksymacyjne Representative sets in matroids (based on chapter of 'Parameterized algorithms') 
07.11.62690 Krzysztof Maziarz 
Optymalizacja Kombinatoryczna A refinement of choosability of graphs 
Between the wellknown concepts of kcolorability and kchoosability (also know as klist colorability) lies a whole spectrum of more refined notions. This allows for seeing kcolorability and kchoosability under one unified framework. Exploring this, one immediately discovers interesting problems  for example, possible strengthenings of the four color theorem. We will take a look at these notions, prove some of their properties, and leave many conjectures and open problems. 
04.02.62636 Rafał Byczek, Bruno Pitrus 
Approximating Edit Distance Within Constant Factor in Truly SubQuadratic Time 
Odległość edycyjna to jeden ze sposobów zmierzenia jak bardzo dwa ciągi znaków są do siebie podobne. Polega on na zliczeniu minimalnej liczby operacji wstawienia, usunięcia lub zmienienia znaku na inny, wymaganej aby przekształcić jedno słowo w drugie. W tej pracy autorzy skupili się na problemie złożoności obliczeniowej aproksymowania odległości edycyjnej pomiędzy parą słów. Problem wyznaczenia dokładnej odległości edycyjnej może być rozwiązany za pomocą klasycznego algorytmu dynamicznego działającego w kwadratowym czasie. W 2010 roku Andoni, Krauthgamer i Onak przedstawili działający w czasie prawie liniowym, algorytm aproksymujący odległość edycyjną z polilogarytmicznym czynnikiem aproksymacji. W 2014 Backurs i Indyk pokazali, że dokładny algorytm działający w czasie O(n^(2δ))implikowałby szybki algorytm dla SAT i fałszywość silnej hipotezy o czasie wykładniczym (SETH). Ponadto, ostatnio w 2017, Abboud i Backurs pokazali, że istnienie algorytmu aproksymującego odległość edycyjną w czasie prawdziwie podkwadratowym z czynnikiem aproksymacji 1 + o(1) implikowałoby fałszywość paru hipotez dotyczących złożoności obwodów boolowskich (circuit complexity). To poddaje w wątpliwość aproksymowalność odległości edycyjnej z dokładnością do czynnika stałego w czasie prawdziwie podkwadratowym. W tej pracy autorzy jednak odpowiedzieli twierdząco na to pytanie, przedstawiając bardzo ciekawy algorytm aproksymujący odległość edycyjną, z stałym czynnikiem aproksymacji i dowodząc, że jego czas działania jest ograniczony od góry przez Õ(n^(2−2/7)). 
04.06.59847 Marcin Briański 
Podstawy Informatyki On the compressibility of finite languages and formal proofs by Sebastian Eberhard and Stefan Hetzl 
We consider the minimal number of productions needed for a grammar to cover a finite language L as the grammatical complexity of L. We study this measure for several types of word and tree grammars and show that it is closely connected to wellknown measures for the complexity of formal proofs in firstorder predicate logic. We construct an incompressible sequence of finite word languages and transfer this and several other results about the complexity of word and tree languages to formal proofs 
22.02.57219 Dawid Tracz 
Algorytmy Randomizowane i Aproksymacyjne Finding Cliques in Social Networks: A New DistributionFree Model (Fox, Roughgarden, Seshadhri, Wei, Wein) 
03.07.43525 Jakub Łabaj 
Optymalizacja Kombinatoryczna Contracting a Planar Graph Efficiently 
Jakub Łabaj. Contracting a Planar Graph Efficiently. slides. 2018. 
29.09.43470 Tomasz Zieliński, Michał Zwonek 
On the Complexity of the (Approximate) Nearest Colored Node Problem 
Mając dany graf G = (V, E) gdzie każdy wierzchołek ma przypisany kolor, pytamy o przybliżoną odległość pomiędzy danym wierzchołkiem v a najbliższym jemu kolorowi c. Prezentujemy wyrocznię o rozciągłości 4k5 wykorzystującą O(kn sigma^(1/k)) przestrzeni i O(log k) czasu zapytania. Następnie dowodzimy, że posiadając estymatę rzędu O(polylog(n)) jesteśmy w stanie w czasie O(1) udzielić odpowiedzi na pytanie o dokładną odległość dist(v, c). Na końcu pokazujemy związek pomiędzy problemem lambdaOuMv a odległością dist(v, c). 
14.09.40791 19.01.59957 Michał Seweryn 
Informatyka Teoretyczna Bumping a ladder 
We show that every 3connected graph which contains many disjoint 2xngrid minors, contains a 2x(n+1)gridminor. We use this result in a qualitative structure theorem for graphs without large 2xn grids. This is a result from a joint paper with Tony Huynh, Gwenaël Joret, Piotr Micek and Paul Wollan 
27.01.40682 Mateusz Tokarz 
Podstawy Informatyki Enumerating Proofs of Positive Formulae by GILLES DOWEK AND YING JIANG 
We provide a semigrammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This method is complete in the sense that each normal proofterm of the formula is produced by some scheme generated by the grammar. As a corollary, we get a similar description of the set of normal proofs of positive formulae for a large class of theories including simple type theory and System F. 
17.10.38053 Mateusz Pabian 
Algorytmy Randomizowane i Aproksymacyjne New approximation algorithm for (1,2)TSP (Adamaszek, Mnich, Paluch) 
05.04.24364 Marcin Muszalski 
Optymalizacja Kombinatoryczna On the queuenumber of graphs with bounded treewidth 
In this talk I will present upper bound for a queuenumber of graphs with bounded treewidth obtained by Veit Wiechert. The new upper bound, 2k  1, improves upon double exponential upper bounds due to Dujmović et al. and Giacomo et al. Additionally I will show his construction of ktrees that have queuenumber at least k + 1. The construction solves a problem of Rengarajan and Veni Madhavan, namely, that the maximal queuenumber of 2trees is equal to 3. Marcin Muszalski. Queuenumber of graphs with bounded treewidth  Veit Wiechert. slides. 2018. 
25.05.24305 Weronika Grzybowska, Paweł Mader 
Hamming distance completeness and sparse matrix multiplication 
Autorzy prezentują polilogarytmiczne redukcje pomiędzy obliczaniem odległości Hamminga a iloczynem skalarnym, w którym miejsce mnożenia zajmuje pewna funkcja binarna na liczbach całkowitych. Dla takich funkcji binarnych należą dominance product, threshold product i odległości l_{2p+1} dla stałego p. Wykorzystując wyżej opisane redukcje, autorzy wykazują równość (z dokładnością do czynników polilogarytmicznych) złożoności wyliczania powyższych funkcji dla dwóch zbiorów wektorów. Dodatkowo, autorzy dowodzą, że APHam (oraz ten sam problem z użyciem innych wymienionych funkcji) mieści się w czasie polilogarytmicznym od mnożenia macierzy rozmiaru n na nd i nd na n, zawierających po nd niezerowych wartości. 
25.07.21516 Paweł Palenica 
Podstawy Informatyki On Randomised Strategies in the λCalculus by Ugo Dal Lago and Gabriele Vanoni 
In this work we introduce randomized reduction strategies  a notion already studied in the context of abstract reduction systems  for the lambdacalculus. We develop a simple framework that allows us to prove if a probabilistic strategy is positive almostsurely normalizing. Then we propose a simple example of probabilistic strategy for the lambdacalculus that has such a property and we show why it is nontrivial with respect to classical deterministic strategies such as leftmostoutermost or rightmostinnermost. We conclude studying this strategy for two classical sub lambda calculi, namely those duplication and erasure are syntactically forbidden. 
11.06.18888 Szymon Łukasz 
Algorytmy Randomizowane i Aproksymacyjne NPhardness of coloring 2colorable hypergraph with polylogarithmically many colors (A. Bhangale) 
We give very short and simple proofs of the following statements: Given a 2colorable 4uniform hypergraph on n vertices, 1) It is NPhard to color it with log^delta n colors for some delta>0. 2) It is quasiNPhard to color it with O({log^{1o(1)} n}) colors. 
31.03.87226 Rafał Burczyński 
Podstawy Informatyki A Hitchhiker’s Guide to descriptional complexity through analytic combinatorics by Sabine Broda, António Machiavelo, Nelma Moreira and Rogério Reis 
Nowadays, increasing attention is being given to the study of the descriptional complexity in the average case. Although the underlying theory for such a study seems intimidating, one can obtain interesting results in this area without too much effort. In this gentle introduction we take the reader on a journey through the basic analytical tools of that theory, giving some illustrative examples using regular expressions. Additionally, new asymptotic averagecase results for several $\epsilonNFA$ constructions are presented, in a unified framework. It turns out that, asymptotically, and in the average case, the complexity gap between the several constructions is significantly larger than in the worst case. Furthermore, one of the $\epsilonNFA$ constructions approaches the corresponding $\epsilonfree NFA$ construction, asymptotically and on average. 
16.02.84598 Wiktor Daniec 
Algorytmy Randomizowane i Aproksymacyjne David Galvin, “Three tutorial lectures on entropy and counting” (rozdział 5) 
David Galvin, “Three tutorial lectures on entropy and counting” (rozdział 5) 
05.08.70908 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna A new variant of the game of cops and robber 
We consider the following metric version of the Cops and Robbers game. Let G be a simple graph and let k≥1 be a fixed integer. In the first round, Cop picks a subset of k vertices B={v_{1},v_{2},...,v_{k}} and then Robber picks a vertex u but keeps it in a secret. Then Cop asks Robber for a vector D_{u}(B)=(d_{1},_{2},...,d_{k}) whose components d_{i}=d_{G}(u,v_{i}), i=1,2,...,k, are the distances from u to the vertices of B. In the second round, Robber may stay at the vertex u or move to any neighbouring vertex which is kept in a secret. Then Cop picks another k vertices and asks as before for the corresponding distances to the vertex occupied by Robber. And so on in every next round. The game stops when Cop determines exactly the current position of Robber. In that case, she is the winner. Otherwise, Robber is the winner (that is if Cop is not able to localise him in any finite number of rounds). Let ζ(G) denote the least integer k for which Cop has a winning strategy. Notice that this parameter is well defined since the inequality ζ(G)≤V(G) holds obviously. The aim of the talk is to present results concerning 2trees, outerplanar graphs and planar graphs. This is a joint work with Przemysław Gordinowicz, Jarosław Grytczuk, Nicolas Nisse, Joanna Sokół, and Małgorzata ŚleszyńskaNowak. 
23.09.70849 Filip Bartodziej, Vladyslav Hlembotskyi 
Finegrained Lower Bounds on Cops and Robbers 
Sumienni policjanci, czy sprytny złodziej? Na tym seminarium dowiemy się kto triumfuje, jak szybko (lub jak wolno) jesteśmy w stanie się o tym przekonać i ilu policjantów wystarczy, aby przyskrzynić nawet samego Frank’a Abagnale’a. Rozważania bedą oparte o grę strategiczna w policjantów i złodziei na grafie (cops and robbers). Uzyskane wyniki opierają sie na założeniu SETH/ETH. 
23.11.68060 Szymon Stankiewicz 
Podstawy Informatyki Encoding Turing Machines into the Deterministic Lambda Calculus by Ugo Dal Lago and Beniamino Accattoli 
This note is about encoding Turing machines into the lambda calculus. The encoding we show is interesting for two reasons: 1. Weakly strategy independent : the image of the encoding is a very small fragment of the lambda  calculus, that we call the deterministic lambda calculus det. Essentially, it is the CPS (continuationpassing style) lambda calculus restricted to weak evaluation (i.e., not under abstractions). In det every term has at most one redex, and so all weak strategies collapse into a single deterministic evaluation strategy, because there are no choices between redexes to be made. The important consequence of this property is that every weak evaluation strategy then allows to simulate Turing machines,as well as any strong strategy reducing weak head redexes (or even only weak head redexes) first. 2. Linear overhead: the simulation is very efficient, when taking the number of betasteps as the time cost model for the deterministic lambda calculus. The simulation in det indeed requires a number of betasteps that is linear in the number of transitions of the encoded Turing machine, which is the best possible overhead. Therefore, not only all weak strategies simulate Turing 
31.03.51743 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna Local Dimension is Unbounded for Planar Posets 
In 1981, Kelly showed that planar posets can have arbitrarily large dimension. However, the posets in Kelly's example have bounded Boolean dimension and bounded local dimension, leading naturally to the questions as to whether either Boolean dimension or local dimension is bounded for the class of planar posets. The question for Boolean dimension was first posed by Nešetril and Pudlák in 1989 and remains unanswered today. The concept of local dimension is quite new, introduced in 2016 by Ueckerdt. In just the last year, researchers have obtained many interesting results concerning Boolean dimension and local dimension, contrasting these parameters with the classic DushnikMiller concept of dimension, and establishing links between both parameters and structural graph theory, pathwidth and treewidth in particular. Here we show that local dimension is not bounded on the class of planar posets. Our proof also shows that the local dimension of a poset is not bounded in terms of the maximum local dimension of its blocks, and it provides an alternative proof of the fact that the local dimension of a poset cannot be bounded in terms of the treewidth of its cover graph, independent of its height. This is a joint work with Jarosław Grytczuk and W.T. Trotter. 
18.05.51684 Jan Mełech, Rafał Burczyński 
A Simple NearLinear Pseudopolynomial Time Randomized Algorithm for Subset Sum 
Celem znanego problemu NPzupełnego SubsetSum jest znalezienie takiego podzbioru multizbioru o mocy n, którego suma elementów wynosi t. Autorzy prezentują krótkie probabilistyczne rozwiązanie bazujące na szybkiej transformacie Fouriera oraz manipulacjach na funkcjach tworzących działające w czasie O((n+t)*polylog(t)) i zwracające odpowiedź z prawdopodobieństwem błędu rzędu O(1/(n+t)). Ten wynik został osiągnięty wcześniej, jednak praca upraszcza rozwiązanie, zawierając je raptem w kilku stronach. 
04.05.49005 08.09.68170 Patryk Mikos 
Informatyka Teoretyczna Does the representation matter? 
The class of unit interval graphs has at least 3 equivalent definitions:
We ask whether the competitive ratio in the online unitinterval graph coloring with bandwidths depends on the chosen graph representation. 
19.07.48895 Vladyslav Hlembotskyi 
Podstawy Informatyki Limited Automata and Regular Languages by Giovanni Pighizzini and Andrea Pisoni 
Limited automata are onetape Turing machines that are allowed to rewrite the content of any tape cell only in the first d visits, for a fixed constant d. In the case d = 1, namely, when a rewriting is possible only during the first visit to a cell, these models have the same power of finite state automata. We prove state upper and lower bounds for the conversion of 1limited automata into finite state automata. In particular, we prove a double exponential state gap between nondeterministic 1limited automata and oneway deterministic finite automata. The gap reduces to single exponential in the case of deterministic 1limited automata. This also implies an exponential state gap between nondeterministic and deterministic 1limited automata. Another consequence is that 1limited automata can have less states than equivalent twoway nondeterministic finite automata. We show that this is true even if we restrict to the case of the oneletter input alphabet. For each d \geq 2, dlimited automata are known to characterize the class of contextfree languages. Using the ChomskySchutzenberger representation for contextfree languages,

23.11.32577 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna A Tight Bound for Shortest Augmenting Paths on Trees 
The shortest augmenting path technique is one of the fundamental ideas used in maximum matching and maximum flow algorithms. Since being introduced by Edmonds and Karp in 1972, it has been widely applied in many different settings. Surprisingly, despite this extensive usage, it is still not well understood even in the simplest case: online bipartite matching problem on trees. In this problem a bipartite tree T=(WB, E) is being revealed online, i.e., in each round one vertex from B with its incident edges arrives. It was conjectured by Chaudhuri et. al. that the total length of all shortest augmenting paths found is O(n log n). In this paper we prove a tight O(n log n) upper bound for the total length of shortest augmenting paths for trees improving over O(n log² n) bound. This is a joint work with Dariusz Leniowski, Piotr Sankowski, and Anna ZychPawlewicz. 
12.01.32519 Dawid Pyczek, Michał Zieliński 
On the WorstCase Complexity of TimSort 
TimSort jest bardzo interesującym algorytmem sortującym, który został wprowadzony do Pythona stosunkowo niedawno, bo w 2002 roku. Ten bardzo popularny algorytm używany jest z powodzeniem na całym świecie. Wynika to z faktu, że działa on wyjątkowo szybko na częściowo posortowanych danych. Aż do niniejszej pracy nie była znana pesymistyczna złożoność tego algorytmu  w pracy pokazane zostanie, że pesymistyczna złożoność algorytmu TimSort wynosi O(n log n). Następnie złożoność algorytmu ograniczymy przez O(n+n log ρ), gdzie ρ to ilość przebiegów. Pierwsza złożoność w bezpośredni sposob wynika z drugiej, ale oba dowody są ciekawe i pomagają lepiej zrozumieć działanie TimSorta. Dodatkowo w wyniku analizy algorytmu autorzy pracy odryli błąd w implementacji TimSorta w Javie. 
28.12.29839 Andrzej Dorobisz 
Informatyka Teoretyczna Induced subgraphs of graphs with large chromatic number 
Based on the paper a proof of a 1985 conjecture of Gyarfas that for all k, ℓ, every graph with sufficiently large chromatic number contains either a clique of cardinality more than k or an induced cycle of length more than ℓ will be presented. 
14.03.29730 Michał Zieliński 
Podstawy Informatyki Lambda Theories allowing Terms with a Finite Number of Fixed Points by BENEDETTO INTRIGILA and RICHARD STATMAN 
A natural question in the lambda calculus asks what is the possible number of fixed points of a combinator (closed term). A complete answer to this question is still missing (Problem 25 of TLCA Open Problems List) and we investigate the related question about the number of fixed points of a combinator in lambdatheories. We show the existence of a recursively enumerable lambda theory where the number is always one or infinite. We also show that there are lambdatheories such that some terms have only two fixed points. In a first example, this is obtained by means of a nonconstructive (more precisely nonr.e.) lambdatheory where the range property is violated. A second, more complex example of a nonr.e. Lambdatheory (with a higher unsolvability degree) shows that some terms can have only two fixed points while the range property holds for every term. 
06.11.10564 Jarosław Duda Instytut Informatyki UJ 
Podstawy Informatyki Krótkie wprowadzenie do ANS, MERW i pól Markova 
Na seminarium spróbuję zainteresować kilkoma z tematów, którymi się zajmowałem, np. kodowaniem Asymmetric Numeral Systems, które jest obecnie używane w produktach m.in. Apple, Facebook, Google. Opowiem też o Maximal Entropy Random Walk, czyli jak optymalnie wybierać błądzenie przypadkowe na grafie  z perspektywy zastosowań m.in. do maksymalizacji ilości przechowywanej informacji, zrozumienia i naprawienia rozbieżności między dyfuzją a mechaniką kwantową, analizy obrazów, sieci społecznych, czy rekonstrukcji traktów nerwowych. Tematem łączącym powyższe będą pola Markova, czyli wielowymiarowe uogólnienie procesów Markova, o których też krótko opowiem z przykładem zastosowania do poprawienia pojemności dysków twardych. Slajdy do seminarium można znaleźć na: http://tiny.cc/2jpiyy 
21.06.2018 
Wykład Wojciecha Szpankowskiego "Analytic Information Theory: From Shannon to Knuth and Back" 
14.04.40791 Mateusz Twaróg, Patryk Urbański, Łukasz Majcher 
Optymalizacja Kombinatoryczna Progress in the Arachne Project 
01.10.37943 Marcin Briański 
Podstawy Informatyki COARSE REDUCIBILITY AND ALGORITHMIC RANDOMNESS by DENIS HIRSCHFELDT, CARL JOCKUSCH, RUTGER KUYPER, AND PAUL SCHUPP 
A coarse description of a set A \subset \omega is a set D \subset \omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse descriptions of a given set A, especially when A is effectively random in some sense. We show that if A is 1random and B is computable from every coarse description D of A, then B is Ktrivial, which implies that if A is in fact weakly 2random then B is computable. Our main tool is a kind of compactness theorem for coneavoiding descriptions, which also allows us to prove the same result for 1 genericity in place of weak 2randomness. In the other direction, we show that if A \leq_T \emptyset is a 1random set, then there is a noncomputable c.e. set computable from every coarse description of A, but that not all Ktrivial sets are computable from every coarse description of some 1random set.

24.04.21653 Krzysztof Maziarz 
Optymalizacja Kombinatoryczna The chromatic number of the plane is at least 5 
The HadwigerNelson problem asks for the minimum number of colors required to color the plane, in such a way, that any two points at distance exactly one are assigned different colors. Albeit its simple definition, no significant progress on the question was made for nearly a century. In the discussed paper, Aubrey D. N. J. de Grey has shown a set of points in the plane, such that 5 colors are necessary to color it properly, thus improving a longstanding lower bound of 4 colors. Interestingly, the smallest such set discovered so far has 1581 vertices. The chromatic number of the plane is at least 5, Aubrey D.N.J. de Grey 
07.12.21625 Szymon Łukasz 
Optymalizacja Kombinatoryczna Dynamic Ffree Coloring of Graphs 
An Ffree coloring is a coloring of a graph such that each color induces an Ffree graph. In this talk we consider dynamic Ffree coloring which can be interpreted as a game of Presenter and Painter. In each move Presenter presents new vertices along with the edges between them and already known vertices. In the same move Presenter can also discolor arbitrary vertices and request Painter to color some vertices. The problem we consider can be stated as follows: For a given graph G, is there a sequence of moves for which the greedy algorithm uses at least k colors during dynamic Ffree coloring of G. We will show that for some classes of graphs this problem is decidable in polynomial time (for fixed F and k) in the case where F is 2connected or F is path of length 2. Piotr Borowiecki, Elżbieta Sidorowicz, Dynamic Ffree Coloring of Graphs, Graphs and Combinatorics 2018, Volume 34, Issue 3, pp 457475 
26.05.18778 Bruno Pitrus 
Podstawy Informatyki Linear lambda terms as invariants of rooted trivalent maps by Noam Zeilberger 
The main aim of the article is to give a simple and conceptual account for the correspondence (originally described by Bodini, Gardy, and Jacquot) between \alpha equivalence classes of closed linear lambda terms and isomorphism classes of rooted trivalent maps on compact oriented surfaces without boundary, as an instance of a more general correspondence between linear lambda terms with a context of free variables and rooted trivalent maps with a boundary of free edges. We begin by recalling a familiar diagrammatic representation for linear lambda terms, while at the same time explaining how such diagrams may be read formally as a notation for endomorphisms of a reflexive object in a symmetric monoidal closed (bi)category. From there, the “easy” direction of the correspondence is a simple forgetful operation which erases annotations on the diagram of a linear lambda term to produce a rooted trivalent map. The other direction views linear lambda terms as complete invariants of their underlying rooted trivalent maps, reconstructing the missing information through a Tuttestyle topological recurrence on maps with free edges. As an application in combinatorics, we use this analysis to enumerate bridgeless rooted trivalent maps as linear lambda terms containing no closed proper subterms, and conclude by giving a natural reformulation of the Four Color Theorem as a statement about typing in lambda calculus.

16.09.84597 10.01.18888 Grzegorz Herman 
Informatyka Teoretyczna Relational parsing: a clean generalized parsing algorithm. 
We propose a new, worstcase cubictime, generalized parsing algorithm for all contextfree languages, based on computing the relations between configurations and transitions in a recursive transition network. The algorithm represents such relations using abstract data types, and for their specific (noncanonical) implementations behaves analogously to generalized LL, LeftCorner, or LR. It features a clean mathematical formulation, and can easily be implemented using only immutable data structures. 
30.01.84488 Bartłomiej Puget 
Podstawy Informatyki STATMAN'S HIERARCHY THEOREM by BRAM WESTERBAAN, BAS WESTERBAAN, RUTGER KUYPER, CARST TANKINK, REMY VIEHOFF AND HENK BARENDREGT 
In the Simply Typed lambda calculus Statman investigates the reducibility relation between types: for types freely generated using \arrow and a single ground type 0, define A \leq B if there exists a lambda definable injection from the closed terms of type A into those of type B. Unexpectedly, the induced partial order is the (linear) wellordering (of order type) \omega + 4.

08.04.68170 Marcin Briański 
Optymalizacja Kombinatoryczna How many ants does it take to find the food? 
In this talk we will consider the ANTS (Ants Nearby Treasure Search) problem: consider n agents (ants), controlled by finite automata (or PDAs) exploring an infinite grid attempting to locate a hidden treasure. The question we want to answer is: how many agents are necessary to accomplish this task in (expected) finite time? Of course, the answer will depend on the way we model this situation. We will consider synchronous as well as asynchronous environment, agents with access to randomness as well as deterministic ones, agents controlled by PDA as well as finite automata and various combinations thereof. In most cases established bounds are tight, however in certain cases there is still ample room for improvement (which some might consider interesting). Yuval Emek, Tobias Langner, David Stolz, Jara Uitto, Roger Wattenhofer, How many ants does it take to find the food?, Theoretical Computer Science Volume 608, Part 3, 10 December 2015, Pages 255267 
02.12.49004 Marcin Muszalski 
Optymalizacja Kombinatoryczna On the Number of Maximum Empty Boxes Amidst n Points 
I will present article written by Adrian Dumitrescu and Minghui Jiang in which they revisit the following problem (along with its higher dimensional variant): 
22.03.46157 Maciej Czerwiński 
Podstawy Informatyki On Type Inference in the Intersection Type Discipline by Gerard Boudol and Pascal Zimmer 
We introduce a new unification procedure for the type inference problem in the intersection type discipline. We show that unification exactly corresponds to reduction in an extended lambda calculus, where one never erases arguments that would be discarded by ordinary βreduction. We show that our notion of unification allows us to compute a principal typing for any strongly normalizing lambda expression. 
28.07.29839 Jakub Szarawski 
Optymalizacja Kombinatoryczna Faster approximation schemes for the twodimensional knapsack problem 
In 2008 Klaus Jansen and Roberto SolisOba presented a polynomial time approximation scheme (PTAS) for the square packing problem. Sandy Heydrich and Andreas Wiese base on their work and show a faster approximation (EPTAS) for the same problem. During the seminar both the common parts of the two papers (such as dividing the squares into large and small ones, dividing the rectangle into cells, frames, rows and blocks) and the new ideas (faster large squares guessing and block size guessing) will be presented. 
15.11.26991 Dominika Salawa 
Podstawy Informatyki The Hiring Problem and Permutations by Margaret Archibald and Conrado Martínez 
The hiring problem has been recently introduced by Broder et al. in last year’s ACMSIAM Symp. on Discrete Algorithms (SODA 2008), as a simple model for decision making under uncertainty. Candidates are interviewed in a sequential fashion, each one endowed with a quality score, and decisions to hire or discard them must be taken on the fly. The goal is to maintain a good rate of hiring while improving the “average” quality of the hired staff. We provide here an alternative formulation of the hiring problem in combinatorial terms. This combinatorial model allows us the systematic use of techniques from combinatorial analysis, e. g., generating functions, to study the problem. 
31.12.73645 Sylwester Klocek 
Optymalizacja Kombinatoryczna Colouring of (P3∪P2)free graphs 
In a paper authors are colouring of (P3∪P2)free graphs, a super class of 2K2 free graphs. During lecture I am going to present three discovered upper bounds of the chromatic number of (P3∪P2) free graphs, and sharper bounds for (P3∪P2 , diamond)free graphs and for (2K2, diamond)free graphs. The first part of a talk will contain an explanation of terminology and notation along with problem statements and results. In the second part, I will focus on proving each result in a sequence of claims and proofs. Arpitha P. Bharathi, Sheshayya A. Choudum, Colouring of (P3∪P2)free graphs, Graphs and Combinatorics, Volume 34 (1), 2018 
04.02.70908 Jacek Krzaczkowski 
Informatyka Teoretyczna Complexity of solving equations 
Solving equations is one of the oldest and well known mathematical problems which for centuries was the driving force of research in algebra. Let us only mention Galois theory, Gaussian elimination or Diophantine Equations. If we consider equations over the ring of integers it is the famous 10th Hilbert Problem on Diophantine Equations, which has been shown to be undecidable. In finite realms such a problem is obviously decidable in nondeterministic polynomial time. The talk is intended to present the latest achievements in searching structural algebraic conditions a finite algebra A has to satisfy in order to have a polynomial time algorithm that decides if an equation of polynomials over A has a solution. We will also present the results on the polynomial equivalence problem in which we ask whether two polynomials over a finite algebra describe the same function. This is joint work with Paweł M. Idziak and Piotr Kawałek.. 
21.06.70794 Rafał Burczyński 
Podstawy Informatyki How to select a loser 
Consider the following game: everyone from a group of n people flips a coin with result either 0 or 1, both equally probable; if no one gets a 0, the round is repeated, otherwise people with 1's are considered "winners" and the game continues only with participants who got 0's. The process continues until there is one person left, who is called "loser". We can picture this process as a binary tree and analyze some of its properties in average case. The analysis is not completely trivial, in particular one may find application for tools such as Mellin transform. 
25.08.54480 Grzegorz Jurdziński 
Optymalizacja Kombinatoryczna Split Packing: An Algorithm for Packing Circles with Optimal WorstCase Density 
Circle packing problem, where one asks whether a given set of circles can be fit into a unit square, is known to be NPhard. I will show that when combined area of circles does not exceed ≈0,539, then it is possible to pack them. The given bound is tight in the meaning that for larger combined area an instance impossible to pack can be found. Proof for this theorem is constructive and gives an algorithm, called Split Packing, for finding a solution for instances satisfying the conditions. Moreover it can also serve as a constantfactor approximation algorithm for the problem of finding a smallest square which can fit given circles. 
13.02.51629 Rafał Burczyński 
Podstawy Informatyki Mellin transforms and asymptotics 
We will introduce Mellin transform, which may be used for the asymptotic analysis of a particular class of sums. I will start with basic properties and then present fundamental correspondence between the asymptotic expansion of a function at 0 or infinity and singularities of its transform. Finally we will show some combinatorial applications of the transform. 
21.04.35315 Maciej Woźniak 
Optymalizacja Kombinatoryczna Find Your Place: Simple Distributed Algorithms for Community Detection 
Graph G = (V_1 \cup V_2, E) is regular clustered graph (with two communities) if:
We define (weak) block reconstruction of graph as twocoloring of vertices that separates V_1 and V_2 up to small "error" fraction of vertices. The reconstruction is said to be strong if separation is exact. I will present simple distributed algorithm (protocol) that produces strong reconstruction for clustered regular graphs within O(log n) iterations. I will also show that this algorithm produces weak reconstruction for nonregular clustered graphs with two communities and discuss an approach to solving this problem for regular graphs with more than two communities. 
09.08.32467 Weronika Grzybowska 
Podstawy Informatyki Average complexity of Moore’s and Hopcroft’s algorithms by Julien David 
In this paper we prove that for the uniform distribution on complete deterministic automata, the average time complexity of Moore’s state minimization algorithm is O(n log (log n)), where n is the number of states in the input automata and the number of letters in the alphabet is fixed. Then, an unusual family of implementations of Hopcroft’s algorithm is characterized, for which the algorithm will be proved to be always faster than Moore’s algorithm. Finally, we present experimental results on the usual implementations of Hopcroft’s algorithm. 
14.12.16149 Anna Kobak 
Optymalizacja Kombinatoryczna On treepartitionwidth 
A treepartition of a graph G is a proper partition of its vertex set into "bags", such that identifying the vertices in each bag produces a forest. The width of a treepartition is the maximum number of vertices in a bag. The treepartitionwidth of G is the minimum width of a treepartition of G. I will prove three theorems presented in the article, showing an upper bound on the treepartitionwidth of all graphs, a lower bound for chordal graphs and a lower bound for graphs with treewidth 2. 
18.01.13412 Bartosz Walczak 
Informatyka Teoretyczna Sparse Kneser graphs are Hamiltonian 
For integers Joint work with Torsten Mütze and Jerri Nummenpalo (arXiv:1711.01636). 
04.04.13302 Vladyslav Hlembotskyi 
Podstawy Informatyki A graph theoretic approach to automata minimality by Antonio Restivo and Roberto Vaglica 
The paper presents a graphtheoretic approach to test the minimality of a deterministic automaton. In particular, we focus on problems concerning the dependence of the minimality of an automaton on the choice of the set F of final states or on the cardinality of the set F . We introduce different minimality conditions of an automaton and show that such conditions can be characterized in graphtheoretic terms. 
24.09.79121 Grzegorz Guśpiel 
Informatyka Teoretyczna On the Complexity of Crossing Minimization 
For a bipartite graph G with vertex bipartition (X, Y), a twolayer drawing of G (on the plane) is a placement of vertices in X and Y in distinct points on two parallel lines L_{X} and L_{Y}, respectively. Then, each edge is drawn by connecting its end vertices by a straight line segment. A bipartite graph with a twolayer drawing is a twolayered graph. We study basic graph problems on twolayered graphs, where the goal is to minimize the number of pairwise crossing edges in the graph structure we seek. The graph structure can be a perfect matching, a Hamiltonian path or an (s, t)path. We investigate the complexity of these problems, obtaining some hardness proofs, FPT algorithms and small kernels.
This is joint work with Akanksha Agrawal, Jayakrishnan Madathil, Saket Saurabh and Meirav Zehavi. 
09.02.79008 Szymon Stankiewicz 
Podstawy Informatyki Introduction to HigherOrder Categorical Logic  continuation 
15.04.62694 Aleksandra Mędrek 
Optymalizacja Kombinatoryczna The Matching Problem in General Graphs is in QuasiNC 
Authors show that the perfect matching problem in general graphs is in quasiNC by presenting a deterministic parallel algorithm which runs in O(log^3 n) time on n^O(log^2 n) processors. The paper extends the framework of Fenner, Gurjar and Thierauf, who proved that finding perfect matching in bipartite graphs is in quasiNC. I describe their algorithm in the first part of my presentation. In the second part I talk about difficulties that arise in the general case and how they are approached. Ola Svensson, Jakub Tarnawski, The Matching Problem in General Graphs is in QuasiNC, FOCS 2017 
04.10.59842 Szymon Stankiewicz 
Podstawy Informatyki Introduction to HigherOrder Categorical Logic by Lambec and Scott 
09.12.43528 Dawid Pyczek 
Optymalizacja Kombinatoryczna Punctured combinatorial Nullstellensätze 
This article presents an extension of Alon’s Nullstellensatz to functions of multiple zeros at the common zeros of some polynomials. It also includes an introduction to the polynomials of multiple variables and other useful definitions. There are also many corollaries useful for polynomial problemsolving. Possibly the presentation will include some geometrical usage of Nullstellensatze extensions. 
12.01.40791 Michael Kompatscher Charles University in Prague 
Informatyka Teoretyczna CSPs of infinite structures and equations in oligomorphic algebras 
In 1998 Feder and Vardi famously conjectures that the constraint satisfaction problem (CSP) of a finite structure is either in P or NPcomplete. Universal algebra turned out to be the main tool in tackling their conjecture and lead to two recent proofs, showing that CSP(A) is in P if the polymorphism algebra associated with A is a Taylor algebra, and NPcomplete otherwise.
For CSPs of structures with infinite domains this universal algebraic approach fails badly in general. However, if the automorphism group of the structure is "sufficiently big", i.e. oligomorphic, many results can be transferred from the finite case. We survey results about the equational structure of oligomorphic algebras and their applications to constraint satisfaction problems. 
27.05.40681 Dawid Pyczek i Jakub Rówiński 
Podstawy Informatyki Asymptotic Density and the Theory of Computability by CARL JOCKUSCH AND PAUL SCHUPP 
The purpose of this paper is to survey recent work on how classical asymptotic density interacts with the theory of computability. We have tried to make the survey accessible to those who are not specialists in computability theory and we mainly state results without proof, but we include a few easy proofs to illustrate the flavor of the subject. In complexity theory, classes such as P and NP are defined by using worstcase measures. That is, a problem belongs to the class if there is an algorithm solving it which has a suitable bound on its running time over all instances of the problem. Similarly, in computability theory, a problem is classified as computable if there is a single algorithm which solves all instances of the given problem. There is now a general awareness that worstcase measures may not give a good picture of a particular algorithm or problem since hard instances may be very sparse. The paradigm case is Dantzig’s Simplex Algorithm for linear programming problems. This algorithm runs many hundreds of times every day for scheduling and transportation problems, almost always very quickly. There are clever examples of Klee and Minty showing that there exist instances for which the Simplex Algorithm must take exponential time, but such examples are not encountered in practice. Observations of this type led to the development of averagecase complexity by Gurevich and by Levin independently. There are different approaches to the averagecase complexity, but they all involve computing the expected value of the running time of an algorithm with respect to some measure on the set of inputs. Thus the problem must be decidable and one still needs to know the worstcase complexity. Another example of hard instances being sparse is the behavior of algorithms for decision problems in group theory used in computer algebra packages. There is often some kind of an easy “fast check” algorithm which quickly produces a solution for “most” inputs of the problem. This is true even if the worstcase complexity of the particular problem is very high or the problem is even unsolvable. Thus many grouptheoretic decision problems have a very large set of inputs where the (usually negative) answer can be obtained easily and quickly. 
30.12.5511097 Wojciech Szpankowski Purdue University USA 
Podstawy Informatyki Analytic Information Theory: From Shannon to Knuth and Back 
04.08.24363 Jakub Rówiński 
Optymalizacja Kombinatoryczna On the 1/3–2/3 Conjecture 
Let (P,≤) be a finite poset. For distinct elements x, y ∈ P , we define P(x ≺ y) to be the proportion of linear extensions of P in which x comes before y. For 0 ≤ α ≤ 1, we say (x,y) is an αbalanced pair 2 if α ≤ P(x ≺ y) ≤ 1 − α. The 1/3–2/3 Conjecture states that every finite partially ordered set which is not a chain has a 1/3balanced pair. Proof of above conjecture as well as stronger condition of having a 1/2balanced pair for certain families of posets will be shown. These include lattices such as the Boolean, set partition, subspace lattices and variety of diagrams. Emily J. Olson, Bruce E. Sagan, On the 1/32/3 Conjecture, Order, 2018 
21.01.21516 Jarosław Duda Instytut Informatyki UJ 
Podstawy Informatyki Some nonstandard approaches to hard computational problems 
I will talk about nonstandard approaches to some problems for which there is not known polynomial time classical algorithm. I will start with briefly explaining mechanism used in Shor algorithm, compressed sensing, and the problem with global optimization formulations used in adiabatic
Slides: https://tinyurl.com/y74nx2t6 
27.08.79121 Piotr Micek 
Informatyka Teoretyczna Seymour's conjecture on 2connected graphs of large pathwidth 
We prove the conjecture of Seymour (1993) that for every apexforest H1 and outerplanar graph H2 there is an integer p such that every 2connected graph of pathwidth at least p contains H1 or H2 as a minor. This is joint work with Tony Huynh, Gwenaël Joret, and David R.Wood. 
06.11.70907 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna News about Combinatorial Nullstellensatz 
I will present some new theorems, proofs and open problems concerning about Combinatorial Nullstellensatz and related problems. 
01.07.51742 Jarek Duda 
Optymalizacja Kombinatoryczna Some nonstandard approaches to hard computational problems 
I will talk about nonstandard approaches to some problems for which there is not known polynomial time classical algorithm. I will start with briefly explaining mechanism used in Shor algorithm and the problem with global optimization formulations used in adiabatic quantum computers. Then show some perspectives on the subsetsum NP complete problem, like geometric, integration and divergence formulations. Then show how Grassmann variables would be useful for the Hamilton cycle problem. Finally discuss the difficulty of the graph isomorphism problem on the most problematic cases: strongly regular graphs, and algebraic perspective on this problem. Jarek Duda. Some unusualapproaches to hard computational problems. slides. 
04.08.49004 09.12.68169 Andrzej Dorobisz 
Informatyka Teoretyczna Online bipartite matching with amortized O(log²n) replacements 
In the online bipartite matching problem with replacements, all the vertices on one side of the bipartition are given, and the vertices on the other side arrive one by one with all their incident edges. The goal is to maintain a maximum matching while minimizing the number of changes (replacements) to the matching. We show that the greedy algorithm that always takes the shortest augmenting path from the newly inserted vertex (denoted the SAP protocol) uses at most amortized O(log²n) replacements per insertion, where n is the total number of vertices inserted. This is the first analysis to achieve a polylogarithmic number of replacements for any replacement strategy, almost matching the Ω(log n) lower bound. The previous best known strategy achieved amortized O(√n) replacements [Bosek, Leniowski, Sankowski, Zych, FOCS 2014].
Based on the paper: Online bipartite matching with amortized O(log²n) replacements by Aaron Bernstein, Jacob Holm and Eva Rotenberg 
19.12.48890 Bartłomiej Puget i Dominika Salawa 
Podstawy Informatyki Chapters 8.5  8.9 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
23.02.32577 Maciej Woźniak, Dawid Pyczek 
Optymalizacja Kombinatoryczna Online Vertex Cover and Matching: Beating the Greedy Algorithm 
Authors study the online vertex cover problem and online matching problem in bipartite graphs and in general graphs. For the case of bipartite graphs their result is optimal waterfilling algorithm with competitive ratio 1/(11/e) . The main contribution of this paper is a 1.901competitive algorithm for vertex cover in general graphs which beats the wellknown trivial 2competitive algorithm. The next major result is a primaldual analysis of given algorithm that implies the dual result of a 0.526competitive algorithm for online fractional matching in general graphs. On the hardness side authors show that no randomized online algorithm can achieve a competitive ratio better than 1.753 and 0.625 for the online fractional vertex cover problem and the online fractional matching problem respectively, even for bipartite graphs. 
14.08.29725 Kamil Rajtar 
Podstawy Informatyki Chapters 8.1  8.4 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
20.10.13411 Grzegorz Bukowiec 
Optymalizacja Kombinatoryczna Feedback Vertex Set Problem 
A Feedback Vertex Set (FVS) is a subset of vertices in a graph such that its removal results in an acyclic graph. The problem of finding a minimal FVS is one of the classic NPcomplete problems. However, in some practical cases, we can assume that its size is fairly small. This motivated an intensive study of the parametrized version of this problem, which asks either for FVS of a size at most k or an information that it doesn't exist. There are several deterministic algorithms known which solve this in time O^{*}(c^{k}), the best one for now being O^{*}(3.592^{k}). 
08.04.10560 Dawid Pyczek i Jakub Rowiński 
Podstawy Informatyki Chapters 7.6  7.9 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
19.02.59956 Paweł Kubiak, Jakub Rówiński 
Optymalizacja Kombinatoryczna Constrained minimum vertex cover in bipartite graphs: complexity and parameterized algorithms 
On bipartite graphs, problem of constrained minimum vertex cover (MINCVCB) is defined as follows: given a bipartite graph G = (V, E) with vertex bipartition V = U ∪ L and two integers k_{u} and k_{l}, decide whether there is a minimum vertex cover in G with at most k_{u} vertices in U and at most k_{l} vertices in L. We show how it is related to practical problems. We prove that (MINCVCB) is NPcomplete. However, there are many parametrized algorithms running in decent time. We describe one of them, whereby linear kernelization method it achieves O(1.26^{ku+kl} +(k_{u} +k_{l})G) time. 
24.03.57218 Grzegorz Herman 
Informatyka Teoretyczna Declarative name resolution for complex, extensible languages 
We present a new, declarative, languageindependent model for name resolution, based on a data flow graph built using simple combinators. The model is expressive enough to capture complex name binding rules of modern programming languages (e.g., partial definitions, C++ argumentdependent lookup). It is also designed to make it straightforward toextend a language with new syntactic constructs, including new categories of names. The model, together with a proofofconcept resolution engine, has been implemented in Haskell, and evaluated on syntax trees of C# programs.
(This is joint work with Katarzyna Bułat.)

09.08.57104 Rafał Burczyński 
Podstawy Informatyki Chapters 7.1  7.5 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
21.01.40814 Jakub Nowak 
Optymalizacja Kombinatoryczna Dulmage–Mendelsohn Decomposition 
In a graph G, let B be the set of vertices covered by every maximum matching in G, and let D = V(G) − B. Further partition B by letting A be the subset consisting of vertices with at least one neighbor outside B, and let C = B − A. The GallaiEdmonds Decomposition of G is the partition of V(G) into the three sets A, C, D. The Dulmage–Mendelsohn decomposition is a partition of the vertices of a bipartite graph into subsets, with the property that two adjacent vertices belong to the same subset if and only if they are paired with each other in a perfect matching of the graph. It is an extension of the GallaiEdmonds decomposition. L. Lovász, M. D. Plummer. Matching theory. NorthHolland Mathematics Studies, 121. Annals of Discrete Mathematics, 29. NorthHolland Publishing Co., Amsterdam. 1986. pp. xxvii+544. ISBN: 0444879161. Chapter 4.3. 
14.10.40790 Lev Deliatynskyi 
Optymalizacja Kombinatoryczna A short proof of the Berge–Tutte Formula and the Gallai–Edmonds Structure Theorem 
This paper studies the maximum matching in a graph. It shows a short proof of a BergeTutte formula and the GallaiEndmonds structure theorem. Authors use Hall's theorem to prove it. Deficiency in a graph (def(S), S⊆V(G)) is o(GS)  S, where o(GS) is the number of odd components in GS. BergeTutte formula says that the maximum size of a matching in an nvertex graph G is 1/2(ndef(G)), where def(G) = max_{S⊆V(G)}def(S). Gallai Edmonds has a sharper formulation which gives considerable information about the structure of maximum size matchings. 
16.11.38052 Tony Huynh Universite de Libre Bruxelles 
Informatyka Teoretyczna Strengthening Convex Relaxations of 0/1Sets using Boolean Formulas 
In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several generalpurpose methods that strengthen relaxations without specific knowledge of the set S of feasible integer points, such as popular linear programming or semidefinite programming hierarchies. On the other hand, various methods have been designed for obtaining strengthened relaxations for very specific sets S that arise in combinatorial optimization. 
04.04.37939 Katarzyna Grzybowska 
Podstawy Informatyki Chapters 6.12  6.15 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
08.06.21625 Jan Derbisz, Franciszek Stokowacki 
Optymalizacja Kombinatoryczna On Low RankWidth Colorings 
We say that a class C of graphs admits low rankwidth colorings if there exist functions N : N → N and Q: N → N such that for all p ∈ N, every graph G ∈ C can be vertex colored with at most N(p) colors such that the union of any i ≤ p color classes induces a subgraph of rankwidth at most Q(i). It turns out that for every graph class C of bounded expansion and every positive integer r, the class {G^{r} : G ∈ C} of rth powers of graphs from C, as well as the classes of unit interval graphs and bipartite permutation graphs admit low rankwidth colorings. Additionally, every graph class admitting low rankwidth colorings is χbounded. 
27.11.18773 Katarzyna Bułat 
Podstawy Informatyki Chapter 6.8  6.11 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
19.03.84597 Krzysztof Maziarz, Tomasz Wesołowski 
Optymalizacja Kombinatoryczna The Generalised Colouring Numbers on Classes of Bounded Expansion 
We introduce two classes of graphs  graphs with bounded expansion and nowhere dense graphs. These notions are a common generalization of proper minor closed classes, classes of graphs with bounded degree, locally planar graphs, to name just a few classes which are studied extensively in combinatorial and computer science contexts. We also present generalized colouring numbers adm_{r}(G), col_{r}(G), and wcol_{r}(G) and show important applications in the theory of abovementioned classes of graphs. Finally, we prove that every graph excluding a fixed topological minor admits a universal order, that is, one order witnessing that the colouring numbers are small for every value of r, and show that it can be efficiently computed. 
23.04.81859 Adam Polak 
Informatyka Teoretyczna Open problems in algorithms and complexity 
During the talk I'll present several interesting open problems, including, but not limited to:

07.09.81745 Filip Bartodziej 
Podstawy Informatyki Chapter 6.1  6.7 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
13.11.65431 Gabriel Jakóbczak 
Optymalizacja Kombinatoryczna Majority coloring games 
A vertex coloring of graph G satisfies the majority rule, if for each vertex v at most half of its neighbors receive the same color as v. A coloring which satisfies the majority rule is called majority coloring. We consider its game version. For given graph G and color set C two players, Alice and Bob, in alternating turns color vertices with respect to the majority rule. Alice wins when every vertex becomes colored, while goal for Bob is to create a vertex which cannot be colored with any color belonging to the set C without breaking the majority rule. Let µ_{g(G)} denote the least number of colors belonging to C for which Alice has winning strategy in game on graph G. We show that if the color set C is finite, there exists a graph G on which Bob has winning strategy. We prove also that for graphs with col(G) = 3 parameter µ_{g(G)} is still unbounded. 
16.12.62693 Patryk Mikos 
Informatyka Teoretyczna Online interval coloring for bounded length intervals 
Online interval coloring was studied by Kierstead and Trotter. They presented an algorithm with competitive ratio 3,and showed a construction which implies that there is no algorithm with competitive ratio strictly less than 3. However, their construction in asymptotic case requires intervals with possibly unbounded length. We are interested in a variant of the online interval coloring problem in which all intervals have lenght between 1 and L. We show that as L tends to infinity the asymptotic competitive ratio tends to 5/2. Moreover we show that for L=1+epsi there is no algorithm with competitive ratio less than 5/3 and for L=2+epsi there is no algotihm with competitive ratio less than 7/4. Finally, we want to know how the asymptotic competitive ratio changes as a function of L. 
02.05.62580 Michał Ziobro 
Podstawy Informatyki Chapter 5 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
08.07.46266 Anna Kobak, Grzegorz Jurdziński 
Optymalizacja Kombinatoryczna The Erdős discrepancy problem  Part II 
Erdős discrepancy problem has waited for the solution for over 70 years until last year Terrence Tao, with a help of Polymath project, has published a paper with its solution. After having our friends given an introduction to the topic and shown the Fourier analytic reduction of the problem last week we will continue presenting the proof. It will include the proof of Elliottype conjecture and a sketch of how to apply a generalised BorweinChoiCoons analysis for the final steps of the main proof. Terence Tao. The Erdős discrepancy problem. Discrete Analysis. Vol. 2 (2016), pp. 120. 
11.08.43528 Tomasz Krawczyk 
Informatyka Teoretyczna Representation and coloring of partially ordered sets under conditions of incomplete information 
The purpose of my talk is to discuss several problems related to coloring and construction of appropriate representation for partially ordered sets (also posets) and graph classes derived from posets. In these problems, we will assume the following two scenarios: in the first scenario, an algorithm receives a poset element one after another. For each new element added, the algorithm takes an irrevocable decision (assigns a color or extends a current representation) just after this element is presented (algorithms that work under such conditions are called online). in the second scenario, an algorithm receives an incomparability graph of some poset and a representation of some parts of this graph, and its task is to check whether this partial representation can be extended to a representation of the whole graph that is appropriate for the considered class of graphs. In the context of online algorithms, we focus our attention on two problems: partitioning posets into chains, which is a special case of online coloring of incomparability graphs, and embedding posets into ddimentional space R^{d}. In the context of extending partial representations problems, we are interested in graph classes whose representations introduce a natural order on vertices of these graphs. We focus our attention on:

27.12.43414 Hanna Palianytsia i Agnieszka Rabiej 
Podstawy Informatyki Chapter 4.5  4.9 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
03.03.27101 Aleksandra Mędrek, Marcin Muszalski 
Optymalizacja Kombinatoryczna The Erdős discrepancy problem  Part I 
Erdős discrepancy problem had remained unresolved for more than 80 years. In 2015 Erdős theorem has been proofed by Terrence Tao. We present first part of his proof where he uses a Fourieranalytic reduction obtained as part of the Polymath5 project which reduces the problem to the case when f is replaced by a (stochastic) completely multiplicative function g. Terence Tao. The Erdős discrepancy problem. Discrete Analysis. Vol. 2, (2016), pp. 120. 
21.08.24249 Miron Ficek 
Podstawy Informatyki Chapter 4 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
02.07.73645 Wojciech Kruk 
Optymalizacja Kombinatoryczna Randomized PrimalDual Analysis of RANKING for Online Bipartite Matching 
We give a simple proof that the RANKING algorithm of Karp, Vazirani and Vazirani is 11/e competitive for the online bipartite matching problem. The proof is via a randomized primaldual argument. Primaldual algorithms have been successfully used for many online algorithm problems, but the dual constraints are always satisfied deterministically. This is the first instance of a nontrivial randomized primaldual algorithm in which the dual constraints only hold in expectation. 
06.08.70907 Bartłomiej Bosek 
Informatyka Teoretyczna A Tight Bound for Shortest Augmenting Paths on Trees 
The shortest augmenting path technique is one of the fundamental ideas used in maximum matching and maximum flow algorithms. Since being introduced by Edmonds and Karp in 1972, it has been widely applied in many different settings. Surprisingly, despite this extensive usage, it is still not well understood even in the simplest case: online bipartite matching problem on trees. In this problem a bipartite tree T=(WB, E) is being revealed online, i.e., in each round one vertex from B with its incident edges arrives. It was conjectured by Chaudhuri et. al. that the total length of all shortest augmenting paths found is O(n log n). In this paper we prove a tight O(n log n) upper bound for the total length of shortest augmenting paths for trees improving over O(n log² n) bound.

21.12.70793 Jakub Czarnowicz 
Podstawy Informatyki Chapter 3 of AN INTRODUCTION TO THE ANALYSIS OF ALGORITHMS by Robert Sedgewick, Philippe Flajolet 
25.02.54480 Sylwester Klocek 
Optymalizacja Kombinatoryczna Online bipartite matching made simple 
We examine the classic online bipartite matching problem studied by Richard M. Karp, Umesh V. Vazirani, and Vijay V. Vazirani. Algorithm attempts to match online new vertices with edges. Such a decision, once made, is irrevocable. The objective is to maximize the size of the resulting matching. We will see a sketch of simple proof of their result that the Ranking algorithm for this problem achieves a competitive ratio of 1 − 1/e. B.E. Birnbaum, C. Mathieu. Online bipartite matching made simple. SIGACT News 39 (1), 8087, 2008. 
15.08.51628 Piotr Wójcik 
Podstawy Informatyki Chapter 4 of Flajolet book "Complex Analysis, Rational and Meromorphic Asymptotic". 
21.10.35314 Zygmunt Łenyk 
Optymalizacja Kombinatoryczna Handwritten graph diagrams recognition 
Graph visualisation problem is well known and there are many solutions to it. The reverse process  graph recognition  has been disregarded so far. Such solution has wide applications  from scientific to didactic. This paper focuses on handwritten graphs. Objects do not necessarily have regular shapes and there might be a lot of noise. Using computer vision techniques, we recognize first vertices and then edges. The result of the algorithm is a list of edges and a generated graph visualisation. 
10.04.32463 Tomasz Kisielewski 
Podstawy Informatyki Logic of Provability by George Boolosa 
Short presentantion of the book Logic of Provability by George Boolos. 
15.06.16149 Szymon Borak 
Optymalizacja Kombinatoryczna On some problems in planar graphs 
We give insight into competitive reachability for outerplanar graphs and also for other classes of graphs with bounded degree. Competitive reachability is a game where two players orient the edges of undirected graph G alternately until all edges of G have been oriented. One player wants to minimize the number of ordered pairs of distinct vertices (x, y) with a directed path from x to y. And the second want to maximize it. Furthermore we focus on harmonious coloring conjecture for outerplanar graphs and further attempts in this area. A harmonious coloring of a graph G is a proper vertex coloring of G in which every pair of colors appears on adjacent vertices at most once. The harmonious chromatic number, denoted by h(G), is the minimum number of colors in a harmonious coloring. Analogically we define harmonious edge coloring in which every pair of colors appears on incident edges at most once. The minimal number of color we denote by h'(G). The conjecture states that h(G)<=h'(G). Finally we tackle the hamiltonian cycles in grid graphs. Grid graph are finite vertex induced subsets of infinite lattice, composed from unitside squares, equilateral triangles or equilateral hexagons. Decide whether the grid graph has hamiltonian cycle is NPhard in general. 
12.01.13302 Tomasz Kisielewski 
Podstawy Informatyki Logic of Provability by George Boolosa 
Short presentantion of the book Logic of Provability by George Boolos.

20.08.59955 Damian Goik 
Informatyka Teoretyczna Succinct progress measures for solving parity games 
The recent breakthrough paper by Calude et al. has given the first algorithm for solving parity games in quasipolynomial time, where previously the best algorithms were mildly subexponential. We devise an alternative quasipolynomial time algorithm based on progress measures, which allows us to reduce the space required from quasipolynomial to nearly linear. Our key technical tools are a novel concept of ordered tree coding, and a succinct tree coding result that we prove using bounded adaptive multicounters, both of which are interesting in their own right. Based on the paper:

14.04.40790 Piotr Wójcik 
Informatyka Teoretyczna On the asymptotic density of valid sentences in firstorder logic about one binary relation 
This study arises from the following question: what is the proportion of tautologies of the given length n among the number of all FO relational sentences of length n? We investigate the simplest language with a fixed signature σ = {r}, where r is a binary relation symbol. The model with four logic symbols and an universal quantifier lead us to discover an unexpected result  the fraction of valid sentences is always greater than a fixed constant and therefore the density, if exists, is positive. The main theorem is derived from the analysis of structural properties of FO formulae, which themselves bear strict resemblance to structural properties of λterms. 
14.08.37997 Kamil Sałaś 
Kryptologia Helios: Webbased OpenAudit Voting 
The talk is based on the paper by Ben Adida with the same title [1]. In addition, we recall ElGamal encryption scheme and zeroknwoledge proofs. Voting with cryptographic auditing, sometimes called openaudit voting, has remained, for the most part, a theoretical endeavor. In spite of dozens of fascinating protocols and recent groundbreaking advances in the field, there exist only a handful of specialized implementations that few people have experienced directly. As a result, the benefits of cryptographically audited elections have remained elusive. We present Helios, the first webbased, openaudit voting system. Helios is publicly accessible today: anyone can create and run an election, and any willing observer can audit the entire process. Helios is ideal for online software communities, local clubs, student government, and other environments where trustworthy, secretballot elections are required but coercion is not a serious concern. With Helios, we hope to expose many to the power of openaudit elections. References [1] Ben Adida, Helios: Webbased OpenAudit Voting, Proceedings of the 17th Conference on Security Symposium, 2008, pp. 335348 
03.06.21515 Jakub Nowak 
Podstawy Informatyki Generic Complexity of Presburger Arithmetic by Alexander N. Rybalov 
Fischer and Rabin proved in that the decision problem for Presburger Arithmetic has at least double exponential worstcase complexity (for deterministic and nondeterministic Turing machines). In paper 4 a theory of genericcase complexity was developed, where algorithmic problems are studied on "most" inputs instead of set of all inputs. An interesting question rises about existing of more efcient (say, polynomial) generic algorithm deciding Presburger Arithmetic on some set of closed formulas of asymptotic density 1 (socalled generic set). We prove, however, that there is not even an exponential generic algorithm working correctly on a set of inputs which (socalled strongly generic set). 
29.06.5197 Wojciech Kruk, Piotr Kruk 
Optymalizacja Kombinatoryczna Ulam Sequences and Ulam Sets 
The Ulam sequence is given by a1=1,a2=2, and then, for n≥3, the element an is defined as the smallest integer that can be written as the sum of two distinct earlier elements in a unique way. This gives the sequence 1,2,3,4,6,8,11,13,16,…, which has a mysterious quasiperiodic behavior that is not understood. Ulam's definition naturally extends to higher dimensions: for a set of initial vectors {v1,…,vk}⊂ℝn, we define a sequence by repeatedly adding the smallest elements that can be uniquely written as the sum of two distinct vectors already in the set. The resulting sets have very rich structure that turns out to be universal for many commuting binary operations. We give examples of different types of behavior, prove several universality results, and describe new unexplained phenomena.

14.08.87334 Piotr Micek 
Informatyka Teoretyczna Ramsey Theory for Binary Trees and the Separation of Treechromatic Number from Pathchromatic Number 
We propose a Ramsey theory for binary trees and prove that for every rcoloring of "strong copies" of a small binary tree in a huge complete binary tree T, we can find a strong copy of a large complete binary tree in T with all small copies monochromatic. As an application, we construct a family of graphs which have treechromatic number at most 2 while the pathchromatic number is bounded. This construction resolves a problem posed by Seymour. Joint work with Fidel BarreraCruz, Stefan Felsner, Tamás Mészáros, Heather Smith, Libby Taylor, and Tom Trotter. 
06.02.87225 Grzegorz Bukowiec 
Podstawy Informatyki The Undecidability of the Generalized Collatz Problem by Stuart A. Kurtz and Janos Simon 
The Collatz problem, widely known as the 3x + 1 problem, asks whether or not a certain simple iterative process halts on all inputs. In this paper, we build on work of J. H. Conway to show that a natural generalization of the Collatz problem is $PI^0_2$ complete. 
14.12.84541 Jan Derbisz 
Kryptologia Subquadratic Greatest Common Divisor 
The binary algorithm is a variant of the Euclidean algorithm that performs well in practice. We present a quasilinear time recursive algorithm that computes the greatest common divisor of two integers by simulating a slightly modified version of the binary algorithm. The structure of the algorithm is very close to the one of the wellknown KnuthSchonhage fast gcd algorithm; although it does not improve on its O(M(n) log n) complexity, the description and the proof of correctness are significantly simpler. This leads to a simplification of the implementation and to better running times. 
06.03.70907 Sylwester Klocek, Maciej Woźniak 
Optymalizacja Kombinatoryczna On the complexity of the chipfiring reachability problem 
In this paper, we study the complexity of the chipfiring reachability problem. We show that for Eulerian digraphs, the reachability problem can be decided in polynomial time, even if the digraph has multiple edges. We also show a special case when the reachability problem can be decided in polynomial time for general digraphs: if the target distribution is recurrent restricted to each strongly connected component. Both of these algorithms are strongly polynomial. As a further positive result, we show that the chipfiring reachability problem is in coNP for general digraphs. We also show that the chipfiring halting problem is in coNP for Eulerian digraph 
02.10.68059 Piotr Wójcik 
Podstawy Informatyki Randombit optimal uniform sampling for rooted planar trees with given sequence of degrees and Applications by O.Bodini, J. David, and Ph. Marchal 
In this paper, we redesign and simplify an algorithm due to Remy et al. for the generation of rooted planar trees that satisfies a given partition of degrees. This new version is now optimal in terms of random bit complexity, up to a multiplicative constant. We then apply a natural process “simulateguessandproof” to analyze the height of a random Motzkin in function of its frequency of unary nodes. When the number of unary nodes dominates, we prove some unconventional height phenomenon. 
08.08.65376 Szymon Policht 
Kryptologia Supersingular isogeny key exchange 
Supersingular isogeny is the newest addition to the postquantum cryptography roster. It is elliptic curve based, but unlike tradidional ECC algorithms, it's quantum resistant. It offers significant key size reduction and computation time speedup compared to other postquantum algorithms. 
29.10.51741 Katrzyna Janocha 
Optymalizacja Kombinatoryczna Proper Orientations of Planar Bipartite Graphs 
An orientation of a graph G is proper if any two adjacent vertices have different indegrees. The proper orientation number χ (G) of a graph G is the minimum of the maximum indegree, taken over all proper orientations of G. In this paper, we show that a connected bipartite graph may be properly oriented even if we are only allowed to control the orientation of a specific set of edges, namely, the edges of a spanning tree and all the edges incident to one of its leaves. As a consequence of this result, we prove that 3connected planar bipartite graphs have proper orientation number at most 6. Additionally, we give a short proof that χ (G) ≤ 4, when G is a tree and this proof leads to a polynomialtime algorithm to proper orient trees within this bound. 
23.06.32576 Anna Kobak 
Optymalizacja Kombinatoryczna Lambda number for the direct product of some family of graphs 
An L(2,1) labeling for a graph G = (V,E) is a function f on V such that  f(u)  f(v) >= 2 if u,v are adjacent and f(u), f(v) are distinct if u,v are vertices of distance two. The lambda(G) for G is the minimum span over all L(2,1) labelings of G. We will show that when m>=6 and n>=3, lambda(Pm x Cn) = 7 if and only if n is not a multiple of 7 and also provide the conditions on m and n such that lambda(Cm x Cn) <= 7. 
28.07.29838 Torsten Ueckerdt Karlsruhe Institute of Technology 
Informatyka Teoretyczna The kStrong Induced Arboricity of a Graph 
Motivated by a connection to vertexdistinguishing colorings, we initiate the study of a new graph covering parameters: The kstrong induced arboricity. For a graph G and a positive integer k, a kstrong induced forest F in G is an induced forest in which every component has at least k edges. An edge in G is called kvalid if it is contained in at least one kstrong induced forest. The kstrong induced arboricity f_{k}(G) is the smallest number m such that all kvalid edges of G can be covered with m kstrong induced forests in G. 
20.01.29729 Maciej Bendkowski 
Podstawy Informatyki Analytic combinatorics: an introduction 
In our talk we outline the main concepts and techniques of analytic combinatorics used to investigate properties of large random algebraic structures. We discuss the central interpretation of generating functions as functions analytic at the origin allowing to relate their analytic properties with the quantitative properties of studied structures. Finally, we briefly excerpt the techniques of singularity analysis allowing us to access the asymptotic form of corresponding counting sequences or investigate the probability distribution of interesting combinatorial parameters.

27.11.27045 Aleksandra Nowak 
Kryptologia The Fully Homomorphic Encryption and Approximate Greatest Common Divisor Problem 
We briefly introduce the definition of fully homomorphic encryption and describe the two main problems on which are based latest FHE schemes: The LWE/RingLWE and AGCD problems. We discuss their advantages and the relations between them. We present the definition of bootstrapping and investigate the FHE scheme based on the AGCD problem as published in [1]. References [1] J. H. Cheon, D. Stehlé, Fully Homomorphic Encryption over the Integers Revisited, EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques, pp. 2443. 
17.02.13411 Grzegorz Bukowiec 
Optymalizacja Kombinatoryczna Even factors of graphs 
An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. It has been shown that if a graph G has an even factor, it also has an even factor F such that E(F) >= 4/7 (E(G) + 1). 4/7 is the best possible ratio here, but we will try to strengthen this lower bound by taking the set of vertices of degree 2 into consideration. 
28.11.76382 Jakub Szarawski 
Optymalizacja Kombinatoryczna A greedy approach to the Turtle Tower problem 
In the Turtle Tower problem we are given n turtles with a mass and capacity for each of them. We are looking for the highest tower possible, regarding that capacity of every turtle in the tower cannot be exeeded by the sum of the masses of turles it carry. Presented solution is faster than commonly known dynamic one. 
31.12.73644 Marcin Pilipczuk University of Warsaw 
Informatyka Teoretyczna Subexponential Parameterized Algorithms for Planar Graphs, ApexMinorFree Graphs and Graphs of Polynomial Growth via Low Treewidth Pattern Covering 
We prove the following theorem. Given a planar graph G and an integer k, it is possible in polynomial time to randomly sample a subset A of vertices of G with the following properties: 1) A induces a subgraph of G of treewidth 2) for every connected subgraph H of G on at most k vertices, the probability that A covers the whole vertex set of H is at least Together with standard dynamic programming techniques for graphs of bounded treewidth, this result gives a versatile technique for obtaining (randomized) subexponential parameterized algorithms for problems on planar graphs, usually with running time bound In the talk I will first focus on the background and motivation, and then highlight the main ideas of the proof by sketching the proof for the case of graph classes of polynomial growth. Based on joint work with Fedor Fomin, Daniel Lokshtanov, Dániel Marx, Michał Pilipczuk, and Saket Saurabh: http://arxiv.org/abs/1604.05999 and http://arxiv.org/abs/1610.07778. 
27.06.73535 Konrad Kalita 
Podstawy Informatyki Java Generics are Turing Complete by Radu Grigore 
This paper describes a reduction from the halting problem of Turing machines to subtype checking in Java. It follows that subtype checking in Java is undecidable, which answers a question posed by Kennedy and Pierce in 2007. It also follows that Java’s type checker can recognize any recursive language, which improves a result of Gil and Levy from 2016. The latter point is illustrated by a parser generator for fluent interfaces. 
02.05.70852 Michał Ziobro 
Kryptologia Introduction to Homomorphic Encryption 
The talk is divided into two parts. In the first part we briefly introduce Fully Homomorphic Encryption and a presentation of a classic example described in [1]. In the second part, we bring up a subject of partially homomorphic encrytpion schemes over finite fields, presented in [2]. References: [1] C. Gentry, Computing Arbitrary Functions of Encrypted Data, 2008 (pdf) 
23.07.57217 Helena Borak, Zygmunt Łenyk 
Optymalizacja Kombinatoryczna Necklaces, Convolutions, and X + Y, A new upper bound for the online square packing 
Necklaces, Convolutions, and X + Y The necklace alignment problem is to find the optimal rotation of the necklaces to best align the beads, when we have two necklaces given, each with n beads at arbitrary positions. Alignment is measured according to the ℓ_p norm of the vector of distances between pairs of beads from opposite necklaces in the best perfect matching. We show surprisingly different results for p = 1, p even, and p = ∞ and how these problems can be reduced to convolution problems which can be solve in subquadratic time. Besides, we say how the necklace alignment problems, and their corresponding convolution problems, are also intrinsically connected to problems on X + Y matrices. A new upper bound for the online square packing In online square packing problem we try to minimise the height of squares on a plane with width 1. Squares come one by one, they can’t overlap and once set, it’s position can’t be changed. A new upper bound (ratio between algorithm result and optimal packing) is found by applying modified version of previously used First Fit Shelf algorithm. 
26.08.54479 Lech Duraj, Adam Polak 
Informatyka Teoretyczna Longest Common Strictly Increasing Subsequecnce 
The Longest Common Increasing Subsequence problem is a variant of classic Longest Common Subsequence problem, which can be solved in quadratic time with a simple dynamic programming algorithm. During the talk we will show a reduction from the Orthogonal Vectors problem to the Longest Common Increasing Subsequence problem which proves that the latter cannot be solved in strongly subquadratic time unless the SETH is false.
Simple modifications of the reduction prove that the problem for k sequences cannot be solved in O(n^{k}^{ε}) time, that the same lower bounds apply to the Longest Common Weakly Increasing Subsequence, and that the assumption of SETH can be replaced with a weaker statement about satisfiability of nondeterministic branching programs. 
14.10.35204 Jarek Duda 
Podstawy Informatyki Boundaries for hashing problem, or how many bits ones individuality costs 
I will talk about informationtheoretic boundaries for the hashing problem, the Bloom filter, and generally about informational content of structures like trees and graphs. While the label size has to grow like logarithm of the population size, neglecting information about the order (lg(n!) bits), we get a linear growth of entropy of population, allowing to bound 'the cost of individuality' asymptotically to ~2.33275 bits per object. 
10.11.18886 Andrzej Głuszyński, Jakub Nowak 
Optymalizacja Kombinatoryczna Local Antimagic Vertex Coloring of a Graph, A short proof of Cayley's tree formula 
Local Antimagic Vertex Coloring of a Graph The edge labelling is called 'local antimagic', if for all vertices sum of labels for incident edges is different for every two adjacent vertices. Such sum induce a correct vertex colouring. The local antimagic chromatic number  X_la(G)  is the minimum number of colours used by any proper local antimagic labelling. In the paper authors present results on this parameter for trees, friendship, wheel and clique graphs. A short proof of Cayley's tree formula Cayley’s tree formula is a very elegant result in Graph Theory. The problem is to find the number of all possible trees on a given set of labeled vertices. For n = 2 and vertex set {v1, v2}, we have only one tree. For n = 3 and vertex set {v1, v2, v3}, we have 3 different trees. Similarly for n = 4, we have 16 trees. We give a short proof of Cayley’s tree formula for counting the number of different labeled trees on n vertices. Alok Bhushan Shukla, A short proof of Cayley's tree formula. 
09.06.16039 Szymon Stankiewicz 
Podstawy Informatyki CANTOR POLYNOMIALS AND THE FUETERPOLYA THEOREM by MELVYN NATHANSON 
A packing polynomial is a polynomial that maps the set N^2 of lattice points with nonnegative coordinates bijectively onto N. Cantor constructed two quadratic packing polynomials, and Fueter and Polya proved analytically that the Cantor polynomials are the only quadratic packing polynomials. 
15.04.13356 Mateusz Jachna 
Kryptologia Secure Hash Algorithms family and the recently found collision for SHA1 
21.12.79065 Piotr Wójcik 
Kryptologia Quantum Authentication with Key Recycling 
We show that a family of quantum authentication protocols introduced in FOCS 2002 can be used to construct a secure quantum channel and additionally recycle all of the secret key if the message is successfully authenticated, and recycle part of the key if tampering is detected. We give a full security proof that constructs the secure channel given only insecure noisy channels and a shared secret key. We also prove that the number of recycled key bits is optimal for this family of protocols, i.e., there exists an adversarial strategy to obtain all nonrecycled bits. Previous works recycled less key and only gave partial security proofs, since they did not consider all possible distinguishers (environments) that may be used to distinguish the real setting from the ideal secure quantum channel and secret key resource. References: [1] Christopher Portmann, Quantum Authentication with Key Recycling (pdf) 
13.03.65431 Aleksandra Mędrek, Marcin Muszalski 
Optymalizacja Kombinatoryczna Planning for Fast Connectivity Updates 
Understanding how a single edge deletion can affect the connectivity of a graph amounts to finding the graph bridges. But when faced with d > 1 deletions, can we establish as easily how the connectivity changes? When planning for an emergency, we want to understand the structure of our network ahead of time, and respond swiftly when an emergency actually happens. We describe a linearspace representation of graphs which enables us to determine how a batch of edge updates can impact the graph. Given a set of d edge updates, in time O(d polylg n) we can obtain the number of connected components, the size of each component, and a fast oracle for answering connectivity queries in the updated graph. The initial representation is polynomialtime constructible. 
16.08.59900 Jan Szczepaniec 
Kryptologia Inclusive Block Chain Protocols 
Distributed cryptographic protocols such as Bitcoin and Ethereum use the block chain to synchronize a global log of events between nodes in their network. Previous research has shown that the mechanics of the block chain and block propagation are constrained: if blocks are created at a high rate compared to their propagation time in the network, many conflicting blocks are created and performance suffers greatly.

05.11.46265 Patryk Urbański 
Optymalizacja Kombinatoryczna Generating Linear Extensions Fast 
One of the most important sets associated with a poset P is its set of linear extensions, E(P). In this paper, we present an algorithm to generate all of the linear extensions of a poset in constant amortized time; that is, in time O(e(P)), where e(P) = E(P). The fastest previously known algorithm for generating the linear extensions of a poset runs in time O(n*e(P)), where n is the number of elements of the poset. Our algorithm is the first constant amortized time algorithm for generating a ``naturally defined'' class of combinatorial objects for which the corresponding counting problem is #Pcomplete. Furthermore, we show that linear extensions can be generated in constant amortized time where each extension differs from its predecessor by one or two adjacent transpositions. The algorithm is practical and can be modified to efficiently count linear extensions, and to compute P(x < y), for all pairs x,y, in time O(n^2 + e(P)). 
02.02.46211 Jakub Cisło, Grzegorz Jurdziński 
Tight Hardness Results for LCS and other Sequence Similarity Measures 
10.12.43527 Manuel Bodirsky TU Dresden 
Informatyka Teoretyczna The tractability conjecture for finitely bounded homogeneous structures 
Finitely bounded homogeneous structures form a large class of infinite structures that can be seen as a generalisation of the class of all finite structures. Many results about finite structures, in particular in the context of the complexity of constraint satisfaction problems, can be generalised to this larger class. In this talk I will present a reformulation of a tractability conjecture for CSPs for this class in terms of polymorphisms, due to Barto and Pinsker (LICS 2016), and I will present a proof that the condition given in the tractability conjecture is decidable (under some Ramseytheoretic assumptions that might hold in general for all reducts of finitely bounded homogeneous structures). 
04.06.43418 Łukasz Lachowski 
Podstawy Informatyki Impossibility of Distributed Consensus with One Faulty Process by MICHAEL J. FISCHER, NANCY A. LYNCH AND MICHAEL S. PATERSO 
The consensus problem involves a asynchronous system of processes, some of which may be unreliable.The problem is for the reliable processes to agree on a binary value. In this paper, it is shown that every protocol for this problem has the possibility of nontermination, even with only one faulty process. By way of contrast, solutions are known for the synchronous case, the “Byzantine Generals” problem. 
11.04.40735 Marcin Briański 
Kryptologia NonInteractive Verifiable Computing: Outsourcing Computation to Untrusted Workers 
The talk is based on the paper with the same title by Rosario Gennaro, Craig Gentry and Bryan Parno. Verifiable Computation enables a computationally weak client to "outsource" the computation of a function F on various inputs x_{1}, ..., x_{k} to one or more workers. The workers return the result of the function evaluation, e.g., y_{i} = F(x_{i}), as well as a proof that the computation of F was carried out correctly on the given value x_{i}. The verification of the proof should require substantially less computational effort than computing F(x_{i}) from scratch. We present a protocol that allows the worker to return a computationally sound, noninteractive proof that can be verified in O(m) time, where m is the bitlength of the output of F. The protocol requires a onetime preprocessing stage by the client which takes O(C) time, where C is the smallest Boolean circuit computing F. Our scheme also provides input and output privacy for the client, meaning that the workers do not learn any information about the values x_{i} or y_{i}. 
01.07.27100 Grzegorz Matecki 
Optymalizacja Kombinatoryczna Boolean dimension of posets 
A boolean dimension bdim(P) of a poset P=(X,<) is a smallest number k for which there is a set l1, l2, ..., lk of labelings X:>N and a boolean formula f(a1, ..., ak) such that the following is true: x < y in P iff f(a1, .., a_k) = 1 where ai =1 iff li(x) < li(x). Generally, it is simple to observe that bdim(P) <= dim(P). Also, it is known that there is a constant c such that bdim(n) <= c log(n) for any poset P of size n. The are few interesting open problems for boolean dimension: 1) Is boolean dimension of the boolean lattice of size n less that n? 2) Is there a constant c such that bdim(P) < c for any planar poset P? 
19.08.27041 Sylwester Klocek, Wojciech Kruk 
The Alternating Stock Size Problem and the Gasoline Puzzle 
27.01.24253 Maciej Bendkowski 
Podstawy Informatyki Boltzmann samplers: random generation of combinatorial structures with an application to lambda calculus 
In their seminal paper, Duchon et al. proposed a surprisingly simple, generalpurpose framework of Boltzmann samplers meant for random generation of combinatorial structures. In this talk we revisit their method and discuss its elegant relation with analytic combinatorics as well as important practical implementation details. Finally, we discuss the application of Boltzmann samplers to the random generation of lambda terms used, e.g. in testing functional programming compilers. 
04.12.21569 Zygmunt Łenyk 
Kryptologia Speeding up modular multiplication using Montgomery and Barrett reduction 
In the talk we present Montgomery and Barrett reductions that are used to speed up modular computations. In both reductions some precomputations are made allowing for replacing subsequent expensive divisions by some fixed modulus with much cheaper operations involving a suitable power of 2. This is particularly useful when many modular divisions by the same modulus are performed (for example in finite field arithmetic or in RSA). 
04.05.2076 Mateusz Twaróg, Łukasz Majcher 
Optymalizacja Kombinatoryczna Combinatorial library core 
Presentation and discussion on core functionalities of the c++ combinatorial library. introduction to classes representing graphs, graph traversing algorithm templates and simple GUI. 
22.09.5087 Michał Zwonek 
Podstawy Informatyki Wielomianowe kodowania 
Rozważany będzie problem istnienia wielomianowej bijekcji, najniższego stopnia, między N^k, a N. Przedstawione będą także problemy otwarte związane z tą tematyką. Materiały do wystąpienia: 1) Elementarny dowód Twierdzenie FeuterPolya (jedyny kwadratowy i bijektywny wielomian N^2>N to funkcja cantore'a) https://arxiv.org/abs/1512. 2) Praca, w której autorzy pokazują nieistnienie wielomianów 3 i 4 stopnia. http://www.sciencedirect.com/ 3) Praca podobnie tematyczna odnosząca się do problemu istnienia wielomianów bijektywnych z pewnego sektora N^2 w N. (To o czym wspomniałem na koniec, opis tego problemu jest też pod koniec w 1) ). Pod koniec pracy jest opisane 6 problemów otwartych związanych z tą tematyką. https://arxiv.org/abs/1305. 4) W podobnej tematyce. http://www.sciencedirect.com/science/article/pii/0022314X78900355

28.02.2017 Michał Dyrek 
Kryptologia LLL algorithm and its applications in Number Theory and Cryptography 
The talk is devoted to the algorithm by A. Lenstra, H. Lenstra and L. Lovász dated 1982 allowing for approximation of Shortest Vector Problem in polynomial time. We will present the idea of the algorithm and highlight its applications such as factoring polynomials over Q, constructing polynomials with small coefficients and connections with attacks on RSA. 
02.10.73644 Wojciech Kruk, Maciej Woźniak 
Optymalizacja Kombinatoryczna A few open problems 
We mentioned the following open problems in graph theory and discrepancy theory: 1. Erdos discrepancy problem 2. Hoang  Reed conjecture 3. Seagull problem  a consequence of Hadwiger's conjecture 
06.11.70906 29.03.5197 Grzegorz Guśpiel 
Informatyka Teoretyczna Partial Visibility Representation Extension Problem 
We study a class of graphs that have a special geometric representation. By a bar visibility representation of an undirected graph we mean a function that associates with each vertex of a graph a horizontal line segment in such a way, that between segments representing two ends of an edge there is a vertical strip (of visibility). In case of directed graphs, we additionally assume that the visibility is from the bottom to the top, that is the line segment representing the source of the edge is below the one for the target. Graphs admitting such representations are well understood and can be recognized in linear time, both in the undirected and in the directed case. We work in a more subtle setting, where line segments are already associated with some vertices of a graph, and the question is if this can be extended to a bar visibility representation of an entire graph. We prove some results on complexity of this kind of problems. This is joint work with Steven Chaplick, Grzegorz Gutowski, Tomasz Krawczyk and Giuseppe Liotta. The manuscript is available here: https://arxiv.org/abs/1512.00174 
23.03.70793 Sylwester Klocek 
Podstawy Informatyki Incompleteness, Undecidability and Automated Proofs by Cristian S. Calude and Declan Thompson 
Incompleteness and undecidability have been used for many years as arguments against automatising the practice of mathematics. The advent of powerful computers and proofassistants – programs that assist the development of formal proofs by humanmachine collaboration – has revived the interest in formal proofs and diminished considerably the value of these arguments. In this paper we discuss some challenges proofassistants face in handling undecidable problems – the very results cited above – using for illustrations the generic proofassistant Isabelle. 
24.01.2017 Kamil Sałaś 
Kryptologia Lower Bounds for Discrete Logarithms 
In the talk we will present the computational complexity of the discrete logarithm in the context of "generic algorithms", that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element is encoded as unique binary string. For discrete logarithm, any generic algorithm must perform Ω(p^1/2) group operations, where p is the largest prime dividing the order of the group. 
19.01.2017 Paweł Petecki Akademia GórniczoHutnicza 
Optymalizacja Kombinatoryczna Symmetry breaking polynomial 
Let G be a graph, and let Γ= Aut G. A coloring c of G is symmetrybreaking if for every nonidentity automorphism φ in Γ, there is some vertex v of G such that c(v)≠c(φ(v)). There has been a lot of work on the minimum number of colors in a symmetrybreaking coloring of G. We discuss here a different problem: counting the number of kcolorings that are symmetry breaking. The tool, as is frequently the case for problems such as this one, is Möbius inversion. To solve this problem we define symmetry breaking polynomial ψ_{G}. For positive integer k (number of colors), ψ_{G}(k) is the number of kcolorings that break all nontrivial symmetries of the graph G. 
01.07.51741 Marian Mrozek 
Informatyka Teoretyczna The discrete charm of Morse theory 
The lecture will start with recalling P.S. Alexandroff's Theorem (1937) on mutual equivalence of posets and T_{0} topologies on finite sets. Next, we will outline the combinatorial version of the classical Morse Theory presented by R. Forman in 1998. Then, we will elaborate Forman's ideas towards the combinatorial topological dynamics with potential applications in Big Data problems and time series. The topics of the lecture will be expanded in a course for PhD students in the summer semester 2016/17. 
16.11.51627 Michał Ziobro 
Podstawy Informatyki Inhabitation in SimplyTyped LambdaCalculus through a LambdaCalculus for Proof Search by Jose Espırito Santo, Ralph Matthes, Luıs Pinto 
Kontynuacja seminarium z 23.11.2016 
17.01.2017 Grzegorz Bukowiec 
Kryptologia A quasipolynomial algorithm for discrete logarithm in finite fields of small characteristic 
Until recently, all the algorithms for computing discrete logarithm had a subexponential complexity of type L(1/3), similar to the factorization problem. In this talk we'll discuss a heuristic algorithm that provides quasipolynomial complexity for discrete logarithm in finite fields of small characteristic and that even for other cases still surpasses the Function Field Sieve method. References: [1] R. Barbulescu, P. Gaudry, A. Joux, E. Thomé, A quasipolynomial algorithm for discrete logarithm in finite fields of small characteristic (pdf) 
24.02.32576 Patryk Mikos 
Informatyka Teoretyczna Online coloring of intervals with bandwidth 
We study the online interval coloring problem with bandwidth. The input is a sequence of pairs J_{i}= (I_{i},w_{i}) where I_{i} is an interval on the real line and w_{i} is a real number from (0,1]. In this setting a proper coloring is a function f:J_{i }→N such that for each color c and any point p on the real line, the sum of bandwidths of intervals containing p and colored by c does not exceed 1. The best known lower bound on the competitive ratio in this problem is 24/7. We present an explicit strategy for Presenter that increases the competitive ratio ifor this problem to at least 4.1626. 
11.07.32462 Patryk Mikos 
Podstawy Informatyki ON THE NUMBER OF DISTINCT LANGUAGES ACCEPTED BY FINITE AUTOMATA WITH n STATES by Michael Domaratzki, Derek Kisman and Jeffrey Shallit 
We give asymptotic estimates and some explicit computations for both the number of distinct languages and the number of distinct finite languages over a kletter alphabet that are accepted by deterministic finite automata (resp. nondeterministic finite automata) with n states. 
10.01.2017 Szymon Policht 
Kryptologia Faster operations on elliptic curves using Edwards curves 
Elliptic curve cryptography is a broad and commonly used section of modernday cryptography. Because of that, the speed of elliptic curve operations directly impacts the performance of many current systems. In this talk we'll show how to speed up those operations using Edwards curves. References: [1] Bernstein D.J., Lange T. (2007) Faster Addition and Doubling on Elliptic Curves. In: Kurosawa K. (eds) Advances in Cryptology – ASIACRYPT 2007. ASIACRYPT 2007. Lecture Notes in Computer Science, vol 4833. Springer, Berlin, Heidelberg (https://eprint.iacr.org/2007/286.pdf) 
12.12.16093 Jan Derbisz, Jakub Łabaj 
Sortowanie przez spacer po drzewie 
Rozważamy następujący problem: wierzchołki drzewa ponumerowane są kolejnymi liczbami naturalnymi, a dodatkowo w wierzchołku x leży skrzynka o numerze p(x), przy czym funkcja p jest permutacją zbioru {1,2,..,n}. Rozważamy chodzącego po drzewie robota, który może w danym momencie trzymać tylko jedną skrzynkę, może też podnieść napotkaną skrzynkę upuszczając aktualnie trzymaną. Celem robota jest posortować skrzynki (przenosząc każdą do wierzchołka o odpowiednim numerze), przechodząc po drzewie najkrótszą możliwą ścieżką. Praca D. Grafa podaje algorytm znajdujący taką ścieżkę w czasie O(n^{2}) oraz dowód, że jeśli drzewo zastąpimy grafem planarnym, problem staje się NPzupełny. 
05.03.13297 Konrad Kalita 
Podstawy Informatyki ANALYTIC MODELS AND AMBIGUITY OF CONTEXTFREE LANGUAGES by Philippe Flajolet 
We establish that several classical contextfree languages are inherently ambiguous by proving that their counting generating functions, when considered as analytic functions, exhibit some characteristic form of transcendental behaviour. To that purpose, we survey some general results on elementary analytic properties and enumerative uses of algebraic functions in relation to formal languages In particular, the paper contains a general density theorem for unambiguous contextfree languages. 
15.01.62693 Łukasz Majcher, Jan Szczepaniec 
Optymalizacja Kombinatoryczna Convex ppartitions of bipartite graphs 
A set of vertices X of a graph G is convex if no shortest path between two vertices in X contains a vertex outside X. We prove that for fixed p ≥ 1, all partitions of the vertex set of a bipartite graph into p convex sets can be found in polynomial time. 
19.02.59955 Maciej Bendkowski 
Informatyka Teoretyczna Boltzmann samplers: a framework for random generation of combinatorial structures with an application to lambda calculus 
In their seminal paper, Duchon et al. proposed a surprisingly simple, generalpurpose framework of Boltzmann samplers meant for random generation of combinatorial structures. In this talk we revisit their method and discuss its elegant relation with analytic combinatorics as well as important practical implementation details. Finally, we discuss the application of Boltzmann samplers to the random generation of lambda terms used, e.g. in testing functional programming compilers. 
07.12.43472 Michał Glapa, Franciszek Stokowacki 
Skojarzenia w grafach metodami algebraicznymi 
Na seminarium omówiony zostanie przełomowa praca z 2006, autorstwa Muchy i Sankowskiego, opisująca algorytm obliczania skojarzeń w grafach za pomocą eliminacji Gaussa. Przedstawiony algorytm ma złożoność zależną od mnożenia macierzy, niższą niż O(n2.5), algorytmu MicaliegoVaziraniego, który bardzo długo był najlepszą znaną metodą. 
15.12.2016 Anna Kobak 
Optymalizacja Kombinatoryczna Open problems in graph theory concerning minors. 
We mentioned following open problems in graph theory:

14.10.40789 Grzegorz Matecki 
Informatyka Teoretyczna TwoDimensional Irregular Packing Problem 
We present results on packing irregular shapes onto given sheets of material. 
29.02.40676 Piotr Wójcik 
Podstawy Informatyki Enumeration and random generation of accessible automata by Frederique Bassino and Cyril Nicaud 
We present a bijection between the A_n of deterministic and accessible automata with n states on a kletters alphabet and some diagrams, which can themselves be represented as partitions of a set of kn + 1 elements into n nonempty subsets. This combinatorial construction shows that the asymptotic order of the cardinality of A_n is related to the Stirling number. Our bijective approach also yields an efficient random sampler, for the uniform distribution, of automata with n states, its complexity is O(n^3/2), using the framework of Boltzmann samplers. 
04.04.37938 Krzysztof Kleiner 
Kryptologia An introduction to quantum computing and cryptography I 
In this talk we're going to discuss quantum informatics and its impact on the field of cryptography. We will introduce the basic concepts of quantum computing as well as cryptography based on Quantum Key Distribution scheme, one of the aspects of quantum informatics which already is being used in practice. Then we will present Shor's algorithm for polynomialtime factorization, responsible for the cryptosystems based on the hardness of factorization or discrete logarithm (in abelian groups) being no longer secure against an adversary with access to a quantum computer.

08.12.2016 Lech Duraj 
Krótka opowieść o mnożeniu macierzy 
W ostatnich latach pojawiają się kolejne, coraz lepsze algorytmy mnożenia macierzy. Każdy z nich jest jednak tylko nieznacznie szybszy od poprzednich, będąc przy tym nierównie trudniejszy w zrozumieniu i analizie. Fakt ten jeszcze bardziej komplikuje otwarte od wielu lat pytanie o złożoność optymalnego algorytmu mnożenia macierzy. Celem prezentacji jest krótkie omówienie technik używanych do ataków na ten niezwykle ważny i trudny problem. Prezentacja oparta jest na przeglądowym wykładzie François Le Galla (autora ostatnich wyników w tym temacie) z 2014 roku. 
08.12.2016 Zygmunt Łenyk 
Optymalizacja Kombinatoryczna Rendezvous on the line. 
This is one of a handful of rendezvous problems where two players must find one another in a certain structured domain. In line case, players are placed on the line with distance 2, without knowing neither on which side is their partner, nor the direction of the line. I'll concentrate on the symmetric case where players must follow a specific (but maybe mixed) strategy. The conjecture is that best expected time of meeting two players equals 4.25. 
25.10.21510 Jakub Brzeski 
Podstawy Informatyki ENUMERATION OF FORMAL LANGUAGES by Michael Domaratzki 
We survey recent results on the enumeration of formal languages. In particular, we consider enumeration of regular languages accepted by deterministic and nondeterministic finite automata with n states, regular languages generated by regular expressions of a fixed length, and !regular languages accepted by Müller automata. We also survey the uncomputability of enumeration of contextfree languages and more general structures. 
06.12.2016 Marek Rusinowski 
Kryptologia Security of instant messaging applications. 
Nowadays billions of people around the world are sharing sensitive information using instant messaging applications. We will look into the current state of IM security, the problems in this area and a few encryption protocolsOTR and Signal Protocol in particularthat provide security features desired by users. 
01.12.2016 Aleksandra Mędrek, Krzysztof Maziarz 
Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back 
Praca Aleksandra Mądrego opisuje nowe podejście do problemu maksymalnego przepływu, z użyciem tzw. przepływów elektrycznych. W tej technice krawędziom przypisywany jest opór, a zadaniem jest zminimalizowanie wydzielonej energii. Dowolną sieć przepływową można zredukować do zadania przepływu elektrycznego, z użyciem pośredniej redukcji poprzez warianty problemu skojarzenia w grafie dwudzielnym. Głównym rezultatem pracy jest algorytm przepływu o złożoności O(m^{10/7}), na seminarium będzie prezentowana prostsza wersja algorytmu, działająca w O(m^{3/2}). 
01.12.2016 Patryk Urbański 
Optymalizacja Kombinatoryczna Coloring Ordinary Maps, Maps of Empires and Maps of the Moon 
A short review of generalized map coloring problems:

01.12.2016 Mateusz Twaróg 
Optymalizacja Kombinatoryczna Second Neighborhood via First Neighborhood in Digraphs 
22.12.84650 Bartosz Walczak 
Informatyka Teoretyczna Coloring curves that cross a fixed curve 
A class of graphs is χbounded if the chromatic number of all graphs in the class is bounded by some function of their clique number. String graphs are intersection graphs of curves in the plane. Significant research in combinatorial geometry has been devoted to understanding the classes of string graphs that are χbounded. In particular, it is known since 2012 that the class of all string graphs is not χbounded. We prove that for every integer t≥1, the class of intersection graphs of curves in the plane each of which crosses a fixed curve in at least one and at most t points is χbounded. This result is best possible in several aspects; for example, the upper bound t on the number of crossings with the fixed curve cannot be dropped. As a corollary, we obtain new upper bounds on the number of edges in socalled kquasiplanar topological graphs. This is joint work with Alexandre Rok. 
04.08.84482 Yauheni Ananchuk 
Podstawy Informatyki ALGEBRAIC FOUNDATIONS FOR QUALITATIVE CALCULI AND NETWORKS by ROBIN HIRSCH, MARCEL JACKSON, AND TOMASZ KOWALSKI 
Binary Constraint Problems have traditionally been considered as Network Satisfaction Problems over some relation algebra. A constraint network is satisfable if its nodes can be mapped into some representation of the relation algebra in such a way that the constraints are preserved. A qualitative representation is like an ordinary representation, but instead of requiring (a ; b) = a j b , as we do for ordinary representations, we only require that. A constraint network is qualitatively satisfable if its nodes can be mapped to elements of a qualitative representation, preserving the constraints. If a constraint network is satisfable then it is clearly qualitatively satisfable, but the converse can fail. However, for a wide range of relation algebras including the point algebra, the Allen Interval Algebra, RCC8 and many others, a network is satisfable if and only if it is qualitatively satisfable. Unlike ordinary composition, the weak composition arising from qualitative representations need not be associative, so we can generalise by considering network satisfaction problems over nonassociative algebras. We prove that computationally, qualitative representations have many advantages over ordinary representations: whereas many finite relation algebras have only infnite representations, every finite qualitatively representable algebra has a finite qualitative representation; the representability problem for (the atom structures of) finite nonassociative algebras is NPcomplete; the network satisfaction problem over a finite qualitatively representable algebra is always ; the validity of equations over qualitative representations is coNPcomplete. On the other hand we prove that there is no finite axiomatisation of the class of qualitatively representable algebra 
29.11.2016 Anna Kobak 
Kryptologia Breaking RSA vs Factoring in generic ring model 
In the talk we present results of Aggarwal and Maurer [1], who showed that a generic ring algorithm for breaking RSA with modulus $N$ can be converted into an algorithm for factoring $N$. The results imply that any attempt at breaking RSA without factoring $N$ will be nongeneric and hence will have to manipulate the particular bitrepresentation of the input modulo $N$. This provides new evidence that breaking RSA may be equivalent to factoring the modulus.
References: [1] D. Aggarwal, U. Maurer, Breaking RSA Generically is Equivalent to Factoring, EUROCRYPT 2009 
24.11.2016 Wojciech Łopata 
Optymalizacja Kombinatoryczna Several open problems from game theory, graph theory and combinatorics. 
I'll briefly introduce the audience to two unrelated areas: book embedding and mechanism design, and walk through some open problems in those areas. 
24.11.2016 Dominika Salawa, Jakub Cisło 
Greedy algorithms for Steiner forest 
Referowana praca rozstrzyga długo otwarty problem: czy budowanie drzewa Steinera zachłannym algorytmem daje wynik gorszy od optymalnego o stałą multiplikatywną? Autorzy (A. Gupta, A. Kumar) dowodzą, że tak, dla stałej równej 96. Jest to pierwsze znane oszacowanie wyniku algorytmu zachłannego, wcześniej podawane algorytmy aproksymacyjne dla tego problemu oparte były o programowanie liniowe. 
23.11.2016 Piotr Danilewski 
Informatyka Teoretyczna Functional Code Building 

23.11.2016 Michał Ziobro 
Podstawy Informatyki Inhabitation in SimplyTyped LambdaCalculus through a LambdaCalculus for Proof Search by Jos´e Espırito Santo, Ralph Matthes, Luıs Pinto 
A new, comprehensive approach to inhabitation problems in simplytyped lambdacalculus is shown, dealing with both decision and counting problems. This approach works by exploiting a representation of the search space generated by a given inhabitation problem, which is in terms of a lambdacalculus for proof search that the authors developed recently. The representation may be seen as extending the CurryHoward representation of proofs by lambdaterms, staying within the methods of lambdacalculus and type systems. Our methodology reveals inductive descriptions of the decision problems, driven by the syntax of the proofsearch expressions, and the end products are simple, recursive decision procedures and counting functions. 
17.11.2016 Patryk Gołębiowski, Wojciech Kruk 
Lower Bounds in the Preprocessing and Query Phases of Routing Algorithms 
Tematem referatu jest praca Colina White'a dotycząca algorytmów poszukiwania ścieżki na grafach o szczególnym własnościach, mających w założeniu modelować rzeczywiste sieci dróg. Autor analizuje najpopularniejsze istniejące algorytmy i podaje dolne ograniczenia na ich złożoność. 
16.11.2016 Bartłomiej Bosek 
Informatyka Teoretyczna Every digraph is majority 4choosable 
A majority coloring of a digraph is a coloring of its vertices such that for each vertex at most half of its outneighbors has the same color as that vertex. A digraph D is majority kchoosable if for any assignment of color lists of size k to the vertices there is a majority coloring of D from these lists. We prove the statement in the title. This gives a positive answer to a question posed recently in 1. This is a joint work with Marcin Anholcer and Jarosław Grytczuk. 
16.11.2016 Michał Zieliński 
Podstawy Informatyki Most programs stop quickly or never halt by Cristian S. Calude and Michael A. Stay 
The aim of this paper is to provide a probabilistic, but nonquantum, analysis of the Halting Problem. Our approach is to have the probability space extend over both space and time and to consider the probability that a random Nbit program has halted by a random time.We postulate an a priori computable probability distribution on all possible runtimes and we prove that given an integer k >0, we can effectively compute a time bound T such that the probability that an Nbit program will eventually halt given that it has not halted by T is smaller than 2^{−k}. We also show that the set of halting programs (which is computably enumerable, but not computable) can be written as a disjoint union of a computable set and a set of effectively vanishing probability. Finally, we show that “long” runtimes are effectively rare. More formally, the set of times at which an Nbit program can stop after the time 2^{N+constant} has effectively zero density. 
15.11.2016 Piotr Kawałek 
Kryptologia Teoretyczne podstawy kryptoanalizy 
Celem referatu jest przedstawienie teoretycznych modeli ataków kryptoanalitycznych oraz tematów pokrewnych wraz z przykładami. 
10.11.2016 Magdalena Gargas, Mateusz Jachna 
Max flows in O(nm) time, or better 
W pracy opisany jest nowy algorytm przepływu działający w czasie O(nm + m16/15 log2 n). Istotny jest fakt, że przez połączenie go z poprzednio znanymi algorytmami daje to pozytywną odpowiedź na pytanie, czy da się obliczyć maksymalny przepływ w czasie O(nm). Autorem pracy jest James B. Orlin. 
09.11.2016 26.10.2016 Adam Polak 
Informatyka Teoretyczna Open problems in online and approximation algorithms 
During the talk I will present several promising open problems including:

09.11.2016 Wojciech Kruk 
Podstawy Informatyki On the generic undecidability of the Halting Problem for normalized Turing machines by Alexander Rybalov 
Hamkins and Miasnikov presented in 2004 a generic algorithm deciding the classical Halting Problem for Turing machines with oneway tape on a set of asymptotic probability one (on a socalled generic set). Rybalov in 2007 showed that there is no generic algorithm deciding this problem on strongly generic sets of inputs (some subclass of generic sets). In this paper we prove that there is no generic algorithm deciding the Halting Problem for normalized Turing machines on generic sets of inputs. Normalized Turing machines have programs with the following natural restriction: internal states with large indices are not allowed at the beginning of the program. This condition does not reduce the class of computable functions because for every Turing machine there exists a normalized Turing machine which computes the same function. Our proof holds for machines with oneway and twoway tape. It also implies that the HamkinsMiasnikov algorithm is not generic for normalized Turing machines. 
08.11.2016 Patryk Gołębiowski 
Kryptologia Advanced Encryption Standard 
Advanced Encryption Standard (AES) is one of the most popular and widely adopted symmetric encryption scheme. In the talk we discuss how it works and why it is considered safe by the U.S. National Institute of Standards and Technology to use it for protecting classified information. 
03.11.2016 Gabriel Jakóbczak 
Optymalizacja Kombinatoryczna Proper orientations of some types of graphs 
Let G be a simple graph. We say that orientation of graph G is proper if for every pair of adjacent veritces u and v their indegrees are different. It was proved by Mieczysław Borowiecki, Jarosław Grytczuk and Monika Pilśniak that for every simple graph exists its proper orientation. Now we can define the proper orientation number of graph G as the minimum of the maximum indegree, taken over all proper orientations of G. We show that for some classes of bipartite graphs their proper orientation number is less than or equal to 6. We also show that this parameter is at most 4 for graphs which are trees and proof of that fact leads to a polynomialtime algorithm of finding proper orientation of such graphs.
Fiachra Knox, Sebastián González Hermosillo de la Maza, Bojan Mohar, and Cláudia Linhares Sales. Proper Orientations of Planar Bipartite Graphs. pages 26, sep 2016. 
03.11.2016 Krzysztof Francuz, Szymon Łukasz 
Fast and simple connectivity in graph timelines 
Referowana praca (autorstwa J. Łąckiego i A. Karczmarza) rozważa grafy, w którym krawędzie podlegają zmianom  są dodawane bądź usuwane. Opisany jest efektywny algorytm odpowiadający na pytania o osiągalność (istnienie ścieżki między dwoma wierzchołkami) i dwuspójność (istnienie dwóch rozłącznych ścieżek) na zadanych przedziałach czasowych. 
27.10.2016 Dawid Pyczek, Jakub Rówiński 
Faster deterministic sorting and priority queues in linear space 
Dolne ograniczenie O(n log n) na problem sortowania obowiązuje tylko, jeśli na sortowanych obiektach nie można wykonać żadnych operacji innych niż porównanie. Jeżeli natomiast sortujemy liczby całkowite, możliwe są szybsze algorytmy  referowana praca Mikkela Thorupa z 1997 opisuje algorytm działający w O (n (log log n)^{2}). 
27.10.2016 Magdalena Gargas 
Optymalizacja Kombinatoryczna The geometry of nesting problems: A tutorial 
26.10.2016 Wojciech Łopata 
Podstawy Informatyki Universality and Almost Decidability by Cristian S. Calude and Damien Desfontaines 
We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a decidable and generic (i.e. a set of natural density one) set whose intersection with S is decidable. Every decidable set is almost decidable, but the converse implication is false. We prove the existence of infinitely many universal functions whose halting sets are generic (negligible, i.e. have density zero) and (not) almost decidable. One result—namely, the existence of infinitely many universal functions whose halting sets are generic (negligible) and not almost decidable—solves an open problem in [9]. We conclude with some open problems. 
25.10.2016 Marcin Briański 
Kryptologia Unifying Zeroknowledge Proofs of Knowledge 
We present a simple zeroknowledge proof of knowledge protocol of which many protocols in the literature are instantiations. These include Schnorr's protocol for proving knowledge of a discrete logarithm, the FiatShamir and GuillouQuisquater protocols for proving knowledge of a modular root, protocols for proving knowledge of representations (like Okamoto's protocol), protocols for proving equality of secret values, a protocol for proving the correctness of a DiffieHellman key, protocols for proving the multiplicative relation of three commitments (as required in secure multiparty computation), and protocols used in credential systems. This shows that a single simple treatment (and proof), at a high level of abstraction, can replace the individual previous treatments. Moreover, one can devise new instantiations of the protocol. [1] Ueli Maurer, Unifying Zeroknowledge Proofs of Knowledge, Progress in Cryptology – AFRICACRYPT 2009, Vol. 5580 LNCS, pp 272286

20.10.2016 Helena Borak 
Optymalizacja Kombinatoryczna Exact algorithms for the twodimensional strip packing problem with and without rotations 
We propose exact algorithms for the twodimensional strip packing problem (2SP) with and without 90 degree rotations. We first focus on the perfect packing problem (PP), which is a special case of 2SP, wherein all given rectangles are required to be packed without wasted space, and design branchandbound algorithms introducing several branching rules and bounding operations. A combination of these rules yields an algorithm that is especially efficient for feasible instances of PP. We then propose several methods of applying the PP algorithms to 2SP. Our algorithms succeed in efficiently solving benchmark instances of PP with up to 500 rectangles and those of 2SP with up to 200 rectangles. They are often faster than existing exact algorithms specially tailored for problems without rotations. 
20.10.2016 Mateusz Twaróg, Patryk Urbański 
Disjoint Set Union with randomized linking 
Algorytm FindUnion w najbardziej znanej wersji implementowany jest przez las zbiorów rozłącznych z kompresją ścieżek i łączeniem według rang. Prezentowana praca, autorstwa Goela, Khanny, Larkina i Tarjana, analizuje złożoność w wersji z arbitralnym (losowym) łączeniem drzew. 
19.10.2016 Bartosz Walczak 
Informatyka Teoretyczna Common tangents of two disjoint polygons in linear time and constant workspace 
A tangent of a polygon is a line touching but not crossing the polygon. Two disjoint polygons can have four, two, or no common tangents, depending on whether the convex hulls of the polygons are disjoint, overlapping, or nested. We describe a very simple lineartime constantworkspace algorithm to compute all common tangents of two disjoint polygons, each given by a readonly array of its corners in a cyclic order. This is joint work with Mikkel Abrahamsen. 
19.10.2016 Pola Kyzioł 
Podstawy Informatyki The domino problem for selfsimilar structures by Sebastian Barbieri and Mathieu Sablik 
We defne the domino problem for tilings over selfsimilar structures of $Z^d$ given by forbidden patterns. In this setting we exhibit nontrivial families of subsets with decidable and undecidable domino problem. 
18.10.2016 Grzegorz Jurdzinski 
Kryptologia Timing attacks 
Cryptosystems like AES or RSA use algorithms which runtime depends on input data or using CPU cache. Basing on this fact an attacker can find secret keys by choosing inputs and carefully measuring time needed for computations. In this talk I will present such attacks and how to prevent them.

13.10.2016 Krzysztof Barański 
Optymalizacja Kombinatoryczna LevelOriented TwoDimensional Packing Algorithms 
The paper includes an overview of several algorithms, their complexities and approximation ratios solving twodimensional strip packing problem: 1) FirstFit Decreasing Height (FFDH)  time complexity: O(nlgn), approximation ratio: <= 17/10 OPT(I) + 1 [with proof] 2) NextFit Decreasing Height (NFDH)  time complexity: O(nlgn), approximation ratio: <= 17/10 OPT(I) + 1 [with proof] 3) BestFit Decreasing Height (BFDH), BottomLeft (BL), Steinberg's algorithm, SplitFit (SF) 
13.10.2016 Grzegorz Bukowiec, Sylwester Klocek 
Algorytm FKT 
Rozstrzygnięcie, czy w grafie istnieje skojarzenie, oraz znalezienie takiego skojarzenia są problemami łatwymi obliczeniowo. Liczenie wszystkich skojarzeń jest jednak problemem #Pzupełnym  wielomianowy algorytm na ten problem pociągałby równość P = NP. Istnieje jednak sposób na policzenie skojarzeń dla pewnej klasy grafów  w szczególności, dla wszystkich grafów planarnych. Algorytm taki  zwany od nazwisk twórców algorytmem FKT  wykorzystuje bliski związek między pojęciami (łatwego obliczeniowo) wyznacznika i (trudnego) permanentu macierzy. 
12.10.2016 Adam Polak 
Informatyka Teoretyczna Why is it hard to beat O(n^2) for Longest Common Weakly Increasing Subsequecnce? 
11.10.2016 Michał Zieliński 
Kryptologia SafeDeflate: compression without leaking secrets 
CRIME and BREACH attacks on TLS/SSL leverage the fact that compression ratio is not hidden by encryption to recover content of secrets. We introduce SafeDeflate—a modification of a standard Deflate algorithm which compression ratio does not leak information about secret tokens. The modification is compatible with existing Deflate and gzip decompressors. We introduce a model in which attacker can obtain ciphertexts of arbitrary compressed plaintext containing secret values. Then we prove that SafeDeflate is secure in this model. 
06.10.2016 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna A new variant of the game of cops and robber 
The talk presents a joint work of Jarosław Grytczuk, Joanna Sokół, Małgorzata ŚleszyńskaNowak. We consider the following metric version of the Cops and Robbers game. Let G be a simple graph and let k≥1 be a fixed integer. In the first round, Cop picks a subset of k vertices B={v_{1},v_{2},…,v_{k}} and then Robber picks a vertex u but keeps it in a secret. Then Cop asks Robber for a vector D_{u}(B)=(d_{1},d_{2},…,d_{k}) whose components d_{i}=d_{G}(u,v_{i}), i=1,2,…,k, are the distances from u to the vertices of B. In the second round, Robber may stay at the vertex u or move to any neighbouring vertex which is kept in a secret. Then Cop picks another k vertices and asks as before for the corresponding distances to the vertex occupied by Robber. And so on in every next round. The game stops when Cop determines exactly the current position of Robber. In that case, she is the winner. Otherwise, Robber is the winner (that is if Cop is not able to localize him in any finite number of rounds). Let ζ(G) denote the least integer k for which Cop has a winning strategy. Notice that this parameter is well defined since the inequality ζ(G)≤V(G) holds obviously. 
05.10.2016 Tomasz Kisielewski 
Podstawy Informatyki Programy które są w stanie przeprowadzać rozumowania o swoich własnościach Proving properties of programs within their language 
Przedstawię wstępną wersję swojego programu badawczego, mającego ====== I will present an initial version of my research program, whosemain goal is to enable proving properties about programs within 
04.07.2016 
The 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, AofA'16 Krakow 
15.06.2016 Piotr Kawałek i Teodor Jerzak 
Podstawy Informatyki Generalised and Quotient Models for Random And/Or Trees and Application to Satisfiability by Antoine Genitrini and Cécile Mailler: 
This article is motivated by the following satisfiability question: pick uniformly at random an and/or Boolean expression of length n, built on a set of k_n Boolean variables. What is the probability that this expression is satisfiable? asymptotically when n tends to infinity? The model of random Boolean expressions developed in the present paper is the model of Boolean Catalan trees, already extensively studied in the literature for a constant sequence. The fundamental breakthrough of this paper is to generalise the previous results for any (reasonable) sequence of integers which enables us, in particular, to solve the above satisfiability question. We also analyse the effect of introducing a natural equivalence relation on the set of Boolean expressions. This new quotient model happens to exhibit a very interesting threshold (or saturation) phenomena.

09.06.2016 Gwenaël Joret Université Libre de Bruxelles 
Algorytmiczne Aspekty Kombinatoryki Improved Approximation Algorithms for Hitting 3Vertex Paths 
We study the problem of deleting a minimum cost set of vertices from a 
08.06.2016 Kamil Pietruszka 
Podstawy Informatyki Regular Combinators for String Transformations by Rajeev Alur Adam Freilich Mukund Raghothaman 
We focus on (partial) functions that map input strings to a monoid such as the set of integers with addition and the set of output strings with concatenation. The notion of regularity for such functions has been defined using twoway finitestate transducers, (oneway) cost register automata, and MSOdefinable graph transformations. In this paper, we give an algebraic and machineindependent characterization of this class analogous to the definition of regular languages by regular expressions. When the monoid is commutative, we prove that every regular function can be constructed from constant functions using the combinators of choice, split sum, and iterated sum, that are analogs of union, concatenation, and Kleene *, respectively, but enforce unique (or unambiguous) parsing. Our main result is for the general case of noncommutative monoids, which is of particular interest for capturing regular stringtostring transformations for document processing. We prove that the following additional combinators suffice for constructing all regular functions: (1) the leftadditive versions of split sum and iterated sum, which allow transformations such as string reversal; (2) sum of functions, which allows transformations such as copying of strings; and (3) function composition, or alternatively, a new concept of chained sum, which allows output values from adjacent blocks to mix. 
02.06.2016 http://wms.mat.agh.edu.pl/~knmd/index.php/ikonferencjanaukowaknmd/harmonogram/ 
Algorytmiczne Aspekty Kombinatoryki Konferencja Studencka na AGH 
01.06.2016 Szymon Borak 
Informatyka Teoretyczna Polynomial time algorithm for finding Hamiltonian cycles in thin grid graphs 
In general, Hamiltonian Cycle Problem is NPcomplete in triangular and square grids. In "Not being(super)thin or solid is hard: A study of grid Hamiltonicity" Arkin et al. claimed HCP for thin triangular grids and thin square grids to be NPcomplete as well. However the arguments they gave are incorrect. In fact we show that thin triangular grids as well as thin square grids always have HC. Moreover we show a linear algorithm for finding a HC in such graphs. 
01.06.2016 Piotr Bejda 
Podstawy Informatyki PATTERN AVOIDANCE IS NOT P RECURSIVE by SCOTT GARRABRANT AND IGOR PAK 
Let F \subset S_k be a finite set of permutations and let C_n (F) denote the number of permutations avoiding the set of patterns F.

25.05.2016 Kolja Knauer Université AixMarseille 
Informatyka Teoretyczna Orienting triangulations  towards Schynyder woods on orientable surfaces 
We show that the edges of any triangulation of a closed surface different from the projective plane and the sphere can be oriented such that every vertex has nonzero outdegree divisble by three. This confirms a conjecture of Barát and Thomassen. We will explain why this is a first step towards the generalization of Schynyder woods from the plane to orientable surfaces and what is know 
19.05.2016 Miloš Stojaković University of Novi Sad 
Algorytmiczne Aspekty Kombinatoryki MakerBreaker games on random graphs 
Of all types of positional games, MakerBreaker games are probably the 
18.05.2016 Pola Kyzioł 
Podstawy Informatyki NPCompleteness of a Combinator Optimization Problem by M. S. Joy and V. J. RaywardSmith 
We consider a deterministic rewrite system for combinatory logic over combinators $S,K,I,B,C,S',B'$, and $C'$. 
28.04.2016 Wojciech Samotij Tel Aviv University 
Algorytmiczne Aspekty Kombinatoryki How does a typical finite metric space look like? 
27.04.2016 Michał Zieliński 
Podstawy Informatyki Beta Reduction is Invariant, Indeed by Beniamino Accattoli and Ugo Dal Lago 
Slot and van Emde Boas weak invariance thesis states that reasonable machines can simulate each other within a polynomially overhead in time.Is lambda calculus a reasonable machine? Is there a way to measure the computational complexity of a lambda term? This paper presents the first complete positive answer to this longstanding problem. Moreover, our answer is completely machineindependent and based over a standard notion in the theory of lambda calculus: the length of a leftmostoutermost derivation to normal form is an invariant cost model. Such a theorem cannot be proved by directly relating lambda calculus with Turing machines or random access machines, because of the size explosion problem: there are terms that in a linear number of steps produce an exponentially long output. The first step towards the solution is to shift to a notion of evaluation for which the length and the size of the output are linearly related. This is done by adopting the linear substitution calculus (LSC), a calculus of explicit substitutions modelled after linear logic proof nets and admitting a decomposition of leftmostoutermost 
21.04.2016 Jarosław Grytczuk 
Algorytmiczne Aspekty Kombinatoryki On some problems in combinatorial number theory 
20.04.2016 Adam Polak 
Informatyka Teoretyczna On subposets of dimension two 
We study the maximum guaranteed size of a dimension two subposet of an nelement poset. A trivial lower bound of the order of n^{1/2} follows from the Dilworth's theorem. We show an upper bound of the order of n^{2/3} improving the n^{0.8295} result by Reiniger and Yeager. We also discuss promising methods for achieving a better lower bound. 
20.04.2016 Wojciech Kruk 
Podstawy Informatyki On the equivalence of different presentations of Turner's bracket abstraction algorithm by Lukasz Czajka 
Turner's bracket abstraction algorithm is perhaps the most wellknown improvement on simple bracket abstraction algorithms. It is also one of the most studied bracket abstraction algorithms. The definition of the algorithm in Turner's original paper is slightly ambiguous 
14.04.2016 Michał Farnik Jagiellonian University 
Algorytmiczne Aspekty Kombinatoryki Hat guessing game on sparse graphs 
13.04.2016 Katarzyna Janocha 
Podstawy Informatyki On the Computing Power of +, , and x by Marcello Mamino 
Modify the BlumShubSmale model of computation replacing the permitted computational primitives (the real field operations) with any finite set B of real functions semialgebraic over the rationals. Consider the class of Boolean decision problems that can be solved 
07.04.2016 Steven Chaplick, Universitat Wurzburg 
Algorytmiczne Aspekty Kombinatoryki Intersection Graphs of Noncrossing Paths 
06.04.2016 Maciej Poleski 
Podstawy Informatyki The Fractal Dimension of SAT Formulas by Carlos Ansotegui, Maria Luisa Bonet, Jesus GiraldezCru and Jordi Levy 
Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed 
30.03.2016 Michał Śliwka Teroplan 
Informatyka Teoretyczna Efficient algorithm for several diverse results in public transport routing system 
We present a solution to problem arising in public transport routing systems: 
30.03.2016 Magdalena Wiercioch 
Podstawy Informatyki Principal types of BCKlambdatermss by Sachio Hirokawa 
BCKlambdaterms are the Iterms in which each variable occurs at most once. The principal type of a lambdaterm is the most general type of the term. In this paper we prove that if two BCKlambdaterms in betanormal form have the same principal type then they are identical. This solves the following problem (Y. Komori, 1987) in more general form: if two closed beta etanormal form BCKlambdaterms are assigned to the same minimal BCKformula, are they identical? A minimal BCKformula is the most general formula among BCKprovable formulas with respect to substitutions for type variables. To analyze type assignment, the notion of "connection" is introduced. A connection is a series of occurrences of a type. in a type assignment figure. Connected occurrences of a type have the same 
23.03.2016 Damian Goik 
Informatyka Teoretyczna Direct solver algorithms for systems created on the basis of adaptive meshes 

23.03.2016 Agnieszka Łupińska 
Podstawy Informatyki PARALLEL STANDARD TRANSLATION BETWEEN LAMBDA CALCULUS AND COMBINATORY LOGIC (wyniki własne) 
The talk is about the parallel approach to the standard translation between Lambda Calculus and Combinatory Logic. Let L be a lambdaterm and C be a combinator produced from L by the standard translation. Each lambda abstraction occurring in L, causes the linear expansion of some paths in the tree of the C combinator. We will show that the tree expansion can be performed parallel in logarithmic time on the path length. We will also discuss whether this procedure can be performed in the constant time. 
17.03.2016 Gabriel Jakóbczak 
Algorytmiczne Aspekty Kombinatoryki Additive chromatic number of several graph families 
02.02.46210 Jakub Cisło, Grzegorz Jurdziński 
Tight Hardness Results for LCS and other Sequence Similarity Measures 
03.03.2016 Jarosław Grytczuk 
Algorytmiczne Aspekty Kombinatoryki Pattern avoiding coloring of the plane 
02.03.2016 Piotr Wójcik 
Podstawy Informatyki Asymptotic properties of first order logic with one binary predicat symbol (wyniki własne) 
Wyniki własne 
24.02.2016 Zygmunt Łenyk 
Podstawy Informatyki Minimum Propositional Proof Length is NPHard to Linearly Approximate (by Michael Alekhnovich, Sam Buss, Shlomo Morany and Toniann Pitassi) 
We prove that the problem of determining the minimum propositional proof length is NPhard to approximate within a factor of 2^log^{1o(1)} n. These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution, Horn resolution, the polynomial calculus, the sequent calculus, the cutfree sequent calculus, as well as the polynomial calculus. Our hardness of approximation results usually apply to proof length measured either by number of symbols or by number of inferences, for treelike or daglike proofs. We introduce the Monotone Minimum (Circuit) Satisfying Assignment problem and reduce it to the problems of approximation of the length of proofs. 
10.02.2016 William Trotter Georgia Institute of Technology 
Informatyka Teoretyczna Dimension and Cut Vertices 
Motivated by quite recent research involving the relationship between the dimension of a poset and graph theoretic properties of its cover graph, we show that for every $d\ge 1$, if $P$ is a poset and the dimension of a subposet $B$ of $P$ is at most~$d$ whenever the cover graph of $B$ is a block of the cover graph of $P$, then the dimension of $P$ is at most $d+2$. We also construct examples which show that this inequality is best possible. 
27.01.2016 Michał Dyrek 
Optymalizacja Kombinatoryczna The Linear Arboricity of Graphs 
A linear forest is a forest in which each connected component is a path. The linear arboricity la(G) of a graph G is the minimum number of linear forests whose union is the set of all edges of G. The linear arboricity conjecture asserts that for every simple graph G with maximum degree D, la(G) <= [(D+1)/2]. Although this conjecture received a considerable amount of attention, it has been proven only for D <= 6, D = 8, D = 10 and the best known general upper bound for la(G) is la(G) <= [3D/5] for even D and la(G) <= [(3D + 2)/5] for odd A. Here we prove that for every e > 0 there is a D_0 so that for every G with maximum degree D > D_0, la(G) <= (1/2 + e) * D. To do this, we first prove the conjecture for every G with an even maximum degree D and with girth g > 50*D. N. Alon, The Linear Arboricity of Graphs 
27.01.2016 Miron Ficak 
Informatyka Teoretyczna On Exact Quantum Query Complexity 
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these functions cannot be obtained by simply computing parities of pairs of bits. We also characterise the model of nonadaptive exact quantum query complexity in terms Based on the paper: On Exact Quantum Query Complexity, by Ashley Montanaro, Richard Jozsa and Graeme Mitchison 
21.01.2016 Jarosław Grytczuk 
Algorytmiczne Aspekty Kombinatoryki Coloring graphs with many colors on cycles 
20.01.2016 Michał Seweryn 
Informatyka Teoretyczna Data Structures on Event Graphs 
We investigate the behavior of data structures when the input and operations Based on the paper: Data Structures on Event Graphs, by Bernard Chazelle and Wolfgang Mulzer 
20.01.2016 Pola Kyzioł 
Optymalizacja Kombinatoryczna Matching in regular and almost regular graphs 
I present an O(n^2*log n)time algorithm that finds a maximum matching in a regular graph with n vertices. More generally, the algorithm runs in O(r*n^2*log n) time if the difference between the maximum degree and the minimum degree is less than r. R. Yuster, Maximum matching in regular and almost regular graphs 
20.01.2016 Wiktor Tendera 
Podstawy Informatyki Some Remarks on Lengths of Propositional Proofs (by Samuel R. Buss) 
We survey the best known lower bounds on symbols and lines in Frege and extended Frege proofs. We prove that in minimum length sequent calculus proofs, no formula is generated twice or used twice on any single branch of the proof. We prove that the number of distinct subformulas in a minimum length Frege proof is linearly bounded by the number of lines. Depth d Frege proofs of m lines can be transformed into depth d proofs of O(m^{d+1}) symbols. We show that renaming Frege proof systems are pequivalent to extended Frege systems. Some open problems in propositional proof length and in logical flow graphs are discussed. 
14.01.2016 Michał Laosń IM PAN, Freie Universitat Berlin 
Algorytmiczne Aspekty Kombinatoryki On the toric ideal of a matroid and related combinatorial problems 
When an ideal is defined only by combinatorial means, one expects to have a combinatorial description of its set of generators. An attempt to achieve this description often leads to surprisingly deep combinatorial questions. White's conjecture is an example. It asserts that the toric ideal associated to a matroid is generated by quadratic binomials corresponding to symmetric exchanges. In the combinatorial language it means that if two multisets of bases of a matroid have equal union (as a multiset), then one can pass between them by a sequence of symmetric exchanges. White's conjecture resisted numerous attempts since its formulation in 1980. We will discuss its relations with other open problems concerning matroids. 
13.01.2016 Piotr Bejda 
Optymalizacja Kombinatoryczna Perfect matchings in O(n log n) time in regular bipartite graphs 
In this paper we consider the wellstudied problem of finding a perfect matching in a dregular bipartite graph on 2n nodes with m=nd edges. The bestknown algorithm for general bipartite graphs (due to Hopcroft and Karp) takes time O(m*sqrt(n)). In regular bipartite graphs, however, a matching is known to be computable in O(m) time (due to Cole, Ost and Schirra). In a recent line of work by Goel, Kapralov and Khanna the O(m) time algorithm was improved first to O'(min(m, n^2.5/d)) and then to O'(min(m,n^2/d)). It was also shown that the latter algorithm is optimal up to polylogarithmic factors among all algorithms that use nonadaptive uniform sampling to reduce the size of the graph as a first step. A. Goel and M. Kapralov and S. Khanna, Perfect matchings in O n log n time in regular bipartite graphs 
13.01.2016 Marcin Zieliński 
Podstawy Informatyki A correspondence between rooted planar maps and normal planar lambda terms (by Noam Zeilberger and Alain Giorgetti) 
A rooted planar map is a connected graph embedded in the plane, with one edge marked and assigned an orientation. A term of the pure lambda calculus is said to be \beta normal if it is fully reduced, and planar if it uses all of its variables exactly once and in lastin, firstout order. We exhibit a bijection between rooted planar maps and normal planar lambda terms (with one free variable), by explaining how Tutte decomposition of rooted planar maps (into vertex maps, maps with an isthmic root, and maps with a nonisthmic root) may be naturally replayed in lambda calculus. 
07.01.2016 Mateusz Michałek IM PAN, Warszawa, Freie Universitaet, Berlin 
Algorytmiczne Aspekty Kombinatoryki Tensors and algorithms for matrix multiplication 
16.12.2015 Michał Kosnowski 
Informatyka Teoretyczna Better Approximation Algorithms for the Maximum Internal Spanning Tree Problem 
We examine the problem of determining a spanning tree of a given graph Based on the paper: Better Approximation Algorithms for the Maximum Internal Spanning Tree Problem, by Martin Knauer and Joachim Spoerhase 
16.12.2015 Krzysztof Barański 
Podstawy Informatyki WORDS IN LINEAR GROUPS, RANDOM WALKS, AUTOMATA AND PRECURSIVENESS (by SCOTT GARRABRANT AND IGOR PAK) 
Fix a finite set S \suset GL(k, Z). Denote by a_n the number of products of matrices in S of length n that are equal to 1. We show that the sequence a_n is not always Precursive. This answers a question of Kontsevich. 
16.12.2015 Krzysztof Kleiner 
Optymalizacja Kombinatoryczna Online Dual Edge Coloring of Paths and Trees 
Extending the results presented on the preceding seminar, we study a dual version of online edge coloring, where the goal is to color as many edges as possible using only a given number, k, of available colors. All of our results are with regard to competitive analysis. For paths, we consider k=2, and for trees, we consider any k>=2. We prove that a natural greedy algorithm called FirstFit is optimal among deterministic algorithms on paths as well as trees. This is the first time that an optimal algorithm for online dual edge coloring has been identified for a class of graphs. For paths, we give a randomized algorithm, which is optimal and better than the best possible deterministic algorithm. Again, it is the first time that this has been done for a class of graphs. For trees, we also show that even randomized algorithms cannot be much better than FirstFit. L. M. Favrholdt, J. W. Mikkelsen, Online Dual Edge Coloring of Paths and Trees 
09.12.2015 Konrad Kalita 
Informatyka Teoretyczna A Fast Parallel Algorithm for MinimumCost Small Integral Flows 
A new approach to the minimumcost integral flow problem for small values of the flow is presented. It reduces the problem to the tests of simple multivariate polynomials over a finite field of characteristic two for nonidentity with zero. In effect, we show that a minimumcost flow of value k in a network with n vertices, a sink and a source, integral edge capacities and positive integral edge costs polynomially bounded in n can be found by a randomized PRAM, with errors of exponentially small probability in n, running in O(k log(kn) + log^{2}(kn)) time and using 2^{k}(kn)^{O(1)} processors. Thus, in particular, for the minimumcost flow of value O(log n), we obtain an RNC^{2} algorithm, improving upon time complexity of earlier NC and RNC algorithms. Based on the paper: A Fast Parallel Algorithm for MinimumCost Small Integral Flows, by Andrzej Lingas and Mia Persson

09.12.2015 Magdalena Wiercioch 
Podstawy Informatyki A Probabilistic ForesttoString Model for Language Generation from Typed Lambda Calculus Expressions (by Wei Lu and Hwee Tou Ng) 
This paper describes a novel probabilistic approach for generating natural language sentences from their underlying semantics in the form of typed lambda calculus. The approach is built on top of a novel reduction based weighted synchronous context free grammar formalism, which facilitates the transformation process from typed lambda calculus into natural language sentences. Sentences can then be generated based on such grammar rules with a log linear model. To acquire such grammar rules automatically in an unsupervised manner, we also propose a novel approach with a generative model, which maps from subexpressions of logical forms to word sequences in natural language sentences. Experiments on benchmark datasets for both English and Chinese generation tasks yield significant improvements over results obtained by two state of the art machine translation models, in terms of both automatic metrics and human evaluation. 
09.12.2015 Mateusz Twaróg 
Optymalizacja Kombinatoryczna OnLine EdgeColoring with a Fixed Number of Colors 
We investigate a variant of online edgecoloring in which there is a fixed number of colors available and the aim is to color as many edges as possible. We prove upper and lower bounds on the performance of different classes of algorithms for the problem. Moreover, we determine the performance of two specific algorithms, FirstFit and NextFit. Specifically, algorithms that never reject edges that they are able to color are called fair algorithms. We consider the four combinations of fair/not fair and deterministic/randomized. We show that the competitive ratio of deterministic fair algorithms can vary only between approximately 0.4641 and 1/2 , and that NextFit is worst possible among fair algorithms. Moreover, we show that no algorithm is better than 4/7 competitive. If the graphs are all kcolorable, any fair algorithm is at least 1/2 competitive. Again, this performance is matched by NextFit while the competitive ratio for FirstFit is shown to be k/(2k  1), which is significantly better, as long as k is not too large. M. Favrholdt, N. Nielsen, OnLine EdgeColoring with a Fixed Number of Colors, Algorithimca 35 (2), 176191, 2003 
02.12.2015 Grzegorz Bukowiec 
Podstawy Informatyki A \lambda to CL translation for strong normalization (by Yohji AKAMA) 
We introduce a simple translation from \lambdacalculus to combinatory logic (CL) such that: A is an SN \lambdaterm iff the translation result of A is an SN term of CL (the reductions are \betareduction in \lambdacalculus and weak reduction in CL). None of the conventional translations from \lambdacalculus to CL satisfy the above property. Our translation provides a simpler SN proof of Godel's \lambdacalculus by the ordinal number assignment method. By using our translation, we construct a homomorphism from a conditionally partial combinatory algebra which arises over SN \lambdaterms to a partial combinatory algebra which arises over SN CLterms. 
02.12.2015 Helena Borak 
Optymalizacja Kombinatoryczna Linear Extensions of Nfree Orders 
We consider the number of linear extensions of an Nfree order P. We give upper and lower bounds on this number in terms of parameters of the corresponding arc diagram. We propose a dynamic programming algorithm to calculate the number. The algorithm is polynomial if a new parameter called activity is bounded by a constant. The activity can be bounded in terms of parameters of the arc diagram. Stefan Felsner , Thibault Manneville, Linear Extensions of Nfree Orders, Order 32 (2), 147155, 2015 
25.11.2015 Grzegorz Bukowiec 
Podstawy Informatyki A \lambda to CL translation for strong normalization (by Yohji AKAMA) 
We introduce a simple translation from \lambdacalculus to combinatory logic (CL) such that: A is an SN \lambdaterm iff the translation result of A is an SN term of CL (the reductions are \betareduction in \lambdacalculus and weak reduction in CL). None of the conventional translations from \lambdacalculus to CL satisfy the above property. Our translation provides a simpler SN proof of Godel's \lambdacalculus by the ordinal number assignment method. By using our translation, we construct a homomorphism from a conditionally partial combinatory algebra which arises over SN \lambdaterms to a partial combinatory algebra which arises over SN CLterms. 
18.11.2015 Maciej Poleski 
Informatyka Teoretyczna Hitting All Maximal Independent Sets of a Bipartite 
We prove that given a bipartite graph G with vertex set V and an integer k, Based on the paper: Hitting All Maximal Independent Sets of a Bipartite, by Jean Cardinal and Gwenaël Joret 
18.11.2015 Marcin Kostrzewa 
Podstawy Informatyki Counting a type's prinipal inhabitants (by Broda and Damas) 
We present a Counting Algorithm that computes the number of lambdaterms in \betanormal form that have a given type as a principal type and produces a list of these terms. The design of the algorithm follows the lines of BenYelles algorithm for counting normal (not neessarily principal) inhabitants of a type. 
18.11.2015 Leszek Jakub Kania 
Optymalizacja Kombinatoryczna Improved Bounds for Online Preemptive Matching 
When designing a preemptive online algorithm for the maximum matching problem, we wish to maintain a valid matching M while edges of the underlying graph are presented one after the other. When presented with an edge e, the algorithm should decide whether to augment the matching M by adding e (in which case e may be removed later on) or to keep M in its current form without adding e (in which case e is lost for good). The objective is to eventually hold a matching M with maximum weight. The main contribution of this paper is to establish new lower and upper bounds on the competitive ratio achievable by preemptive online algorithms. L. Epstein, A. Levin, D. Segev, O. Weimann, Online Preemptive Matching, arXiv 2012 
05.11.2015 Adam Gągol Jagiellonian University 
Algorytmiczne Aspekty Kombinatoryki On the Lonely Runner Problem II 
04.11.2015 Bartłomiej Poleszak 
Podstawy Informatyki CardBased Protocols for Any Boolean Function (by Takuya Nishida, Yuichi Hayashi, Takaaki Mizuki, and Hideaki Sone ) 
Cardbased protocols that are based on a deck of physical cards achieve secure multiparty computation with informationtheoretic secrecy. Using existing AND, XOR, NOT, and copy protocols, one can naively construct a secure computation protocol for any given (multivariable) Boolean function as long as there are plenty of additional cards. However, an explicit sufficient number of cards for computing any function has not been revealed thus far. In this paper, we propose a general approach to constructing an efficient protocol so that six additional cards are sufficient for any function to be securely computed. Further, we prove that two additional cards are sufficient for any symmetric function. 
04.11.2015 Jakub Cieśla 
Optymalizacja Kombinatoryczna Computing TreeDepth Faster Than 2^n 
A connected graph has treedepth at most k if it is a subgraph of the clusure of a rooted tree whose height is at most k. The autors give an algorithm which for a given nvertex graph G, in time O(1.9602^n) computes the treedepth of G. The algorithm is based on combinatorial results revealing the structure of minimal rooted trees whose closures contain G. F. V. Fomin, A. C. Giannopoulou, M. Pilipczuk, Computing TreeDepth Faster Than 2^n, Algorithmica 73 (1), 202216, 2015 
28.10.2015 Ariel Gabizon Technion, Israel 
Informatyka Teoretyczna QuasiLinear Size Zero Knowledge from LinearAlgebraic PCPs 
A probabilistically checkable proof (PCP) enables, e.g., checking the satisfiability of a 3SAT formula ɸ, while only examining a constant number of locations in the proof. A long line of research led to the construction of PCPs with length that is quasilinear in n := ɸ. In a zero knowledge PCP with knowledge bound K, reading any K symbols of the proof reveals no additional information besides the validity of the statement; e.g., no information is revealed about the assignment satisfying ɸ. Kilian, Petrank, and Tardos gave a transformation from any PCP into a ZKPCP with knowledge bound K, for any desired K. A drawback of their transformation is that it requires multiplying the proof length by a factor of (at least) K^6. In this work, we show how to construct PCPs that are zero knowledge for knowledge bound K and of length quasilinear in K and n, provided that the prover is forced to write the proof in two rounds. In this model, which we call duplex PCP (DPCP), the verifier gets an oracle string from the prover, then replies with some randomness, and then gets another oracle string from the prover, and it can make up to K queries to both oracles. Deviating from previous works, our constructions do not invoke the PCP Theorem as a blackbox but rely on algebraic properties of a specific family of PCPs. We show that if the PCP has a certain linear algebraic structure (which many constructions have, including [BFLS91,ALMSS98,BS08]) we can add the zero knowledge property at virtually no cost while introducing only minor modifications in the algorithms of the prover and verifier. We believe that our linearalgebraic characterization of PCPs may be of independent interest, as it gives a simplified way to view previous wellstudied PCP constructions. Joint work with Eli BenSasson, Alessandro Chiesa and Madars Virza 
28.10.2015 Karol Banyś 
Optymalizacja Kombinatoryczna Fast Algorithm for Partial Covers in Words 
In this article autors introduce a new notion of αpartial cover, which can be viewed as a relaxed variant of cover, that is, a factor covering at least α positions in w. They develop a data structure of O(n) size (where n=w) that can be constructed in O(nlogn) time which they apply to compute all shortest αpartial covers for a given α. They also employ it for an O(nlogn)time algorithm computing a shortest αpartial cover for each α=1,2,…,n. Tomasz Kociumaka, Solon P. Pissis, Jakub Radoszewski , Wojciech Rytter, Tomasz Waleń, Fast Algorithm for Partial Covers in Words, Algorithmica 73 (1), 217233, 2015 
28.10.2015 Zbigniew Gołębiewski (PWr) 
Podstawy Informatyki On the number of lambda terms with prescribed size of their De Bruijn representation 
John Tromp introduced the socalled 'binary lambda calculus' as a way to encode lambda terms in terms of binary words. Later, Grygiel and Lescanne conjectured that the number of binary lambda terms with m free indices and of size n (encoded as binary words of length n) is o( n^−3/2 \tau^−n ) for \tau ≈ 1.963448 . We generalize the proposed notion of size and show that for several classes of lambda terms, including binary lambda terms with m free indices, the number of terms of size n is \Theta ( n^−3/2 \rho^−n ) with some class dependent constant \rho, which in particular disproves the above mentioned conjecture. A way to obtain lower and upper bounds 
21.10.2015 Ariel Gabizon Technion, Israel 
Informatyka Teoretyczna Representative sets for multisets 
In this talk I will explain this notion. Then, to illustrate its usefulness, I will show how it was used by Fomin, Lokshtanov and Saurabh to design a fast algorithm for finding long simple paths in a directed graph. Finally, I will describe a recent work where we generalize the notion of a representative set to a family of multisets and derive algorithmic applications.
Based on the paper Fast Algorithms for Parameterized Problems with Relaxed Disjointness Constraints with Daniel Lokshtanov and Michał Pilipczuk 
21.10.2015 Maciej Poleski 
Podstawy Informatyki On the Recursive Enumerability of FixedPoint Combinators (by Mayer Goldberg) 
We show that the set of fixedpoint combinators forms a recursively enumerable subset of a larger set of terms we call nonstandard fixedpoint combinators. These terms are observationally equivalent to fixedpoint combinators in any computable context, but the set of nonstandard fixedpoint combinators is not recursively enumerable. 
21.10.2015 Paweł Kubiak 
Optymalizacja Kombinatoryczna Lower bounds for dynamic algorithms 
In my presentation I will discus some elementary dynamic problems (Single source reachability and Dynamic diameter) and then I will present interesting reduction from this problems to Orthogonal Vectors Problems. These reductions imply that if it would be possible to solve SSR in O(m^(1ε)) or do 1.3 approximation of DD in O(m^(2ε)) then SETH will be refuted. 
14.10.2015 Katarzyna Janocha 
Optymalizacja Kombinatoryczna Conditional hardness and equivalences for graph problems 
Some graph problems (such as such as APSP, negative triangle, distance product or radius) do not have any known solutions better then the naive ones. We show subquadraic and subcubic reductions between them, proving that in case of finding a faster algorithm for any of the problems would be equivalent of reducing the complexity of each of them. We separate algorithms for sparse and dense graphs and focus on basic methods for both classes. V. Williams, Conditional hardness and equivalences for graph problems 
14.10.2015 Łukasz Lachowski 
Podstawy Informatyki On the Complexity of the standard translation from Lambda Calculus to Combinatory Logic (wyniki własne) 
Kontynuacja 
07.10.2015 Zygmunt Łenyk 
Optymalizacja Kombinatoryczna Hardness for Easy Problems (overview) 
Introduction into a young branch of algorithmics. We discuss why we are stuck during developing fast algorithms to some wellknown problems. Problems in P and suitable reductions form equivalence classes of problems, inside which improving asymptotic time of any of them would automatically improve the rest. At the bottom of these classes lie problems such as: 3SUM, allpairsshortestpaths, orthogonal vectors. Their complexities are guarded by strong conjectures which, if proven wrong, would revoke widely believed conjectures such as SETH. Amir Abboud, Arturs Backurs, Piotr Indyk and Virginia V. Williams, Hardness for easy problems  An introduction, 2015 
07.10.2015 Łukasz Lachowski 
Podstawy Informatyki On the Complexity of the standard translation from Lambda Calculus to Combinatory Logic (wyniki własne) 
We investigate the complexity of the standard translation between 
10.06.2015 Grzegorz Świrski 
Podstawy Informatyki Near semirings and lambda calculus by Rick Statman 
A connection between lambda calculus and the algebra of near semirings is discussed. Among the results is the following completeness theorem. A firstorder equation in the language of binary associative distributive algebras is true in all such algebras if and only if the interpretations of the first order terms as lambda terms betaeta convert to one another. A similar result holds for equations containing free variables. 
03.06.2015 Łukasz Lachowski 
Informatyka Teoretyczna An Algorithmic Characterization of Polynomial Functions over Z_{p^n} 
In this paper we consider polynomial representability of functions defined over Z_{p^n} , where p is a prime and n is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to determine whether a given function over Z_{p^n} is polynomially representable or not, and (ii) finds the polynomial if it is polynomially representable. The previous characterizations given by Kempner (Trans. Am. Math. Soc. 22(2):240266, 1921) and Carlitz (Acta Arith. 9(1), 6778, 1964) are existential in nature and only lead to an exhaustive search method, i.e. algorithm with complexity exponential in size of the input. Our characterization leads to an algorithm whose running time is linear in size of input. We also extend our result to the multivariate case. References: Ashwin Guha, Ambedkar Dukkipati, An Algorithmic Characterization of Polynomial Functions over Z_{p^n}, Algorithmica (2015) 71:201218 
03.06.2015 Radosław Smyrek 
Podstawy Informatyki Best Response Analysis in Two Person Quantum Games by Azharuddin Shaik, Aden Ahmed 
In this paper, we find particular use for a maximally entangled initial state that produces a quantized version of two player two strategy games. When applied to a variant of the wellknown game of Chicken, our construction shows the existence of new Nash equilibria with the players receiving better payoffs than those found in literature. 
27.05.2015 Paweł Zegartowski 
Informatyka Teoretyczna CacheOblivious Hashing 
The hash table, especially its external memory version, is one of the most important index structures in large databases. Assuming a truly random hash function, it is known that in a standard external hash table with block size b, searching for a particular key only takes expected average t_q=1+1/2^Ω(b) disk accesses for any load factor α bounded away from 1. However, such nearperfect performance is achieved only when b is known and the hash table is particularly tuned for working with such a blocking. In this paper we study if it is possible to build a cacheoblivious hash table that works well with any blocking. Such a hash table will automatically perform well across all levels of the memory hierarchy and does not need any hardwarespecific tuning, an important feature in autonomous databases. We first show that linear probing, a classical collision resolution strategy for hash tables, can be easily made cacheoblivious but it only achieves t_q=1+Θ(α/b) even if a truly random hash function is used. Then we demonstrate that the block probing algorithm (Pagh et al. in SIAM Rev. 53(3):547558, 2011) achieves t_q=1+1/2^Ω(b), thus matching the cacheaware bound, if the following two conditions hold: (a) b is a power of 2; and (b) every block starts at a memory address divisible by b. Note that the two conditions hold on a real machine, although they are not stated in the cacheoblivious model. Interestingly, we also show that neither condition is dispensable: if either of them is removed, the best obtainable bound is t_q=1+O(α/b), which is exactly what linear probing achieves. References: Rasmus Pagh, ZheweiWei, Ke Yi, Qin Zhang, CacheOblivious Hashing, Algorithmica (2014) 69:864883 
27.05.2015 Bartłomiej Ryniec 
Podstawy Informatyki GENERIC COMPLEXITY OF UNDECIDABLE PROBLEMS by ALEXEI G. MYASNIKOV AND ALEXANDER N. RYBALOV 
In this paper we study generic complexity of undecidable problems. It turns out that some classical undecidable problems are, in fact, strongly undecidable, i.e., they are undecidable on every strongly generic subset of inputs. For instance, the classical Halting Problem is strongly undecidable. Moreover, we prove an analog of the Rice's theorem for strongly undecidable problems, which provides plenty of examples of strongly undecidable problems. Then we show that there are natural superundecidable problems, i.e., problem which are undecidable on every generic (not only strongly generic) subset of inputs. In particular, there are finitely presented semigroups with superundecidable word problem. To construct strongly and superundecidable problems we introduce a method of generic amplification (an analog of the amplification in complexity theory). Finally, we construct absolutely undecidable problems, which stay undecidable on every nonnegligible set of inputs. Their construction rests on generic immune sets. 
20.05.2015 Łukasz Majcher 
Informatyka Teoretyczna List Coloring in the Absence of a Linear Forest 
The kCOLORING problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The LIST kCOLORING problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,...,k}. Let P_n denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that LIST kCOLORING can be solved in polynomial time for graphs with no induced rP_1+P_5, hereby extending the result of Hoàng, Kami´nski, Lozin, Sawada and Shu for graphs with no induced P_5. Our result is tight; we prove that for any graph H that is a supergraph of P_1 + P_5 with at least 5 edges, already LIST 5COLORING is NPcomplete for graphs with no induced H. References: JeanFrançois Couturier, Petr A. Golovach, Dieter Kratsch, Daniël Paulusma, List Coloring in the Absence of a Linear Forest, Algorithmica (2015) 71:2135 
13.05.2015 Krzysztof Kulig 
Informatyka Teoretyczna Metrical Service Systems with Multiple Servers 
The problem of metrical service systems with multiple servers ((k,l)MSSMS), proposed by Feuerstein (LATIN'98: Theoretical Informatics, Third Latin American Symposium, 1998), is to service requests, each of which is an lpoint subset of a metric space, using k servers in an online manner, minimizing the distance traveled by the servers. We prove that Feuerstein's deterministic algorithm for (k,l) MSSMS actually achieves an improved competitive ratio of k\cdot({k+l}\choose{l})1) on uniform metrics. References: Ashish Chiplunkar, Sundar Vishwanathan, Metrical Service Systems with Multiple Servers, Algorithmica (2015) 71:219231 
13.05.2015 Bartosz Badura 
Podstawy Informatyki Havannah and TwixT are pspacecomplete by Édouard Bonnet, Florian Jamain, and Abdallah Saffidine 
Numerous popular abstract strategy games ranging from hex and havannah to lines of action belong to the class of connection games. Still, very few complexity results on such games have been obtained since hex was proved pspacecomplete in the early eighties. We study the complexity of two connection games among the most widely played. Namely, we prove that havannah and twixt are pspacecomplete. The proof for havannah involves a reduction from generalized geography and is based solely on ringthreats to represent the input graph. On the other hand, the reduction for twixt builds up on previous work as it is a straightforward encoding of hex. 
06.05.2015 Maciej Solon 
Informatyka Teoretyczna Minimum Fillin of Sparse Graphs: Kernelization and Approximation 
The MINIMUM FILLIN problem is to decide if a graph can be triangulated by adding at most k edges. The problem has important applications in numerical algebra, in particular in sparse matrix computations. We develop kernelization algorithms for the problem on several classes of sparse graphs. We obtain linear kernels on planar graphs, and kernels of size O(k^{3/2}) in graphs excluding some fixed graph as a minor and in graphs of bounded degeneracy. As a byproduct of our results, we obtain approximation algorithms with approximation ratios O(log k) on planar graphs and O(√k·log k) on Hminorfree graphs. These results significantly improve the previously known kernelization and approximation results for MINIMUM FILLIN on sparse graphs. References: Fedor V. Fomin, Geevarghese Philip, Yngve Villanger; Minimum Fillin of Sparse Graphs: Kernelization and Approximation, Algorithmica (2015) 71:120 
06.05.2015 Leszek Jakub Kania 
Podstawy Informatyki Fast algorithm finding the shortest reset words by A. Kisielewicz J. Kowalski, and M. Szykuła 
In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far and it works well in practice. The main idea is to use a bidirectional BFS and radix (Patricia) tries to store and compare resulted subsets. We give both theoretical and practical arguments showing that the branching factor is reduced efficiently. As a practical test we perform an experimental study of the length of the shortest reset word for random automata with n states and 2 input letters. We follow Skvorsov and Tipikin, who have performed such a study using a SAT solver and considering automata up to n = 100 states. With our algorithm we are able to consider much larger sample of automata with up to n = 300 states. In particular, we obtain a new more precise estimation of the expected length of the shortest reset word = 2.5 sqrt{n − 5}. 
29.04.2015 Agnieszka Łupińska 
Informatyka Teoretyczna Strong ConflictFree Coloring for Intervals 
We consider the kstrong conflictfree (kSCF) coloring of a set of points on a line with respect to a family of intervals: Each point on the line must be assigned a color so that the coloring is conflictfree in the following sense: in every interval I of the family there are at least k colors each appearing exactly once in I .We first present a polynomialtime approximation algorithm for the general problem; the algorithm has approximation ratio 2 when k=1 and 5−2/k when k≥2. In the special case of a family that contains all possible intervals on the given set of points, we show that a 2approximation algorithm exists, for any k≥1. We also provide, in case k=O(polylog(n)), a quasipolynomial time algorithm to decide the existence of a kSCF coloring that uses at most q colors. References: Panagiotis Cheilaris, Luisa Gargano, Adele A. Rescigno, Shakhar Smorodinsky, Strong ConflictFree Coloring for Intervals, Algorithmica (2014) 70:732749 
29.04.2015 Marcin Kostrzewa 
Podstawy Informatyki A Short Note on Typeinhabitation: FormulaTrees vs. Game Semantics by S. Alves, S. Broda 
This short note compares two different methods for exploring typeinhabitation in the simply typed lambdacalculus, highlighting their similarities. 
22.04.2015 Marcin Regdos 
Informatyka Teoretyczna An O(n^4) Time Algorithm to Compute the Bisection Width of Solid Grid Graphs 
The bisection problem asks for a partition of the n vertices of a graph into two sets of size at most \ceil{n/2}, so that the number of edges connecting the sets is minimised. A grid graph is a finite connected subgraph of the infinite twodimensional grid. It is called solid if it has no holes. Papadimitriou and Sideri (Theory Comput Syst 29:97110, 1996) gave an O(n^5) time algorithm to solve the bisection problem on solid grid graphs. We propose a novel approach that exploits structural properties of optimal cuts within a dynamic program. We show that our new technique leads to an O(n^4) time algorithm. References: Andreas Emil Feldmann, Peter Widmayer, An O(n^4) Time Algorithm to Compute the Bisection Width of Solid Grid Graphs, Algorithmica (2015) 71:181200 
22.04.2015 Agnieszka Łupińska 
Podstawy Informatyki The Converse principal Type Algorithm by Roger Hindley 
One chapter from the book Basic Simple Type Theory 
15.04.2015 Maciej Bendkowski 
Informatyka Teoretyczna Contention Resolution under Selfishness 
In many communications settings, such as wired and wireless localarea networks, when multiple users attempt to access a communication channel at the same time, a conflict results and none of the communications are successful. Contention resolution is the study of distributed transmission and retransmission protocols designed to maximize notions of utility such as channel utilization in the face of blocking communications. An additional issue to be considered in the design of such protocols is that selfish users may have incentive to deviate from the prescribed behavior, if another transmission strategy increases their utility. The work of Fiat et al. (in SODA'07, pp.179188, SIAM, Philadelphia 2007) addresses this issue by constructing an asymptotically optimal incentivecompatible protocol. However, their protocol assumes the cost of any single transmission is zero, and the protocol completely collapses under nonzero transmission costs. In this paper we treat the case of nonzero transmission cost c.We present asymptotically optimal contention resolution protocols that are robust to selfish users, in two different channel feedback models. Our main result is in the Collision Multiplicity Feedback model, where after each time slot, the number of attempted transmissions is returned as feedback to the users. In this setting, we give a protocol that has expected cost Θ(n+c·log n) and is in o(1)equilibrium, where n is the number of users. References: George Christodoulou, Katrina Ligett, Evangelia Pyrga, Contention Resolution under Selfishness, Algorithmica (2014) 70:675693 
15.04.2015 Agnieszka Łupińska 
Podstawy Informatyki The principal Type Algorithm by Roger Hindley 
One chapter from the book Basic Simple Type Theory 
14.04.2015 Maciej Solon 
Algorytmy Randomizowane i Aproksymacyjne Graphs defined by forbidden patterns. 
01.04.2015 Maciej Bendkowski 
Podstawy Informatyki Über Tautologien, in welchen keine Variable mehr als zweimal vorkommt von S. Jaśkowski 
CONTINUATION 
25.03.2015 Lech Duraj, Grzegorz Gutowski, Jakub Kozik 
Informatyka Teoretyczna Chip games and paintability 
We present a natural family of chip games with strong ties to paintability, online 2coloring of hypergraphs and MakerBraker games. We solve some of those games and as a result we obtain interesting results in aforementioned areas. One of those results is that the difference between paintabilty and choosability of a graph can be arbitrarily large. 
18.03.2015 Jarosław Duda 
Informatyka Teoretyczna Asymmetric Numeral Systems: adding fractional bits to Huffman coder 
Entropy coding is an integral part of most data compression systems. There were previously used mainly two approaches: Huffman coding which is fast but approximates probabilities with powers of 1/2 (suboptimal compression ratio), and arithmetic coding which uses nearly accurate probabilities at cost of being an order of magnitude slower (more expensive). I will talk about new approach: Asymmetric Numeral Systems (ANS), which while using nearly accurate probabilities, has turned out to allow for even faster implementations than Huffman coding. Consequently, succeeding compressors have already switched to ANS in recent months. 
18.03.2015 Agnieszka Łupińska 
Podstawy Informatyki The principal Type Algorithm by Roger Hindley 
One chapter from the book Basic Simple Type Theory 
11.03.2015 Piotr Danilewski Universität des Saarlandes 
Informatyka Teoretyczna AnyDSL  a host for any language 
In a multidomain project, there is no single programming language that can be used to program everything. Instead, a combination of generalpurpose and domainspecific languages (DSLs) are used. Unfortunately, many domains lack a good, representative DSL, due to domain diversity and difficulty of creating a new compiler. Moreover, the communication across the languages is limited, often requiring the data to be serialized, and reducing the quality of optimization and compiletime verification. In our talk we present our approach to solve these problems, by introducing a new metamorphic language  AnyDSL. The parsing and execution of AnyDSL can be interleaved and the latter can influence the former  e.g. by introducing a new grammar with which parsing should resume. Regardless of the language the source is written in, all code is translated into a lowlevel, functional representation in continuous passing style (AIR). AIR serves as a "meeting point", permitting interDSL communication. AIR can be interpreted or compiled to LLVM bytecode and then to machine code. New grammars are defined also within AnyDSL. Unlike typical parser generators, grammar productions and actions are given as functions. AIR supports dynamic staging  a flexible way to define partial evaluation strategies. With it the overhead of having multiple layers of languages can be resolved early. It also allows the DSL designer to specify domain specific optimizations. After all those transformations, AIR can be compiled to machine code that is efficient, with performance comparable to programs written in generalpurpose languages. In our talk we present a new metamorphic language  AnyDSL. AnyDSL permits the native parser to be exchanged with a custom DSL. Regardless of the DSL however, all code is translated into a lowlevel, functional representation in continuous passing style (AIR). New grammars are defined also within AnyDSL, but unlike typical parser generators, grammar productions and actions are given as functions. AIR supports dynamic staging  a flexible way to define partial evaluation strategies to resolve overheads and define domain specific optimizations. AIR can be compiled to machine code, and produced programs have performance comparable to those produced by generalpurpose languages. 
04.03.2015 Maciej Bendkowski 
Podstawy Informatyki Über Tautologien, in welchen keine Variable mehr als zweimal vorkommt von S. Jaśkowski 
H. Thiele hat im Jahre 1960 das Problem gestellt, das implikative Teilsystem des Aussagenkalküls mit dem Axiomen B,C,K zu untersuchen. Hier wird für dieses System und für ein anderes, in dem das letzte Axiom durch ein schwächeres, nämlich I ersetzt wird, ein Entscheidungsverfahren angegeben. Die Methode beruht auf einer Untersuchung von gewissen allgemeinen Eigenschaften der Ausdrücke, in welchen keine Satzvariable mehr als zweimal vorkommt. Dabei wird eine dreiwertige Matrix benutzt. 
28.01.2015 Michał Zając 
Informatyka Teoretyczna Improved Explicit Data Structures in the Bitprobe Model 
Buhrman et al. [SICOMP 2002] studied the membership problem in the bitprobe model, presenting both randomized and deterministic schemes for storing a set of size n from a universe of size m such that membership queries on the set can be answered using t bit probes. Since then, there have been several papers focusing on deterministic schemes, especially for the first nontrivial case when n=2. The most recent, due to Radhakrishnan, Shah, and Shannigrahi [ESA 2010], describes nonexplicit schemes (existential results) for t≥3 using probabilistic arguments. We describe a fully explicit scheme for n=2 that matches their space bound of Θ(m^{2/5}) bits for t=3 and, furthermore, improves upon it for t>3, answering their open problem. Our structure (consisting of query and storage algorithms) manipulates blocks of bits of the query element in a novel way that may be of independent interest. We also describe recursive schemes for n≥3 that improve upon all previous fully explicit schemes for a wide range of parameters. References: Moshe Lewenstein, J. Ian Munro, Patrick K. Nicholson and Venkatesh Raman, Improved Explicit Data Structures in the Bitprobe Model, ESA 2014, LNCS 8737, pp. 630–641, 2014 
28.01.2015 21.01.2015,Radosław Smyrek 
Podstawy Informatyki Symmetry groups of boolean functions by Mariusz Grech, Andrzej Kisielewicz 
We prove that every abelian permutation group, but known exceptions, is the symmetry group of a boolean function. This solves the problem posed in the book by Clote and Kranakis. In fact, our result is proved for a larger class of permutation groups, namely, for all subgroups of direct sums of regular permutation groups. 
22.01.2015 Adam Polak 
Algorytmiczne Aspekty Kombinatoryki Tools for Multicoloring with Applications to Planar Graphs and Partial kTrees 
21.01.2015 Bartosz Badura 
Kryptologia A Formal Treatment of Onion Routing 
Anonymous channels are necessary for a multitude of privacyprotecting protocols. Onion routing is probably the best known way to achieve anonymity in practice. However, the cryptographic aspects of onion routing have not been sufficiently explored: no satisfactory definitions of security have been given, and existing constructions have only had adhoc security analysis for the most part. We provide a formal definition of onionrouting in the universally composable framework, and also discover a simpler definition (similar to CCA2 security for encryption) that implies security in the UC framework. We then exhibit an efficient and easy to implement construction of an onion routing scheme satisfying this definition. References: J. Camenisch, A. Lysyanskaya, A Formal Treatment of Onion Routing, Proc CRYPTO'05, pp. 169187 
21.01.2015 Andrzej Głuszyński 
Informatyka Teoretyczna Data Structures for Storing Small Sets in the Bitprobe Model 
We study the following set membership problem in the bit probe model: given a set S from a finite universe U, represent it in memory so that membership queries of the form "Is x in S?" can be answered with a small number of bitprobes. We obtain explicit schemes that come close to the information theoretic lower bound of Buhrman et al. [STOC 2000, SICOMP 2002] and improve the results of Radhakrishnan et al. [ESA 2001] when the size of sets and the number of probes is small. We show that any scheme that stores sets of size two from a universe of size m and answers membership queries using two bitprobes requires space Ω(m^{4/7}). The previous best lower bound (shown by Buhrman et al. using information theoretic arguments) was Ω(√m). The same lower bound applies for larger sets using standard padding arguments. This is the first instance where the information theoretic lower bound is found to be not tight for adaptive schemes. We show that any nonadaptive three probe scheme for storing sets of size two from a universe of size m requires Ω(√m) bits of memory. This extends a result of Alon and Feige [SODA 2009] to small sets. References: Jaikumar Radhakrishnan, Smit Shah and Saswata Shannigrahi, Data Structures for Storing Small Sets in the Bitprobe Model, ESA 2010, Part II, LNCS 6347, pp. 159–170, 2010. 
20.01.2015 Maciej Poleski 
Optymalizacja Kombinatoryczna An online version of Rota's basis conjecture 
Rota's basis conjecture states that in any square array of vectors whose rows are bases of a fixed vector space the vectors can be rearranged within their rows in such a way that afterwards not only the rows are bases, but also the columns. We discuss an online version of this conjecture, in which the permutation used for rearranging the vectors in a given row must be determined without knowledge of the vectors further down the array. The paper contains surprises both for those who believe this online basis conjecture at first glance, and for those who disbelieve it. References: Guus P. Bollen, Jan Draisma, An online version of Rota's basis conjecture, Journal of Algebraic Combinatorics, October 2014 
14.01.2015 Konrad Witaszczyk 
Kryptologia How to Reinitialize a Hash Chain 
Hash Chains are used extensively in various cryptographic systems such as onetime passwords, server supported signatures, secure address resolution, certificate revocation, micropayments etc. However, currently they suffer from the limitation that they have a finite number of links which when exhausted requires the system to be reinitialized. In this paper, we present a new kind of hash chain which we call a Reinitializable Hash Chain (RHC). A RHC has the property that if its links are exhausted, it can be securely reinitialized in a nonrepudiable manner to result in another RHC. This process can be continued indefinitely to give rise to an infinite length hash chain, or more precisely, an infinite number of finite length hash chains tied together. Finally we illustrate how a conventional hash chain (CHC) may be profitable replaced with a RHC in cryptographic systems. References: Leslie Lamport, Password Authentication with Insecure Communication, PDF Yuanchao Zhao, Daoben Li, An Improved Elegant Method to Reinitialize Hash Chains, PDF Vipul Goyal, How to Reinitialize a Hash Chain, PDF 
14.01.2015 Andrzej Dorobisz 
Informatyka Teoretyczna Scheduling parallel jobs to minimize the makespan 
We consider the NPhard problem of scheduling parallel jobs with release dates on identical parallel machines to minimize the makespan. A parallel job requires simultaneously a prespecified, jobdependent number of machines when being processed. We prove that the makespan of any nonpreemptive listschedule is within a factor of 2 of the optimal preemptive makespan. This gives the bestknown approximation algorithms for both the preemptive and the nonpreemptive variant of the problem. We also show that no listscheduling algorithm can achieve a better performance guarantee than 2 for the nonpreemptive problem, no matter which priority list is chosen. Listscheduling also works in the online setting where jobs arrive over time and the length of a job becomes known only when it completes; it therefore yields a deterministic online algorithm with competitive ratio 2 as well. In addition, we consider a different online model in which jobs arrive one by one and need to be scheduled before the next job becomes known. We show that no listscheduling algorithm has a constant competitive ratio. Still, we present the first online algorithm for scheduling parallel jobs with a constant competitive ratio in this context. We also prove a new informationtheoretic lower bound of 2.25 for the competitive ratio of any deterministic online algorithm for this model. Moreover, we show that 6/5 is a lower bound for the competitive ratio of any deterministic online algorithm of the preemptive version of the model jobs arriving over time. References: Johannes Berit, Scheduling parallel jobs to minimize the makespan, J of Schedulling, 9(2006), 433–452 
14.01.2015 Bartłomiej Ryniec 
Podstawy Informatyki Infinite time Turing machines with only one tape by Joel David Hamkins, Daniel Evan Seabold 
Infinite time Turing machines with only one tape are in many respects fully as powerful as their multitape cousins. In particular, the two models of machine give rise to the same class of decidable sets, the same degree structure and, at least for functions f:R → N, the same class of computable functions. Nevertheless, there are infinite time computable functions f:R→R that are not onetape computable, and so the two models of infinitary computation are not equivalent. Surprisingly, the class of onetape computable functions is not closed under composition; but closing it under composition yields the full class of all infinite time computable functions. Finally, every ordinal which is clockable by an infinite time Turing machine is clockable by a onetape machine, except certain isolated ordinals that end gaps in the clockable ordinale 
13.01.2015 Helena Borak 
Optymalizacja Kombinatoryczna Variants of Hat Guessing Games 
Hat problems have become a popular topic in recreational mathematics. In a typical hat problem, each of n players tries to guess the color of the hat they are wearing by looking at the colors of the hats worn by some of the other players. In this paper we consider several variants of the problem, united by the common theme that the guessing strategies are required to be deterministic and the objective is to maximize the number of correct answers in the worst case. We also summarize what is currently known about the worstcase analysis of deterministic hatguessing problems with a finite number of players. References: S.Butler, M.T.Hajiaghayi, R.D.Kleinberg, T.Leighton, Hat Guessing Games 
13.01.2015 Andrzej Dorobisz. 
Algorytmy Randomizowane i Aproksymacyjne Treewidth. Courcelle's theorem. 
07.01.2015 Paweł Zegartowski 
Kryptologia The Padding Oracle attacks: theoretical background with practical exemplification 
In many standards, such as. SSL/TLS, IPSEC, WTLS, messages are first preformatted, then encrypted in CBC mode with a block cipher. Decryption needs to check if the format is valid. Validity of the format is easily leaked from communication protocols in a chosen ciphertext attack since the receiver usually sends an acknowledgment or an error message.This is a side channel. Since year 2002 the padding oracle attacks are known to be a working example of Chosen Ciphertext Attack possible to perform on various realworld cryptosystems using padding in their vital areas of calculation. The lecture attempts to describe the nature of a padding oracle attack and to point drawbacks of cryptosystems that make them vulnerable for attack of this kind. Moreover the POODLE attack shall be presented as an example of practical application of padding oracle attack against the SSLv3 protocol possible to be used also against servers using newer security protocols (like TLS 1.x). References: Serge Vaudenay, Security Flaws Induced by CBC Padding Applications to SSL, IPSEC, WTLS, EUROCRYPT 2002. Juliano Rizzo, Thai Duong, Practical Padding Oracle Attacks, USENIX WOOT 2010 Möller, Bodo; Duong, Thai; Kotowicz, Krzysztof, This POODLE Bites: Exploiting The SSL 3.0 Fallback, Google Security Advisory 2014 
07.01.2015 Łukasz Kapica 
Informatyka Teoretyczna On an online scheduling problem for parallel jobs 
The nonpreemptive online scheduling of parallel jobs is addressed. In particular we assume that the release dates and the processing times of the jobs are unknown. It is already known that for this problem Garey and Graham's list scheduling algorithm achieves the competitive factor 2−1/m for the makespan if m identical machines are available and if each job requires only a single machine for processing. Here, we show that the same factor also holds in the case of parallel jobs. References: Edwin Naroska, Uwe Schwiegelshohn, On an online scheduling problem for parallel jobs, Information Processing Letters, 81(2002), 297–304. 
07.01.2015 Michał Seweryn 
Podstawy Informatyki A Formalisation of the MyhillNerode Theorem Based on Regular Expressions by Chunhan Wu, Xingyuan Zhang, Christian Urban 
There are numerous textbooks on regular languages. Many of them focus on finite automata for proving properties. Unfortunately, automata are not so straightforward to formalise in theorem provers. The reason is that natural representations for automata are graphs, matrices or functions, none of which are inductive datatypes. Regular expressions can be defined straightforwardly as a datatype and a corresponding reasoning infrastructure comes for free in theorem provers. We show in this paper that a central result from formal language theory—the MyhillNerode Theorem—can be recreated using only regular expressions. From this theorem many closure properties of regular languages follow. 
17.12.2014 Łukasz Majcher 
Kryptologia Searching for Elements in Black Box Fields and Applications 
We introduce the notion of a black box field and discuss the problem of explicitly exposing field elements given in a black box form. We present several subexponential algorithms for this problem using a technique due to Maurer. These algorithms make use of elliptic curves over finite fields in a crucial way. We present three applications for our results: (1) We show that any algebraically homomorphic encryption scheme can be broken in expected subexponential time. The existence of such schemes has been open for a number of years. (2) We give an expected subexponential time reduction from the problem of finding roots of polynomials over finite fields with low straight line complexity (e.g. sparse polynomials) to the problem of testing whether such polynomials have a root in the field. (3) We show that the hardness of computing discretelog over elliptic curves implies the security of the DiffieHellman protocol over elliptic curves. Finally in the last section of the paper we prove the hardness of exposing black box field elements in a field of characteristic zero. References: Dan Boneh, Richard J. Lipton, Algorithms for BlackBox Fields and their Application to Cryptography, Proceeding CRYPTO'96 pp. 283297 
17.12.2014 Bartosz Wlaczak 
Informatyka Teoretyczna Minors and dimension 
Streib and Trotter proved in 2012 that posets with bounded height and with planar cover graphs have bounded dimension. Later, Joret et al. proved that the dimension is bounded for posets with bounded height whose cover graphs have bounded treewidth. Recently, I proved that posets of bounded height whose cover graphs exclude a fixed (topological) minor have bounded dimension. This generalizes both the aforementioned results and verifies a conjecture of Joret et al. In this talk, I will introduce the problems of bounding the dimension of posets with sparse cover graphs and the main structural theorems used in the proof of the latter result: the RobertsonSeymour and GroheMarx structural decomposition theorems. I will also briefly describe the idea of the proof. 
17.12.2014 Agnieszka Łupińska 
Podstawy Informatyki Relevant Logic and the Philosophy of Mathematics by Edwin Mares 
This paper sets out three programmes that attempt to use relevant logic as the basis for a philosophy of mathematics. Although these three programmes do not exhaust the possible approaches to mathematics through relevant logic, they are fairly representative of the current state of the field. The three programmes are compared and their relative strengths and weaknesses set out. At the end of the paper I examine the consequences of adopting each programme for the realist debate about mathematical objects. 
16.12.2014 Marcin Dziaduś 
Optymalizacja Kombinatoryczna Fivelistcoloring of planar graphs 
Let G be a plane graph with outer cycle C, let u,v be vertices of C and let (L(x):x in V(G)) be a family of sets such that L(u)=L(v)=2, L(x) has at least three elements for every vertex x of C \ {u,v} and L(x) has at least five elements for every vertex x of G \ V(C). We prove a conjecture of Hutchinson that G has a proper coloring f such that f(x) belongs to L(x) for every vertex x of G. References: Luke Postle, Robin Thomas, Fivelistcoloring graphs on surfaces I. Two lists of size two in planar graphs, Journal of Combinatorial Theory, Series B 
16.12.2014 Grzegorz Gutowski. 
Algorytmy Randomizowane i Aproksymacyjne st orientations of planar graphs. 
10.12.2014 Krzysztof Kulig 
Kryptologia How to Leak a Secret 
In this paper we formalize the notion of a ring signature, which makes it possible to specify a set of possible signers without revealing which member actually produced the signature.Unlike group signatures, ring signatures have no group managers, no setup procedures, no revocation procedures, and no coordination:any user can choose any set of possible signers that includes himself,and sign any message by using his secret key and the others' public keys,without getting their approval or assistance. Ring signatures provide an elegant way to leak authoritative secrets in an anonymous way, to sign casual email in a way which can only be verified by its intended recipient, and to solve other problems in multiparty computations. The main contribution of this paper is a new construction of such signatures which is unconditionally signerambiguous, provably secure in the random oracle model,and exceptionally efficient:adding each ring member increases the cost of signing or verifying by a single modular multiplication and a single symmetric encryption. References: Ronald L. Rivest, Adi Shamir, Yael Tauman, How to Leak a Secret, Advances in Cryptology — ASIACRYPT 2001 LNCS vol. 2248, 2001, pp 552565 
10.12.2014 26.11.2014,Tomasz Kołodziejski 
Informatyka Teoretyczna Opaque sets or how to find a pipe 
We'll tackle the problem of finding the smallest set in a given class that meets every line intersecting a given convex set. Such a set is know as a barrier. Particularly interesting barrier classes are: connected sets, polylines and arbitrary segment barriers. The algorithmic approach yields various approximation constants around 1.6. Little is known about the exact barriers even for simple figures. Algorithms and proofs will be presented most of which require only basic planar geometry knowledge will little calculus (Cauchy surface area formula will be presented with no proof). 
10.12.2014 Pierre Lescanne (l'École Normale Supérieure de Lyon) 
Podstawy Informatyki Boltzmann samplers 
09.12.2014 Karol Banyś 
Optymalizacja Kombinatoryczna Online Load Balancing and Correlated Randomness 
This paper looks at online load balancing, in a setting where each job can only be served by a subset of the servers. The subsets are revealed only on arrival, and can be arbitrary. The cost of an allocation is the sum of cost for each server, which in turn is a convex increasing function of the number of jobs allocated to it. There are no departures. References: S. Moharir, S. Sanghavi. Online Load Balancing and Correlated Randomness. 50th Annual Allerton Conference, 2012 U. Vazirani V. Vazirani A. Mehta, A. Saberi. Adwords and generalized online matching. Proceedings of FOCS, 2005 
04.12.2014 Jarosław Grytczuk 
Algorytmiczne Aspekty Kombinatoryki Problems and results in combinatorial number theory 
03.12.2014 Piotr Bejda 
Kryptologia Using hash functions as a hedge against chosen ciphertext attack 
The cryptosystem recently proposed by Cramer and Shoup is a practical public key cryptosystem that is secure against adaptive chosen ciphertext attack provided the Decisional DiffieHellman assumption is true. Although this is a reasonable intractability assumption, it would be preferable to base a security proof on a weaker assumption, such as the Computational DiffieHellman assumption. Indeed, this cryptosystem in its most basic form is in fact insecure if the Decisional DiffieHellman assumption is false. In this paper we present a practical hybrid scheme that is just as efficient as the scheme of of Cramer and Shoup; indeed, the scheme is slightly more efficient than the one originally presented by Cramer and Shoup; we prove that the scheme is secure if the Decisional DiffieHellman assumption is true; we give strong evidence that the scheme is secure if the weaker, Computational DiffieHellman assumption is true by providing a proof of security in the random oracle model. References: R. Cramer and V. Shoup. A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In Advances in Cryptology  Crypto'98, pages 13–25, 1998 V. Shoup. Using hash functions as a hedge against chosen ciphertext attack, in Proc. Eurocrypt 2000 
03.12.2014 Agnieszka Łupińska 
Podstawy Informatyki General information in relevant logic by Edwin D. Mares 
There are numerous textbooks on regular languages. Many of them focus on finite automata for proving properties. Unfortunately, automata are not so straightforward to formalise in theorem provers. The reason is that natural representations for automata are graphs, matrices or functions, none of which are inductive datatypes. Regular expressions can be defined straightforwardly as a datatype and a corresponding reasoning infrastructure comes for free in theorem provers. We show in this paper that a central result from formal language theory—the MyhillNerode Theorem—can be recreated using only regular expressions. From this theorem many closure properties of regular languages follow. 
02.12.2014 Andrzej Dorobisz 
Optymalizacja Kombinatoryczna Random Walks that Find Perfect Objects and the Lov´asz Local Lemma 
We give an algorithmic local lemma by establishing a sufficient condition for the uniform random walk on a directed graph to reach a sink quickly. Our work is inspired by Moser's entropic method proof of the Lov´asz Local Lemma (LLL) for satisfiability and completely bypasses the Probabilistic Method formulation of the LLL. In particular, our method works when the underlying state space is entirely unstructured. Similarly to Moser's argument, the key point is that algorithmic progress is measured in terms of entropy rather than energy (number of violated constraints) so that termination can be established even under the proliferation of states in which every step of the algorithm (random walk) increases the total number of violated constraints. References: Dimitris Achlioptas, Fotis Iliopoulos, Random Walks that Find Perfect Objects and the Lovasz Local Lemma, FOCS 2014 
27.11.2014 Grzegorz Guśpiel 
Algorytmiczne Aspekty Kombinatoryki Homomorphisms of Edgecoloured Graphs 
26.11.2014 Pola Kyzioł 
Kryptologia Another look at nonstandard discrete log and DiffieHellman problems 
We examine several versions of the onemorediscretelog and onemoreDiffieHellman problems. In attempting to evaluate their intractability, we find conflicting evidence of the relative hardness of the different problems. Much of this evidence comes from natural families of groups associated with curves of genus 2, 3, 4, 5, and 6. This leads to questions about how to interpret reductionist security arguments that rely on these nonstandard problems. References: N. Koblitz, A. Menezes, Another look at nonstandard discrete log and DiffieHellman problems, J. Math. Cryptology 2 (2008), pp. 311326 
26.11.2014 Konrad Witaszczyk 
Podstawy Informatyki Problems of Proof compexity by Jan Krajicek, Stephen A. Cook and Robert A. Reckhow 
The ultimate goal of proof complexity is to show that there is no universal propositional proof system allowing for efficient proofs of all tautologies. This is equivalent to showing that the computational complexity class NP is not closed under the complementation. By the universality propositional proof systems subsume methods from other parts of mathematics used for proving the nonexistence statements. Because of this, even the partial results known at present (lower bounds for some specific proof systems) revealed interesting links of proof complexity to logic, algebra, combinatorics, computational complexity. We will explain some basic points of proof complexity and give few informal examples in order to motivate the main concepts and problems of proof complexity. 
25.11.2014 18.11.2014,Jakub Brzeski 
Optymalizacja Kombinatoryczna Markov Chains and Random Walks on Graphs 
References: D. Aldous and J. A. Fill, Reversible Markov Chains and Random Walks on Graphs, monograph, 2014. L. Lovász, Random walks on graphs: a survey, Combinatorics, Paul Erdős is eighty, Vol. 2 (Keszthely, 1993), 353–397, Bolyai Soc. Math. Stud., 2, János Bolyai Math. Soc., Budapest, 1996. 
25.11.2014 18.11.2014,Patryk Mikos 
Algorytmy Randomizowane i Aproksymacyjne Kernelization and Linear Programming Techniques 
19.11.2014 Patryk Mikos 
Kryptologia A practical public key cryptosystem probably secure against adaptive chosen ciphertext attack 
A new public key cryptosystem is proposed and analyzed. The scheme is quite practical, and is provably secure against adaptive chosen ciphertext attack under standard intractability assumptions. There appears to be no previous cryptosystem in the literature that enjoys both of these properties simultaneously. 
19.11.2014 Bartosz Badura 
Podstawy Informatyki On the Complexity of TrickTaking Card Games by Edouard Bonnet, Florian Jamain, and Abdallah Saffidine 
Determining the complexity of perfect information tricktaking card games is a long standing open problem. This question is worth addressing not only because of the popularity of these games among human players, e.g., DOUBLE DUMMY BRIDGE, but also because of its practical importance as a building block in stateoftheart playing engines for CONTRACT BRIDGE, SKAT, HEARTS, and SPADES. We define a general class of perfect information twoplayer tricktaking card games dealing with arbitrary numbers of hands, suits, and suit lengths. We investigate the complexity of determining the winner in various fragments of this game class. Our main result is a proof of PSPACEcompleteness for a fragment with bounded number of hands, through a reduction from Generalized Geography. Combining our results with W¨astlund's tractability results gives further insight in the complexity landscape of tricktaking card games. 
19.11.2014 
A practical public key cryptosystem probably secure against adaptive chosen ciphertext attack 
13.11.2014 Patryk Mikos 
Algorytmiczne Aspekty Kombinatoryki A hats game puzzle and generalized covers 
12.11.2014 Kamil Sałaś 
Kryptologia Simple Unpredictable PseudoRandom Number Generator 
References: L. Blum, M. Blum, M. Shub, A Simple Unpredictable PseudoRandom Number Generator, SIAM Journal on Computing 15(2) pp. 364383 
12.11.2014 29.10.2014,Adam Polak 
Informatyka Teoretyczna On treewidth parametrization of nonpreemptive multicoloring problem 
In the multicoloring problem we are given a graph in which every vertex has some nonnegative integer demand. We have to assign to each vertex a set of colors of the size of the demand of this vertex, in such a way that the sets of any two neighboring vertices are disjoint. In the nonpreemptive version of the problem each set of colors has to be an interval of the natural numbers. The goal is either to minimize the sum of the assigned colors, or to minimize the number of different colors used. In this talk we will discuss the fixed parameter tractability of both these problems when parametrized by the treewidth of the input graph and the maximum demand, the treewidth and the number of different demands, and the treewidth itself. 
06.11.2014 Dorota Kapturkiewicz 
Algorytmiczne Aspekty Kombinatoryki Monotone paths in bounded degree graphs 
05.11.2014 Bartłomiej Ryniec 
Podstawy Informatyki Social Networks with Competing Products by Krzysztof Apt and Evangelos Markakis 
We introduce a new threshold model of social networks, in which the nodes influenced by their neighbours can adopt one out of several alternatives. We characterize social networks for which adoption of a product by the whole network is possible (respectively necessary) and the ones for which a unique outcome is guaranteed. These characterizations directly yield polynomial time algorithms that allow us to determine whether a given social network satisfies one of the above properties. We also study algorithmic questions for networks without unique outcomes. We show that the problem of determining whether a final network exists in which all nodes adopted some product is NPcomplete. In turn, we also resolve the complexity of the problems of determining whether a given node adopts some (respectively, a given) product in some (respectively, all) network(s). Further, we show that the problem of computing the minimum possible spread of a product is NPhard to approximate with an approximation ratio better than W(n), in contrast to the maximum spread, which is efficiently computable. Finally, we clarify that some of the above problems can be solved in polynomial time when there are only two products. 
04.11.2014 Jakub Cieśla 
Optymalizacja Kombinatoryczna Finding All MaximallyMatchable Edges in a Bipartite Graph 
We consider the problem of finding all maximallymatchable edges in a bipartite graph G = (V, E), i.e., all edges that are included in some maximum matching. We show that given any maximum matching in the graph, it is possible to perform this computation in linear time O(n + m) (where n = V and m = E). Hence, the time complexity of finding all maximallymatchable edges reduces to that of finding a single maximum matching. References: T. Tassa, Finding all maximallymatchable edges in a bipartite graph, Theoret. Comput. Sci. 423 (2012), 50–58. 
29.10.2014 Maciej Bendkowski 
Podstawy Informatyki INFINITE TIME TURING MACHINES AND AN APPLICATION TO THE HIERARCHY OF EQUIVALENCE RELATIONS ON THE REALS by SAMUEL COSKEY AND JOEL DAVID HAMKINS 
We describe the basic theory of infinite time Turing machines and some recent developments, including the infinite time degree theory, infinite time complexity theory, and infinite time computable model theory. We focus particularly on the application of infinite time Turing machines to the analysis of the hierarchy of equivalence relations on the reals, in analogy with the theory arising from Borel reducibility. We define a notion of infinite time reducibility, which lifts much of the Borel theory into the class $Delta^1_2$ in a satisfying way. 
28.10.2014 Marcin Ziemiński 
Optymalizacja Kombinatoryczna Perfect Matchings in O(n log n) Time in Regular Bipartite Graphs 
In this paper, we give a randomized algorithm that finds a perfect matching in a dregular graph and runs in O(n log n) time (both in expectation and with high probability). The algorithm performs an appropriately truncated random walk on a modified graph to successively find augmenting paths. Our algorithm may be viewed as using adaptive uniform sampling, and is thus able to bypass the limitations of (nonadaptive) uniform sampling established in earlier work. We also show that randomization is crucial for obtaining o(nd) time algorithms by establishing an (nd) lower bound for any deterministic algorithm. References: A. Goel, M. Kapralov, S. Khanna, Perfect matchings in O(n log n) time in regular bipartite graphs, Proceedings of the 2010 ACM International Symposium on Theory of Computing (STOC'10), 39–46, ACM, New Yo 
22.10.2014 Grzegorz Gutowski 
Informatyka Teoretyczna Open Problem Session 
A few interesting and promising open problems, including, but not limited to: * Coloring trianglefree graphs, * Complexity of graph classes defined by forbidden ordered subgraphs, * Reconstructing random strings from random substrings, * Scheduling multiprocessor jobs, * Storing small sets in just a few bits, * Colorful homomorphisms of planar graphs, * Domination games. 
22.10.2014 Łukasz Lachowski 
Podstawy Informatyki Typed combinatory logic by Henk Barendregt 
Basic properties of typed combinatory logic 
21.10.2014 Patryk Mikos 
Optymalizacja Kombinatoryczna Maximum Matching in Regular and Almost Regular Graphs 
An O(n^2*log(n))time algorithm that finds a maximum matching in a regular graph with n vertices. More generally, the algorithm runs in O(r*n^2 log n) time if the difference between the maximum degree and the minimum degree is less than r. This running time is faster than applying the fastest known general matching algorithm that runs in O(√nm)time for graphs with m edges, whenever m = ω(rn1.5 log n). References: R. Yuster, Maximum matching in regular and almost regular graphs, Algorithmica 66 (2013), no. 1, 87–92. 
21.10.2014 Adam Gągol 
Algorytmiczne Aspekty Kombinatoryki Ternary pattern avoidance in partial words 
15.10.2014 Michał Staromiejski 
Kryptologia On Shoup's lower bound technique for generic algorithms for discrete logarithm problem 
15.10.2014 Łukasz Lachowski 
Podstawy Informatyki Combinatrory Logic by Henk Barendregt 
Basic properties of combinatory logic 
14.10.2014 07.10.2014,Bartłomiej Bosek 
Optymalizacja Kombinatoryczna Incremental algorithm on bipartite graphs 
The talk presents the jont work of Bartłomiej Bosek, Darek Leniowski, Piotr Sankowski, and Anna Zych. We investigated the problem of maintaining maximum size matchings in incremental bipartite graphs. In this problem a bipartite graph G between n clients and n servers is revealed online. The clients arrive in an arbitrary order and request to be matched to a subset of servers. In our model we allow the clients to switch between servers and want to maximize the matching size between them, i.e., after a client arrives we find an augmenting path from a client to a free server. Our goals in this model are twofold. First, we want to minimize the number of times clients are reallocated between the servers. Second, we want to give fast algorithms that recompute such reallocation. References: Bartłomiej Bosek, Dariusz Leniowski, Piotr Sankowski, Anna Zych. Online bipartite matching in offline time. In Proceedings of the 55th Symposium on Foundations of Computer Science, FOCS14, pp. 384393, 2014. 
08.10.2014 Jakub Brzeski 
Kryptologia Continued Fractions: theory and applications 
In the talk we focus on the most important (and interesting) properties of the continued fractions together with examples of their applications. 
08.10.2014 Łukasz Lachowski 
Podstawy Informatyki Combinatrory Logic by Henk Barendregt 
Basic properties of combinatory logic 
12.06.2014 Andrzej Głuszyński 
Kryptologia Factoring with General Number Field Sieve 
The number field sieve (NFS) is the most efficient classical algorithm known for factoring integers larger than 100 digits. Heuristically, its complexity for factoring an integer n is of the form L[1/3, (64/9)^{1/3}]. The principle of the NFS can be understood as an improvement to the simpler rational and quadratic sieve which base on searching for smooth numbers. NFS had some spectacular successes with integers in certain special forms, most notably the factorization of the 155 decimal digit ninth Fermat number F9 = 2^512 + 1. References: Peter Stevenhagen, The number field sieve. Algorithmic Number Theory, MSRI Publication Vol. 44, 2008 Carl Pomerance, The number field sieve, Proceedings of Symposis in Applied Mathematics, Vol. 48. 1994 
11.06.2014 Radosław Smyrek 
Informatyka Teoretyczna Shortest Path Problems on a Polyhedral Surface (by Atlas F. Cook IV, CarolaWenk) 
We describe algorithms to compute edge sequences, a shortest path map, and the Fréchet distance for a convex polyhedral surface. Distances on the surface are measured by the length of a Euclidean shortest path. We describe how the star unfolding changes as a source point slides continuously along an edge of the convex polyhedral surface. We describe alternative algorithms to the edge sequence algorithm of Agarwal et al. (SIAM J. Comput. 26(6):1689–1713, 1997) for a convex polyhedral surface. Our approach uses persistent trees, star unfoldings, and kinetic Voronoi diagrams. We also show that the core of the star unfolding can overlap itself when the polyhedral surface is nonconvex. References: Atlas F. Cook IV, CarolaWenk, Shortest Path Problems on a Polyhedral Surface, Algorithmica (2014) 69:58–77 
11.06.2014 Gabriel Fortin 
Podstawy Informatyki "The safe lambda calculus" by William Blum and C.H. Luke Ong. 
Safety is a syntactic condition of higherorder grammars that constrains occurrences of variables in the production rules according to their typetheoretic order. In this paper, we introduce the safe lambda calculus, which is obtained by transposing (and generalizing) the safety condition to the setting of the simplytyped lambda calculus. In contrast to the original deﬁnition of safety, our calculus does not constrain types (to be homogeneous). We show that in the safe lambda calculus, there is no need to rename bound variables when performing substitution, as variable capture is guaranteed not to happen. We also propose an adequate notion of βreduction that preserves safety. In the same vein as Schwichtenberg's 1976 characterization of the simplytyped lambda calculus, we show that the numeric functions representable in the safe lambda calculus are exactly the multivariate polynomials; thus conditional is not deﬁnable. We also give a characterization of representable word functions. We then study the complexity of deciding betaeta equality of two safe simplytyped terms and show that this problem is PSPACEhard. Finally we give a gamesemantic analysis of safety: We show that safe terms are denoted by Pincrementally justiﬁed strategies. Consequently pointers in the game semantics of safe λterms are only necessary from order 4 onwards. 
05.06.2014 Krzysztof Kleiner 
Kryptologia Zeroknowledge proofs 
A zeroknowledge proof is a protocol providing that one site can prove to the other that a certain statement is true without revealing any other information. We demand that if the prover knows the proof of the statement, it will be accepted, that otherwise it will get rejected with liberally high probability and that the distribution of the protocol transcript is the same (perfect zeroknowledge proofs) or computationally indistinguishable (computational zeroknowledge proofs) from the output of some probabilistic Turing Machine, which doesn't have access to any of the prover's private information. References: O. Goldreich, S. Micali, A. Wigderson, Proofs that Yield Nothing But their Validity and a Methodology of Cryptographic Protocol Design, Journal of the Association for Computing Machinery: Vol 38, No 1, July 1991, pp 69172 
04.06.2014 Gabriel Fortin 
Informatyka Teoretyczna On Cutwidth Parameterized by Vertex Cover (by Marek Cygan et al.) 
We study the CUTWIDTH problem, where the input is a graph G, and the objective is find a linear layout of the vertices that minimizes the maximum number of edges intersected by any vertical line inserted between two consecutive vertices. We give an algorithm for CUTWIDTH with running time O(2^k n^O(1)). Here k is the size of a minimum vertex cover of the input graph G, and n is the number of vertices in G. Our algorithm gives an O(2^{n/2}n^O(1)) time algorithm for CUTWIDTH on bipartite graphs as a corollary. This is the first nontrivial exact exponential time algorithm for CUTWIDTH on a graph class where the problem remains NPcomplete. Additionally, we show that CUTWIDTH parameterized by the size of the minimum vertex cover of the input graph does not admit a polynomial kernel unless NP ⊆ coNP/poly. Our kernelization lower bound contrasts with the recent results of Bodlaender et al. (ICALP, Springer, Berlin, 2011; SWAT, Springer, Berlin, 2012) that both TREEWIDTH and PATHWIDTH parameterized by vertex cover do admit polynomial kernels. References: Marek Cygan, Daniel Lokshtanov, Marcin Pilipczuk, Michał Pilipczuk, Saket Saurabh, On Cutwidth Parameterized by Vertex Cover, Algorithmica (2014) 68:940–953 
04.06.2014 Maciej Bendkowski 
Podstawy Informatyki On the shortest combinatory logic term without weak normalisation. 
Combinatory logic is a formal notation for function abstraction, eliminating the notion of bound variables. In our presentation, we give proofs of nonnormalization for two different Sterms, i.e. combinatory logic terms consisting of only one combinator S and term application, and present a computerassisted proof of the least combinatory logic term without normal form. We will then discuss the decidability of normalization in the set of Sterms. 
03.06.2014 M. Solon, P. Wójcik 
Algorytmy Randomizowane i Aproksymacyjne Polynomial coloring of 3colorable graphs. 
29.05.2014 Andrzej Dorobisz 
Kryptologia Breaking RSA may not be equivalent to factoring 
This talk is based on the paper by D. Boneh and R. Venkatesan. Abstract of the paper: We provide evidence that breaking lowexponent RSA cannot be equivalent to factoring integers. We show that an algebraic reduction from factoring to breaking lowexponent RSA can be converted into an efficient factoring algorithm. Thus, in effect an oracle for breaking RSA does not help in factoring integers. Our result suggests an explanation for the lack of progress in proving that breaking RSA is equivalent to factoring. We emphasize that our results do not expose any weakness in the RSA system. 
28.05.2014 Krzysztof Pasek 
Informatyka Teoretyczna Online Square Packing with Gravity (by S.P.Fekete, T.Kamphans, N.Schweer) 
We analyze the problem of packing squares in an online fashion: Given a semiinfinite strip of width 1 and an unknown sequence of squares of side length in [0, 1] that arrive from above, one at a time. The objective is to pack these items as they arrive, minimizing the resulting height. Just like in the classical game of Tetris, each square must be moved along a collisionfree path to its final destination. In addition, we account for gravity in both motion (squares must never move up) and position (any final destination must be supported from below). A similar problem has been considered before; the best previous result is by Azar and Epstein, who gave a 4competitive algorithm in a setting without gravity (i.e., with the possibility of letting squares "hang in the air") based on ideas of shelf packing: Squares are assigned to different horizontal levels, allowing an analysis that is reminiscent of some binpacking arguments. We apply a geometric analysis to establish a competitive factor of 3.5 for the bottomleft heuristic and present a 34/13≈2.6154competitive algorithm. References: Sándor P. Fekete, Tom Kamphans, Nils Schweer, Online Square Packing with Gravity, Algorithmica (2014) 68:1019–1044 
28.05.2014 Radosław Smyrek 
Podstawy Informatyki A hierarchy of hereditarily finite sets by Laurence Kirby 
This article defines a hierarchy on the hereditarily finite sets which reflects the way sets are built up from the empty set by repeated adjunction, the addition to an already existing set of a single new element drawn from the already existing sets. The structure of the lowest levels of this hierarchy is examined, and some results are obtained about the cardinalities of levels of the hierarchy. 
27.05.2014 20.05.2014 13.05.2014 Adam Gągol 
Algorytmy Randomizowane i Aproksymacyjne Constraint Satisfaction, Packet Routing, and the Lovász Local Lemma (by Harris and Srinivasan) 

22.05.2014 Jakub Brzeski 
Kryptologia Breaking RSA may be as difficult as factoring 
This talk is based on the paper of Daniel R. L. Brown, who shows that if factoring is hard, then straight line programs cannot efficiently solve the low public exponent RSA problem. More precisely, no efficient algorithm can take an RSA public key as input and then output a straight line program that efficiently solves the low public exponent RSA problem for the given public key  unless factoring is easy. References: Daniel R. L. Brown, Breaking RSA May Be As Difficult As Factoring, Cryptology ePrint Archive: Report 2005/380, http://eprint.iacr.org/2005/380 
21.05.2014 Szymon Borak 
Informatyka Teoretyczna Competitivereachability for special classes of graphs 
The reachability r(D) of a directed graph D is the number of ordered pairs of distinct vertices (x, y) with a directed path from x to y. Two players maximizer and minimizer play the following game on graph G. They orient the edges of G alternately until all edges of G have been oriented. The maximizer attempts to maximize the reachability, while the minimizer attempts to minimize the reachability, of the resulting digraph. If both players play optimally, then the reachability is fixed. Competitivereachability is a value of reachability for the optimal play on graph G. We determine the competitivereachability for outerplanar graphs and some other special classes of graphs. 
21.05.2014 Konrad Witaszczyk 
Podstawy Informatyki On the classification of recursive languages by John Case, Efim Kinber, Arun Sharma, and Frank Stephanc. 
A onesided classifier for a given class of languages converges to 1 on every language from the class and outputs 0 infinitely often on languages outside the class. A twosided classifier, on the other hand, converges to 1 on languages from the class and converges to 0 on languages outside the class. The present paper investigates onesided and twosided classification for classes of recursive languages. Theorems are presented that help assess the classifiability of natural classes. The relationships of classification to inductive learning theory and to structural complexity theory in terms of Turing degrees are studied. Furthermore, the special case of classification from only positive data is also investigated. 
15.05.2014 Michał Masłowski 
Kryptologia Timing attacks 
Fast implementations of AES and RSA use algorithms with nonconstant time that attackers can affect by choosing inputs or using CPU cache. This allows recovering secret keys in local or remote attacks. This talk presents these algorithms, resulting timing attacks and mitigation techniques. References: David Brumley, Dan Boneh, Remote timing attacks are practical, https://crypto.stanford.edu/~dabo/papers/ssltiming.pdf Paul C. Kocher, Timing attacks on implementations of DiffieHellman, RSA, DSS, and other systems, http://www.cryptography.com/public/pdf/TimingAttacks.pdf Daniel J. Bernstein, Cachetiming attacks on AES, http://cr.yp.to/papers.html#cachetiming 
15.05.2014 Jarosław Grytczuk 
Algorytmiczne Aspekty Kombinatoryki Nonrepetitive coloring of the plane 
14.05.2014 Grzegorz Gutowski, Jakub Kozik 
Informatyka Teoretyczna Lower bound for online graph coloring of bipartite graphs 
In this talk we propose a strategy for Presenter in online graph coloring game. The strategy constructs bipartite graphs and forces any online coloring algorithm to use 2 log n  10 colors, where n is the number of vertices in the constructed graph. This is best possible up to an additive constant. References: http://arxiv.org/abs/1404.7259 
14.05.2014 Patryk Zaryjewski 
Podstawy Informatyki ON THE AVERAGE STATE COMPLEXITY OF PARTIAL DERIVATIVE AUTOMATA: AN ANALYTIC COMBINATORICS APPROACH by SABINE BRODA, ANTONIO MACHIAVELO, NELMA MOREIRA and ROGERIO REIS 
The partial derivative automaton is usually smaller than other nondeterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton. By estimating the number of regular expressions that have \epsilon as a partial derivative, we compute a lower bound of the average number of mergings of states in A_pos and describe its asymptotic behaviour. This depends on the alphabet size, k, and for growing k's its limit approaches half the number of states in Apos. The lower bound corresponds to consider the A_pd automaton for the marked version of the regular expression, i.e. where all its letters are made different. Experimental results suggest that the average number of states of this automaton, and of the A_pd automaton for the unmarked regular expression, are very close to each other. 
08.05.2014 Kamil Sałaś 
Kryptologia Data Encryption Standard 
Short introduction to Data Encryption Standard. Detailed analysis of encryption function. Security: brute force and differential cryptanalysis. Overview of Triple DES. 
07.05.2014 Maciej Gawron 
Podstawy Informatyki Constructions of asymptotically shortest kradius sequences by Jaromczyk, Zbigniew Lonc, Mirosław Truszczynski 
Let k be a positive integer. A sequence s over an nelement alphabet A is called a kradius sequence if every two symbols from A occur in s at distance of at most k. Let f_k(n) denote the length of a shortest kradius sequence over A. We provide constructions demonstrating that (1) for every fixed k and for every fixed ε > 0, f_k(n) = 1 / 2k n^2 + O(n^{1+ε}) and (2) for every k = n^α, where α is a fixed real such that 0 < α < 1, f_k(n) = 1/2k n^2 + O(n^β ), for some β < 2 − α. Since fk(n) 1/2k n^2 − n/2k , the constructions give asymptotically optimal kradius sequences. Finally, (3) we construct optimal 2radius sequences for a 2pelement alphabet, where p is a prime. 
30.04.2014 Bartłomiej Ryniec 
Podstawy Informatyki Multiparty communication complexity and very hard functions by Pavol Duriš 
A boolean function f(x_1, . . . , x_n) with x_i ∈ {0, 1}^m for each i is hard if its nondeterministic multiparty communication complexity (introduced in [in: Proceedings of the 30th IEEE FOCS, 1989, p. 428–433]), C(f), is at least nm. Note that C(f) n*m for each f(x_1, . . . , x_n) with x_i ∈ {0, 1}^m for each i. A boolean function is very hard if it is hard and its complementary function is also hard. In this paper, we show that randomly chosen boolean function f(x_1, . . . , x_n) with x_i ∈ {0, 1}^m for each i is very hard with very high probability (for n 3 and m large enough). In [in: Proceedings of the 12th Symposium on Theoretical Aspects of Computer Science, LNCS 900, 1995, p. 350–360], it has been shown that if f(x_1, . . . , x_k , . . . , x_n) = f_1 (x_1, . . . , x_k ) · f_2(x_{k+1}, . . . , x_n), where C(f_1) > 0 and C(f_2) > 0, then C(f) = C(f1) + C(f2).We prove here an analogical result: If f(x_1, . . . , x_k , . . . , x_n) = f_1(x_1, . . . , x_k ) ⊕ f_2(x_{k+1}, . . . , x_n) then DC(f) = DC(f1) + DC(f2), where DC(g) denotes the deterministic multiparty communication complexity of the function g and "⊕" denotes the parity function. 
24.04.2014 Wojciech Lubawski 
Algorytmiczne Aspekty Kombinatoryki Rota basis conjecture for sparse paving matroids 
23.04.2014 Maciej Gazda Eindhoven University of Technology 
Podstawy Informatyki Zielonka's Recursive Algorithm for Parity Games 
Parity games are infinite duration, two player games played on a finite directed graph. Vertices of the graph are labelled with natural numbers (called priorities) and the winning condition is determined by the parity of the most significant (typically maximal) priority encountered inifnitely often. The games are memoryless determined, moreover, the problem of finding the winning partition of a given game belongs to both NP and coNP complexity classes. On the other hand, no polynomial algorithm solving parity games has been found (the best one due to Jurdziński, Paterson and Zwick has subexponential running time with sqrt(n) in the exponent). In my talk, I will give a brief introduction to this intriguing computational problem, and then focus on one of the earliest and simplest solving algorithms, namely Zielonka's recursive algorithm. Even though its worstcase running time is not particularly impressive as compared to more sophisticated solvers, the experimental study of Friedmann and Lange has shown that in practice it works very well. In order to understand why it is the case, in our recent work with Tim Willemse we have analysed the performance of two variants of the algorithm (standard and optimised) on certain subclasses of parity games (dull, weak, and solitaire). Moreover, we have provided a tighter lower bound on its worstcase running time. 
17.04.2014 Szymon Policht 
Kryptologia Stream ciphers 
Stream ciphers are one of the most important branches of privatekey cryptography. They offer strong security, combined with high speed and ease of implementation. In this talk, we define them and discuss ways to convert block ciphers to stream ones. Additionally, we introduce a powerful way of creating such ciphers  linear feedback shift registers. References: Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone, Handbook of Applied Cryptography, chapter 6 Oded Goldreich, Foundations of Cryptography vol. 2  Basic Applications, sections 5.3.15.3.2 
16.04.2014 Arkadiusz Olek 
Informatyka Teoretyczna Better Approximation Algorithms for the Maximum Internal Spanning Tree Problem, (by M.Knauer, J.Spoerhase) 
We examine the problem of determining a spanning tree of a given graph such that the number of internal nodes is maximum. The best approximation algorithm known so far for this problem is due to Prieto and Sloper and has a ratio of 2. For graphs without pendant nodes, Salamon has lowered this factor to 7/4 by means of local search. However, the approximative behaviour of his algorithm on general graphs has remained open. In this paper we show that a simplified and faster version of Salamon's algorithm yields a 5/3approximation even on general graphs. In addition to this, we investigate a node weighted variant of the problem for which Salamon achieved a ratio of 2·Δ(G)−3. Extending Salamon's approach we obtain a factor of 3+ε for any ε>0. We complement our results with worst case instances showing that our analyses are tight. References: Martin Knauer, Joachim Spoerhase, Better Approximation Algorithms for the Maximum Internal Spanning Tree Problem, Algorithmica, DOI 10.1007/s0045301398277 
16.04.2014 Agnieszka Łupińska 
Podstawy Informatyki Efficient Bracket Abstraction Using Iconic Representations for Combinators by Antoni Diller 
Some fundamental properties of a new univariate bracket abstraction algorithm employing a string representation for combinators are established. In particular, if the input term has length n, where n > 1, the algorithm is called fewer than n times to produce the abstract. Furthermore, the space required to store the abstract, in the worst case, is of the order O(n). This algorithm also has a number of features that make it worthy of further attention. When it is used to abstract a variables from an input term of length n, where n > 1, fewer than an new combinators are introduced into the abstract. However, the total size of the string representations of these combinators grows quadratically in the number of variables abstracted and the space required to store the abstract, in the worst case, is of the order O(a^2 n). Fortunately, a closely related singlesweep, multivariate algorithm exists, using an array representation for combinators, which produces an abstract whose storage requirement, in the worst case, is of the order O(an). 
15.04.2014 Grzegorz Gutowski, Jakub Kozik 
Algorytmy Randomizowane i Aproksymacyjne Lower bounds for online graph colorings (cont.) 
(join work with P. Micek and X. Zhu) 
10.04.2014 Anna Dymek 
Kryptologia Pseudorandom generators 
Many encryption techniques use "random variables", and proofs of their correctness are based on the low probability of guessing the value of that "random variables". For that we need random generators, or so called "pseudorandom generators", which give us values indistinguishable from truly random ones. In the talk we define pseudorandom generators, discuss their existence and describe their relations with other problems. References: O. Goldreich, Foundations of Cryptography vol. 1  Basic Techniques, chapter 3 
10.04.2014 Wojciech Lubawski 
Algorytmiczne Aspekty Kombinatoryki Graph arboricity and matroids online 
Kolorowanie krawędzi grafu nazwiemy poprawnym, jeśli zbiory jednokolorowe nie zawierają cykli. Wzorując się na przykładach z kolorowania wierzchołków grafu, rozważymy kilka różnych dwuosobowych gier, w których prezenter ujawnia część informacji o grafie, jak na przykład: należenie danej krawędzi do grafu, listę kolorów dozwolonych dla danej krawędzi grafu, zbiór krawędzi na których można użyć danego koloru itp., a algorytm ma za zadanie doprowadzić do poprawnego pokolorowania wszystkich krawędzi grafu. Liczbę kolorów zapewniającą algorytmowi strategię wygrywającą powiążemy z najmniejszą liczbą kolorów potrzebną do poprawnego pokolorowania offline krawędzi grafu. Otrzymane wyniki uogólnimy do matroidów. 
09.04.2014 Adam Polak 
Informatyka Teoretyczna A Generalization of the Convex Kakeya Problem, (by Ahn et al.) 
Given a set of line segments in the plane, not necessarily finite, what is a convex region of smallest area that contains a translate of each input segment? This question can be seen as a generalization of Kakeya's problem of finding a convex region of smallest area such that a needle can be rotated through 360 degrees within this region. We show that there is always an optimal region that is a triangle, and we give an optimal Θ(n log n)time algorithm to compute such a triangle for a given set of n segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then placing the segments with their midpoint at the origin and taking their convex hull results in an optimal solution. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallestperimeter region containing a translate of every rotated copy of G. References: HeeKap Ahn, SangWon Bae, Otfried Cheong, Joachim Gudmundsson, Takeshi Tokuyama, Antoine Vigneron, A Generalization of the Convex Kakeya Problem, Algorithmica, DOI 10.1007/s004530139831y 
09.04.2014 Aleksandra Piktus 
Podstawy Informatyki Improved constructions of quantum automata by Andris Ambainis, Nikolajs Nahimovs 
We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use 4/epsion log (2p) states to recognize a language that requires p states classically. The construction is both substantially simpler and achieves a better constant in the front of log p than the previously known construction. Our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some results in this direction. 
08.04.2014 01.04.2014, 
Algorytmy Randomizowane i Aproksymacyjne Cancelled (all participants are invited to the lecture of prof. A. Ruciński.) 
03.04.2014 Michał Farnik 
Algorytmiczne Aspekty Kombinatoryki Beyond the Shannon's Bound 
Let G=(V,E) be a multigraph of maximum degree D. The edges of G can be colored with at most 3D/2 colors by Shannon's theorem. We study lower bounds on the size of subgraphs of G that can be colored with D colors. Shannon's Theorem gives a bound of DE/floor(3D/2). However, for D=3, Kamiński and Kowalik showed that there is a 3edgecolorable subgraph of size at least 7E/9, unless G has a connected component isomorphic to K_3+e (a K_3 with an arbitrary edge doubled). We extend this line of research by showing that G has a Dedge colorable subgraph with at least DE/(floor(3D/2)1) edges, unless D is even and G contains D/2 K_3 or D is odd and G contains (D1)/2 K_3+e. Moreover, the subgraph and its coloring can be found in polynomial time. Our results have applications in approximation algorithms for the Maximum kEdgeColorable Subgraph problem. For every even k>=4 we obtain a (2k+2)/(3k+2)approximation and for every odd k>=5 we get a (2k+1)/3kapproximation. When 4<= k<= 13 this improves over earlier algorithms due to Feige et al. This is joint work with Łukasz Kowalik and Arkadiusz Socała. 
02.04.2014 Łukasz Janiszewski 
Podstawy Informatyki Exploiting independent subformulas: A faster approximation scheme for #kSAT by Manuel Schmitt , Rolf Wanka 
We present an improvement on Thurley's recent randomized approximation scheme for #kSAT where the task is to count the number of satisfying truth assignments of a Boolean function Φ given as an nvariable kCNF. We introduce a novel way to identify independent substructures of Φ and can therefore reduce the size of the search space considerably. Our randomized algorithm works for any k. For #3SAT, it runs in time O(ε−2 · 1.51426n), for #4SAT, it runs in time O(ε−2 · 1.60816n), with error bound ε. 
27.03.2014 Michał Staromiejski 
Kryptologia Bezout theorem and associativity of addition on elliptic curves 
27.03.2014 Michał Masłowski 
Algorytmiczne Aspekty Kombinatoryki Maximizing the number of nonnegative subsets 
26.03.2014 Jakub Adamek 
Informatyka Teoretyczna A Universal Randomized Packet Scheduling Algorithm (by Łukasz Jeż) 
We give a memoryless scaleinvariant randomized algorithm REMIX for Packet Scheduling that is e/(e−1)competitive against an adaptive adversary. REMIX unifies most of previously known randomized algorithms, and its general analysis yields improved performance guarantees for several restricted variants, including the sbounded instances. In particular, REMIX attains the optimum competitive ratio of 4/3 on 2bounded instances. Our results are applicable to a more general problem, called Item Collection, in which only the relative order between packets' deadlines is known. REMIX is the optimal memoryless randomized algorithm against adaptive adversary for that problem References: Łukasz Jeż, A Universal Randomized Packet Scheduling Algorithm, Algorithmica (2013) 67:498–515, DOI 10.1007/s0045301297000 
26.03.2014 Michał Marczyk 
Podstawy Informatyki CAP theorem 
We will examine Gilbert and Lynch's proof of Brewer's conjecture. The latter states that it is impossible for a distributed service to be simultaneously consistent, available and partitiontolerant (for certain natural definitions of these terms). We will then consider the realworld impact of the theorem. Based on Gilbert, Lynch, "Brewer's Conjecture and the Feasibility of Consistent, Available, PartitionTolerant Web Services". 
19.03.2014 Seminar cancelled 
Podstawy Informatyki DAY OF FACULTY OF MATHEMATICS AND COMPUTER SCIENCE 
18.03.2014 Grzegorz Gutowski, Jakub Kozik 
Algorytmy Randomizowane i Aproksymacyjne Lower bounds for online graph colorings 
(join work with P. Micek and X. Zhu) 
13.03.2014 Grzegorz Guśpiel 
Kryptologia Optimal Asymmetric Encryption Padding (OAEP) 
We discuss the encryption scheme OAEP, long considered to be the first one to achieve both good performance and provable security. The latter was not obtained, however, due to a mistake in the proof. We present the scheme and the flawed proof. abstract of the paper: Given an arbitrary kbit to kbit trapdoor permutation f and a hash function, we exhibit an encryption scheme for which (i) any string x of length slightly less than k bits can be encrypted as f(r_x), where r_x is a simple probabilistic encoding of x depending on the hash function; and (ii) the scheme can be proven semantically secure assuming the hash function is "ideal." Moreover, a slightly enhanced scheme is shown to have the property that the adversary can create ciphertexts only of strings for which she "knows" the corresponding plaintexts  such a scheme is not only semantically secure but also nonmalleable and secure against chosenciphertext attack. References: M. Bellare, P. Rogaway, Optimal Asymmetric Encryption  How to Encrypt with RSA, http://cseweb.ucsd.edu/~mihir/papers/oae.pdf 
13.03.2014 Grzegorz Gutowski 
Algorytmiczne Aspekty Kombinatoryki Coloring 3colorable graphs online 
12.03.2014 Michał Dyrek 
Informatyka Teoretyczna Balanced Partitions of Trees and Applications (by A.E.Feldmann, L.Foschini) 
We study the problem of finding the minimum number of edges that, when cut, form a partition of the vertices into k sets of equal size. This is called the kBALANCED PARTITIONING problem. The problem is known to be inapproximable within any finite factor on general graphs, while little is known about restricted graph classes. We show that the kBALANCED PARTITIONING problem remains APXhard even when restricted to unweighted tree instances with constant maximum degree. If instead the diameter of the tree is constant we prove that the problem is NPhard to approximate within n^c, for any constant c<1. If vertex sets are allowed to deviate from being equalsized by a factor of at most 1+ε, we show that solutions can be computed on weighted trees with cut cost no worse than the minimum attainable when requiring equalsized sets. This result is then extended to general graphs via decompositions into trees and improves the previously best approximation ratio from O(log^{3/2}(n)/ε^2) [Andreev and Räcke in Theory Comput. Syst. 39(6):929–939, 2006] to O(log n). This also settles the open problem of whether an algorithm exists for which the number of edges cut is independent of ε. References: Andreas Emil Feldmann, Luca Foschini, Balanced Partitions of Trees and Applications, Algorithmica DOI 10.1007/s0045301398023 
06.03.2014 Wojciech Łopata 
Kryptologia Introduction to provable security 
We discuss several definitions of cryptosystem security as a resistance against "chosenciphertext" attacks, and reveal weaknesses of RSA and ElGamal encryption schemes. Then I describe CramerShoup encryption, and prove that if the Decision DiffieeHellman Problem is hard, then CramerShoup encryption is indistinguishabilitysecure from chosenciphertext attack. 
06.03.2014 Adam Gągol 
Algorytmiczne Aspekty Kombinatoryki Application of probabilistic method in some colourings of bounded pathwidth graphs 
05.03.2014 26.02.2014,Adam Gągol 
Informatyka Teoretyczna Natural proofs (by A. Razborov, S. Rudich) 
The notion of natural proof is introduced. We argue that the known proofs of lower bounds on the complexity of explicit Boolean functions in nonmonotone models fall within our definition of natural. We show, based on a hardness assumption, that natural proofs can not prove superpolynomial lower bounds for general circuits. Without the hardness assumption, we are able to show that they can not prove exponential lower bounds (for general circuits) for the discrete logarithm problem. We show that the weaker class of AC^0natural proofs which is sufficient to prove the parity lower bounds of Furst, Saxe, and Sipser, Yao, and Hastad is inherently incapable of proving the bounds of Razborov and Smolensky. We give some formal evidence that natural proofs are indeed natural by showing that every formal complexity measure, which can prove superpolynomial lower bounds for a single function, can do so for almost all functions, which is one of the two requirements of a natural proof in our sense. References: Alexander A. Razborov, Steven Rudich, Natural proofs, Journal of Computer and System Sciences, 55(1997), 2435 
05.03.2014 Robert Obryk 
Podstawy Informatyki Cryptographic Accumulators 
A cryptographic accumulator is a less wellknown cousin of a cryptographic hash function: it allows a digest of a multiset to be constructed one element at a time. One can also extend this notion in a few ways: allow removing elements already added to the digest, or provide witnesses that prove validity of operations on the digest without giving away what operations they were. This talk will present the basic notion of accumulators and their properties, give example implementations (secure under the typical assumptions) and hint at their possible uses. 
04.03.2014 Igor Adamski 
Algorytmy Randomizowane i Aproksymacyjne Outerstring graphs are chibounded 
References: Alexandre Rok, Bartosz Walczak, Outerstring graphs are chibounded, preprint 
26.02.2014 Adam Polak 
Podstawy Informatyki Open problems for pattern languages 
A pattern is a string built of terminals and variables. A language generated by a given pattern consists of words produced by substituting variables with arbitrary strings of terminals. Of course every occurrence of the same variable has to be substituted with the same string. Pattern languages were first studied in the context of machine learning but soon attracted formal languages researchers. Despite their very simple definition they have numerous interesting properties. During the seminar we will discuss several intriguing computational and structural problems involving pattern languages and their relation to the Chomsky hierarchy. Some of them were recently solved and some remain open. Papers about pattern languages: http://www.tks.informatik.unifrankfurt.de/data/doc/dissertation.pdf http://link.springer.com/chapter/10.1007%2F3540569391_81 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36.3057&rep=rep1&type=pdf http://www.sciencedirect.com/science/article/pii/S0890540109001023 http://www.tks.informatik.unifrankfurt.de/data/doc/dlt2010.pdf http://www.comp.nus.edu.sg/~sanjay/paps/regpat.pdf http://www.sciencedirect.com/science/article/pii/S030439751300577X 
23.01.2014 Karol Kosiński 
Algorytmiczne Aspekty Kombinatoryki A generalization of Thue freeness for partial words 
22.01.2014 Maciej Solon 
Informatyka Teoretyczna Scheduling with an Orthogonal Resource Constraint 
We address a scheduling problem that arises in highly parallelized environments like modern multicore CPU/GPU computer architectures where simultaneously active jobs share a common limited resource, e.g., memory cache. The scheduler must ensure that the demand for the common resource never exceeds the available capacity. This introduces an orthogonal constraint to the classical minimum makespan scheduling problem. Such a constraint also arises in other contexts where a common resource is shared across machines. We study the nonpreemptive case of this problem and present a (2+\epsi)approximation algorithm which relies on the interplay of several classical and modern techniques in scheduling like grouping, jobclassification, and the use of configurationLPs. This improves upon previous bound of 3 that can be obtained by list scheduling approaches, and gets close to the (3/2−\epsi)inapproximability bound. If the number of machines or the number of different resource requirements are bounded by a constant we obtain a polynomial time approximation scheme. References: Martin Niemeier, Andreas Wiese, Scheduling with an Orthogonal Resource Constraint, Algorithmica, DOI 10.1007/s0045301398295 
22.01.2014 Maciej Bendkowski 
Podstawy Informatyki An upper bound for reduction sequences in the typed lambdacalculus by H. Schwichtenberg 
It is well known that the full reduction tree for any term of the typed λ–calculus is finite. However, it is not obvious how a reasonable estimate for its height might be obtained. Here we note that the head reduction tree has the property tha the number of its nodes with conversions bounds the length of any reduction sequence. The height of that tree, and hence also the number of its nodes, can be estimated using a technique due to Howard [3], which in turn is based on work of Sanchis [4] and Diller [1]. This gives the desired upper bound. The method of Gandy [2] can also be used to obtain a bound for the length of arbitrary reduction sequences; this is carried out in [5]. However, the bound derived here, apart from being more intelligible, is also better. 
21.01.2014 Maciej Solon 
Algorytmy Randomizowane i Aproksymacyjne On the number of edges in families of pseudodiscs 
References: Piotr Micek, Rom Pinchasi, On the number of edges in families of pseudodiscs, preprint 
16.01.2014 Jaroslaw Grytczuk 
Algorytmiczne Aspekty Kombinatoryki Three variations on the theme of Szemeredi 
15.01.2014 Michał Sapalski 
Informatyka Teoretyczna LinearTime Algorithms for Tree Root Problems 
Let T be a tree on a set V of nodes. The pth power T^p of T is the graph on V such that any two nodes u and w of V are adjacent in T^p if and only if the distance of u and w in T is at most p. Given an nnode medge graph G and a positive integer p, the pth tree root problem asks for a tree T , if any, such that G = T^p. Given an nnode medge graph G, the tree root problem asks for a positive integer p and a tree T , if any, such that G = T^p. Kearney and Corneil gave the best previously known algorithms for both problems. Their algorithm for the former (respectively, latter) problem runs in O(n^3) (respectively, O(n^4)) time. In this paper, we give O(n+m)time algorithms for both problems. References: MawShang Chang, MingTat Ko, HsuehI Lu, LinearTime Algorithms for Tree Root Problems, Algorithmica, DOI 10.1007/s004530139815y 
15.01.2014 Konrad Witaszczyk 
Podstawy Informatyki Analytic aspects of the shuffle product by Marni Mishna, Mike Zabrocki 
There exist very lucid explanations of the combinatorial origins of rational and algebraic functions, in particular with respect to regular and context free languages. In the search to understand how to extend these natural correspondences, we find that the shuffle product models many key aspects of Dfinite generating functions, a class which contains algebraic. We consider several different takes on the shuffle product, shuffle closure, and shuffle grammars, and give explicit generating function consequences. In the process, we define a grammar class that models Dfinite generating functions. 
14.01.2014 Maciej Bendkowski 
Algorytmy Randomizowane i Aproksymacyjne List Colouring When The Chromatic Number Is Close To the Order Of The Graph 
References: B. Reed, B. Sudakov, List Colouring When The Chromatic Number Is Close To the Order Of The Graph, Combinatorica December 2004, Volume 25, Issue 1, pp 117123 
09.01.2014 Marcin Dziaduś 
Algorytmiczne Aspekty Kombinatoryki Coloring intersection graphs of pseudodiscs 
08.01.2014 Andrzej Dorobisz 
Informatyka Teoretyczna Linear Recognition and Embedding of Fibonacci Cubes 
Fibonacci strings are binary strings that contain no two consecutive 1s. The Fibonacci cube Γ_h is the subgraph of the hcube induced by the Fibonacci strings. These graphs are applicable as interconnection networks and in theoretical chemistry, and lead to the Fibonacci dimension of a graph. We derive a new characterization of Fibonacci cubes. The characterization is the basis for an algorithm which recognizes these graphs in linear time. Moreover, a graph which was recognized as a Fibonacci cube can be embedded into a hypercube using Fibonacci strings within the same time bound. References: Aleksander Vesel, Linear Recognition and Embedding of Fibonacci Cubes, Algorithmica, DOI 10.1007/s0045301398393 
08.01.2014 Michał Bejda 
Podstawy Informatyki Generalized satisfability problems: minimal elements and phase transitions by Nadia Creignoua, Herve Daud 
We develop a probabilistic model on the generalized satisfability problems defned by Schaefer (in: Proceedings of the 10th STOC, San Diego, CA, USA, Association for Computing Machinery, New York, 1978, pp. 216–226) for which the arity of the constraints is fixed in order to study the associated phase transition. We establish new results on minimal elements associated with such generalized satis"ability problems. These results are the keys of the exploration we conduct on the location and on the nature of the phase transition for generalized satisfability. We first prove that the phase transition occurs at the same scale for every reasonable problem and we provide lower and upper bounds for the associated critical ratio. Our framework allows one to get these bounds in a uniform way, in particular, we obtain a lower bound proportional to the number of variables for kSAT without analyzing any algorithm. Finally, we reveal the seed of coarseness for the phase transition of generalized satisfability: 2XORSAT. 
07.01.2014 Aneta Pawłowska 
Algorytmy Randomizowane i Aproksymacyjne Three Topics in Online List Coloring 
References: J. Carraher, S. Loeb, T. Mahoney, G. Puleo, M. Tsai, D.B. West,Three Topics in Online List Coloring, preprint 
19.12.2013 Jan Volec (University of Warwick) 
Algorytmiczne Aspekty Kombinatoryki Compactness and finitely forcible graphons 
Graphons are limit objects that are associated with convergent sequences of graphs. Problems from extremal combinatorics led to a study of graphons determined by finitely many subgraph densities, which are referred to as finitely forcible graphons. In 2011, Lovasz and Szegedy asked several questions about the complexity of the topological space of socalled typical vertices of a finitely forcible graphon can be. In particular, they conjectured that the space is always compact. We disprove the conjecture by constructing a finitely forcible graphon such that the associated space of typical vertices is not compact. In fact, our construction actually provides an example of a finitely forcible graphon with the space which is even not locally compact. This is a joint work with Roman Glebov and Dan Kral. 
18.12.2013 Bartłomiej Ryniec 
Informatyka Teoretyczna Preprocess, Set, Query! 
Thorup and Zwick (J.ACM 52(1):1–24, 2005 and STOC'01) in their seminal work introduced the notion of distance oracles. Given an nvertex weighted undirected graph with m edges, they show that for any integer k ≥ 1 it is possible to preprocess the graph in O˜(m n^{1/k}) time and generate a compact data structure of size O(k n^{1+1/k}). For each pair of vertices, it is then possible to retrieve an estimated distance with multiplicative stretch 2k−1 in O(k) time. For k=2 this gives an oracle of O(n^{1.5}) size that produces in constant time estimated distances with stretch 3. Recently, Patrascu and Roditty (In: Proc. of 51st FOCS, 2010) broke the theoretical statusquo in the field of distance oracles and obtained a distance oracle for sparse unweighted graphs of O(n^{5/3}) size that produces in constant time estimated distances with stretch 2. In this paper we show that it is possible to break the stretch 2 barrier at the price of nonconstant query time in unweighted undirected graphs.We present a data structure that produces estimated distances with 1+ε stretch. The size of the data structure is O(n m^{1−ε'}) and the query time is O˜(m^{1−ε'}). Using it for sparse unweighted graphs we can get a data structure of size O(n^{1.87}) that can supply in O(n^{0.87}) time estimated distances with multiplicative stretch 1.75. References: Ely Porat, Liam Roditty, Preprocess, Set, Query! Algorithmica (2013) 67:516–528 
18.12.2013 Łukasz Janiszewski 
Podstawy Informatyki . Exploiting independent subformulas: A faster approximation scheme for #kSAT by Manuel Schmitt , Rolf Wanka 
We present an improvement on Thurley's recent randomized approximation scheme for #kSAT where the task is to count the number of satisfying truth assignments of a Boolean function Φ given as an nvariable kCNF. We introduce a novel way to identify independent substructures of Φ and can therefore reduce the size of the search space considerably. Our randomized algorithm works for any k. For #3SAT, it runs in time O(ε−2 · 1.51426n), for #4SAT, it runs in time O(ε−2 · 1.60816n), with error bound ε. 
17.12.2013 10.12.2013,Damian Królik 
Algorytmy Randomizowane i Aproksymacyjne Sumpaintability of generalized thetagraphs 
References: J. Carraher, T. Mahoney, G.J. Puleo, D.B. West , Sumpaintability of generalized thetagraphs, preprint 
11.12.2013 Agnieszka Dymel 
Informatyka Teoretyczna Online Coloring of Bipartite Graphs with and without Advice 
In the online version of the wellknown graph coloring problem, the vertices appear one after the other together with the edges to the already known vertices and have to be irrevocably colored immediately after their appearance. We consider this problem on bipartite, i.e., twocolorable graphs. We prove that at least \floor{1.13746·log_2(n) − 0.49887} colors are necessary for any deterministic online algorithm to be able to color any given bipartite graph on n vertices, thus improving on the previously known lower bound of \floor{log_2(n)}+1 for sufficiently large n. Recently, the advice complexity was introduced as a method for a finegrained analysis of the hardness of online problems. We apply this method to the online coloring problem and prove (almost) tight linear upper and lower bounds on the advice complexity of coloring a bipartite graph online optimally or using 3 colors. Moreover, we prove that O(√n) advice bits are sufficient for coloring any bipartite graph on n vertices with at most \ceil{log_2(n)} colors. References: Maria Paola Bianchi, HansJoachim Böckenhauer, Juraj Hromkovic, Lucia Keller, Online Coloring of Bipartite Graphs with and without Advice Algorithmica, DOI 10.1007/s0045301398197 
11.12.2013 Michał Dyrek 
Podstawy Informatyki Boundary properties of the satisfiability problems by Vadim Lozin , Christopher Purcell 
The satisfiability problem is known to be NPcomplete in general and for many restricted instances, such as CNF formulas with at most 3 variables per clause and at most 3 occurrences per variable, or planar formulas. The latter example refers to graphs representing satisfiability instances. These are bipartite graphs with vertices representing clauses and variables, and edges connecting variables to the clauses containing them. Finding the strongest possible restrictions under which the problem remains NPcomplete is important for at least two reasons. First, this can make it easier to establish the NP completeness of new problems by allowing easier transformations. Second, this can help clarify the boundary between tractable and intractable instances of the problem. In this paper, we address the second issue and reveal the first boundary property of graphs representing satisfiability instances. 
04.12.2013 Sebastian Syta 
Informatyka Teoretyczna Online Unweighted Knapsack Problem with Removal Cost 
We study the online unweighted knapsack problem with removal cost. The input is a sequence of items u_1,u_2,...,u_n, each of which has a size and a value, where the value of each item is assumed to be equal to the size. Given the ith item u_i, we either put u_i into the knapsack or reject it with no cost. When u_i is put into the knapsack, some items in the knapsack are removed with removal cost if the sum of the size of u_i and the total size in the current knapsack exceeds the capacity of the knapsack. Here the removal cost means a cancellation charge or disposal fee. Our goal is to maximize the profit, i.e., the sum of the values of items in the last knapsack minus the total removal cost occurred. We consider two kinds of removal cost: unit and proportional cost. For both models, we provide their competitive ratios. Namely, we construct optimal online algorithms and prove that they are best possible. References: Xin Han, Yasushi Kawase, Kazuhisa Makino, Online Unweighted Knapsack Problem with Removal Cost, Algorithmica DOI 10.1007/s004530139822z 
04.12.2013 Przemysław Jedynak 
Podstawy Informatyki A MyhillNerode theorem for automata with advice by Alex Kruckman, Sasha Rubin, John Sheridan 
An automaton with advice is a finite state automaton which has access to an additional fixed infinite string called an advice tape. We refine the MyhillNerode theorem to characterize the languages of finite strings that are accepted by automata with advice. We do the same for tree automata with advice. 
28.11.2013 21.11.2013,Grzegorz Gutowski 
Algorytmiczne Aspekty Kombinatoryki The weak 3flow conjecture and the weak circular flow conjecture 
27.11.2013 Michał Bejda 
Informatyka Teoretyczna Data Structures on Event Graphs 
We investigate the behavior of data structures when the input and operations are generated by an event graph. This model is inspired by Markov chains. We are given a fixed graph G, whose nodes are annotated with operations of the type insert, delete, and query. The algorithm responds to the requests as it encounters them during a (random or adversarial) walk in G. We study the limit behavior of such a walk and give an efficient algorithm for recognizing which structures can be generated. We also give a nearoptimal algorithm for successor searching if the event graph is a cycle and the walk is adversarial. For a random walk, the algorithm becomes optimal. References: Bernard Chazelle, Wolfgang Mulzer, Data Structures on Event Graphs, Algorithmica DOI 10.1007/s0045301398384 
27.11.2013 Adam Polak 
Podstawy Informatyki On the satisfiability threshold and clustering of solutions of random 3SAT formulas, by Elitza Maneva, Alistair Sinclair 
We study the structure of satisfying assignments of a random 3Sat formula. In particular, we show that a random formula of density 4:453 almost surely has no nontrivial ``core'' assignments. Core assignments are certain partial assignments that can be extended to satisfying assignments, and have been studied recently in connection with the Survey Propagation heuristic for random Sat. Their existence implies the presence of clusters of solutions, and they have been shown to exist with high probability below the satisfiability threshold for kSat with k 9 [D. Achlioptas, F. RicciTersenghi, On the solutionspace geometry of random constraint satisfaction problems, in: Proc. 38th ACM Symp. Theory of Computing, STOC, 2006, pp. 130 139]. Our result implies that either this does not hold for 3Sat, or the threshold density for satisfiability in 3Sat lies below 4.453. The main technical tool that we use is a novel simple application of the first moment method 
26.11.2013 Wojciech Łopata 
Algorytmy Randomizowane i Aproksymacyjne ConflictFree Colourings of Uniform Hypergraphs With Few Edges 
References: A.V. Kostochka, M. Kumbhat, T. Łuczak, ConflictFree Colourings of Uniform Hypergraphs With Few Edges, Combinatorics, Probability and Computing Volume 21 Issue 4, July 2012 
20.11.2013 Damian Krolik 
Informatyka Teoretyczna Parameterized Analysis of Paging and List Update Algorithms 
It is wellestablished that input sequences for paging and list update have locality of reference. In this paper we analyze the performance of algorithms for these problems in terms of the amount of locality in the input sequence. We define a measure for locality that is based on Denning's working set model and express the performance of well known algorithms in terms of this parameter. This explicitly introduces parameterizedstyle analysis to online algorithms. The idea is that rather than normalizing the performance of an online algorithm by an (optimal) offline algorithm, we explicitly express the behavior of the algorithm in terms of two more natural parameters: the size of the cache and Denning's working set measure. This technique creates a performance hierarchy of paging algorithms which better reflects their experimentally observed relative strengths. It also reflects the intuition that a larger cache leads to a better performance. We also apply the parameterized analysis framework to list update and show that certain randomized algorithms which are superior to MTF in the classical model are not so in the parameterized case, which matches experimental results. References: Reza Dorrigiv, Martin R. Ehmsen, Alejandro LópezOrtiz, Parameterized Analysis of Paging and List Update Algorithms, Algorithmica, DOI 10.1007/s0045301398005 
20.11.2013 Andrzej Dorobisz 
Podstawy Informatyki Regular Languages Accepted by Quantum Automata by Alberto Bertoni and Marco Carpentieri 
In this paper we analyze some features of the behaviour of quantum automata. In particular we prove that the class of languages recognized by quantum automata with isolated cut point is the class of reversible regular languages. As a more general result, we give a bound on the inverse error that implies the regularity of the language accepted by a quantum automaton 
14.11.2013 Robert Obryk 
Algorytmiczne Aspekty Kombinatoryki Network routing as a multiparty game with asynchronous moves 
13.11.2013 Maciej Bendkowski 
Informatyka Teoretyczna Analyses of Cardinal Auctions 
We study cardinal auctions for selling multiple copies of a good, in which bidders specify not only their bid or how much they are ready to pay for the good, but also a cardinality constraint on the number of copies that will be sold via the auction. We perform first known Price of Anarchy type analyses with detailed comparison of the classical VickreyClarkeGroves (VCG) auction and one based on minimum pay property (MPP) which is similar to Generalized Second Price auction commonly used in sponsored search. Without cardinality constraints, MPP has the same efficiency (total value to bidders) and at least as much revenue (total income to the auctioneer) as VCG; this also holds for certain other generalizations of MPP (e.g., prefix constrained auctions, as we show here). In contrast, our main results are that, with cardinality constraints, (a) equilibrium efficiency of MPP is 1/2 of that of VCG and this factor is tight, (b) in equilibrium MPP may collect as little as 1/2 the revenue of VCG. References: Mangesh Gupte, Darja Krushevskaja, S. Muthukrishnan, Analyses of Cardinal Auctions, Algorithmica DOI 10.1007/s004530139832x 
13.11.2013 Kamil Jarosz 
Podstawy Informatyki On the strongly generic undecidability of the Halting Problem by Alexander Rybalov 
It has been shown in [J.D. Hamkins, A. Miasnikov, The halting problem is decidable on a set of asymptotic probability one, Notre Dame J. Formal Logic 47(4) (2006) 515–524] that the classical Halting Problem for Turing machines with oneway tape is decidable on a "large" set of Turing machines (a socalled generic set). However, here we prove that the Halting Problem remains undecidable when restricted to an arbitrary "very large" set of Turing machines (a socalled strongly generic set). Our proof is independent of a Turing machine model. 
12.11.2013 Tomasz Krawczyk, Bartosz Walczak 
Algorytmy Randomizowane i Aproksymacyjne Coloring subtree overlap graphs with O(log lgo n) colors. 
07.11.2013 Karol Kosiński 
Algorytmiczne Aspekty Kombinatoryki On some properties of (strongly) nonrepetitive sequences 
06.11.2013 Karol Różycki 
Informatyka Teoretyczna Oblivious Algorithms for the Maximum Directed Cut Problem 
We introduce a special family of randomized algorithms for Max DICUT that we call oblivious algorithms. Let the bias of a vertex be the ratio between the total weight of its outgoing edges and the total weight of all its edges. An oblivious algorithm selects at random in which side of the cut to place a vertex v, with probability that only depends on the bias of v, independently of other vertices. The reader may observe that the algorithm that ignores the bias and chooses each side with probability 1/2 has an approximation ratio of 1/4, whereas no oblivious algorithm can have an approximation ratio better than 1/2 (with an even directed cycle serving as a negative example). We attempt to characterize the best approximation ratio achievable by oblivious algorithms, and present results that are nearly tight. The paper also discusses natural extensions of the notion of oblivious algorithms, and extensions to the more general problem of Max 2AND. References: Uriel Feige, Shlomo Jozeph, Oblivious Algorithms for the Maximum Directed Cut Problem, Algorithmica DOI 10.1007/s004530139806z 
06.11.2013 Michał Masłowski 
Podstawy Informatyki The Halting Problem Is Decidable on a Set of Asymptotic Probability One by Joel David Hamkins and Alexei Miasnikov 
The halting problem for Turing machines is decidable on a set of asymptotic probability one. The proof is sensitive to the particular computational models. 
05.11.2013 Grzegorz Guśpiel 
Algorytmy Randomizowane i Aproksymacyjne On the construction of 3chromatic hypergraphs with few edges. 
References: Heidi Gebauer, On the construction of 3chromatic hypergraphs with few edges, JCTA 120 (2013) 
30.10.2013 Igor Adamski 
Informatyka Teoretyczna Linked Dynamic Tries with Applications to LZCompression in Sublinear Time and Space 
The dynamic trie is a fundamental data structure with applications in many areas of computer science. This paper proposes a new technique for maintaining a dynamic trie T of size at most 2^w nodes under the unitcost RAM model with a fixed word size w. It is based on the idea of partitioning T into a set of linked small tries, each of which can be maintained efficiently. Our method is not only spaceefficient, but also allows the longest common prefix between any query pattern P and the strings currently stored in T to be computed in o(P) time for small alphabets, and allows any leaf to be inserted into or deleted from T in o(logT) time. To demonstrate the usefulness of our new data structure, we apply it to LZcompression. Significantly, we obtain the first algorithm for generating the LZ78 encoding of a given string of length n over an alphabet of size σ in sublinear (o(n)) time and sublinear (o(n log σ) bits) working space for small alphabets (σ = 2^{o(log n \cdot \frac{log log log n}{(log log n)^2})). Moreover, the working space for our new algorithm is asymptotically less than or equal to the space for storing the output compressed text, regardless of the alphabet size. References: Jesper Jansson, Kunihiko Sadakane, WingKin Sung, Linked Dynamic Tries with Applications to LZCompression in Sublinear Time and Space, Algorithmica DOI 10.1007/s0045301398366 
30.10.2013 Agnieszka Łupińska 
Podstawy Informatyki Design and Implementation of a Parallel Priority Queue on Manycore Architectures by Xi He, Dinesh Agarwal, and Sushil K. Prasad 
An efficient parallel priority queue is at the core of the effort in parallelizing important nonnumeric irregular computations such as discrete event simulation scheduling and branchandbound algorithms. GPGPUs can provide powerful computing platform for such nonnumeric computations if an efficient parallel priority queue implementation is available. In this paper, aiming at finegrained applications, we develop an efficient parallel heap system employing CUDA. To our knowledge, this is the first parallel priority queue implementation on manycore architectures, thus represents a breakthrough. By allowing wide heap nodes to enable thousands of simultaneous deletions of highest priority items and insertions of new items, and taking full advantage of CUDA's data parallel SIMT architecture, we demonstrate up to 30fold absolute speedup for relatively finegrained compute loads compared to optimized sequential priority queue implementation on fast multicores. Compared to this, our optimized multicore parallelization of parallel heap yields only 23 fold speedup for such finegrained loads. This parallelization of a treebased data structure on GPGPUs provides a roadmap for future parallelizations of other such data structures. 
24.10.2013 Wiktor Kuropatwa 
Algorytmiczne Aspekty Kombinatoryki Distortioncolouring of cubic bipartite multigraphs 
23.10.2013 Wojciech Łopata 
Informatyka Teoretyczna An Algorithmic Characterization of Polynomial Functions over Z_{p^n} 
We consider polynomial representability of functions defined over Z_{p^n}, where p is a prime and n is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to determine whether a given function over Z_{p^n} is polynomially representable or not, (ii) finds the polynomial if it is polynomially representable. The previous characterizations given by Kempner (Trans. Am. Math. Soc. 22(2):240–266, 1921) and Carlitz (Acta Arith. 9(1), 67–78, 1964) are existential in nature and only lead to an exhaustive search method, i.e. algorithm with complexity exponential in size of the input. Our characterization leads to an algorithm whose running time is linear in size of input. We also extend our result to the multivariate case. References: Ashwin Guha, Ambedkar Dukkipati, An Algorithmic Characterization of Polynomial Functions over Z_{p^n}, Algorithmica DOI 10.1007/s0045301397997 
23.10.2013 Michał Marczyk 
Podstawy Informatyki Consistency in distributed systems, part II: avoiding synchronization with CRDTs (based on a paper by Shapiro, Preguiça, Baquero, Zawirski) 
In this closing part of a twopart series we will consider CRDTs, a systematic approach to eventual consistency. We will examine both the statebased and the operationbased approach, with some concrete examples. Finally, we will return to our motivating discussion from part I in considering how a system may incorporate both an eventually consistent data store and a limited dose of consensus to achieve excellent functional guarantees in a distributed setting. Key source: Shapiro, Preguiça, Baquero, Zawirski, "A comprehensive study of Convergent and Commutative Replicated Data Types", http://hal.inria.fr/inria00555588/ 
17.10.2013 Jakub Kozik 
Algorytmiczne Aspekty Kombinatoryki Random Greedy Coloring of Uniform Hypergraphs 
16.10.2013 Jerzy MarcinkowskiUniversity of Wrocław 
Informatyka Teoretyczna Finite Controllability and Bounded Derivation Depth 
FC (Finite controllability) and BDD (the Bounded Derivation Depth property) are two properties of Datalog/TGD programs. BDD is equivalent to Positive First Order rewritability  the very useful property that allows us to use (all the optimizations of) DBMS in order to compute the certain answers to queries in the presence of a theory. Finite Controllability of a theory T means that if the certain answer to a query Q, for a database instance D , in the presence of T is 'no' then this 'no' is never a result of an unnatural assumption that the counterexample can be infinite. We conjecture that for any theory T the property BDD implies FC. We prove this conjecture for the case of binary signatures. References: Tomasz Gogacz, Jerzy Marcinkowski: On the BDD/FC conjecture. Proceedings of PODS 2013 (the 32nd ACM SIGMODSIGACTSIGART Symposium on Principles of Database Systems) 
16.10.2013 Marek Markiewicz 
Podstawy Informatyki Cellular Automata on a Toeplitz Space. 
Toeplitz Space is a set of regular quasiperiodic biinfinite words over a finite alphabet with at least two different letters endowed with a Besicovitch metric. It is an invariant set for every Cellular Automaton. During the talk I will present some properties of this space and I will discuss how CA behave on it. I will also present an idea of examining the continuity of evolution of a CA and show some very basic results in this topic. 
14.10.2013 W. Hugh WoodinUC Berkeley 
Informatyka Teoretyczna The Continuum Hypothesis and the search for Mathematical Infinitynew place and date: Oct 14, 2013, 16:00,Polska Akademia Umiejętności, Kraków, Sławkowska 17 
By middle of the 20th century the problem of the Continuum Hypothesis was widely regarded as one of the prominent problems in all of Mathematics. Remarkably, this question cannot be solved on the basis of the basic principles (these are the ZFC axioms) on which the entire subject is based. This discovery of Cohen, 50 years ago this summer, is arguably one of the major discoveries in the history of modern Mathematics. But does this mean that the question of the Continuum Hypothesis has no answer? Any "solution" must involve the adoption of new principles but which principles should one adopt? Alternatively, perhaps the correct assessment of Cohen's discovery is that the entire enterprise of the mathematical study of Infinity is ultimately doomed because the entire subject is simply a human fiction without any true foundation. In this case, any "solution" to the Continuum Hypothesis is just an arbitrary (human) choice. Over the last few years a scenario has emerged by which with the addition of a single new principle not only can the problem of the Continuum Hypothesis be resolved, but so can all of the other problems which Cohen's method has been used to show are also unsolvable (and there have been many such problems). Moreover the extension of the basic (ZFC) principles by this new principle would be seen as an absolutely compelling option based on the fundamental intuitions on which the entire mathematical conception of Infinity is founded. However, this scenario critically depends upon the outcome of a single conjecture. If this conjecture is false then the entire approach, which is the culmination of nearly 50 years of research, fails or at the very least has to be significantly revised. Thus the mathematical study of Infinity has arguably reached a tipping point. But which way will it tip? 
10.10.2013 Dawid Ireno 
Algorytmiczne Aspekty Kombinatoryki The Cinderella Game on Holes and Antiholes 
09.10.2013 Michał Marczyk 
Podstawy Informatyki Consistency in distributed systems, part I: achieving consensus with Raft (presenting research by Ongaro & Ousterhout) 
In this opening part of a twopart series we will consider Raft, a new protocol for achieving consensus in a distributed system. Raft matches Paxos as far as efficiency is concerned, but is designed to be more readily understandable and more amenable to implementation without tweaks and additional optimizations. To motivate the discussion, we will briefly consider the concept of a distributed system and the circumstances in which such systems may or may not require consensus to make progress safely. Key source: Ongaro, Ousterhout, "In Search of an Understandable Consensus Algorithm" (draft, 20130910), https://ramcloud.stanford.edu/wiki/download/attachments/11370504/raft.pdf 
03.10.2013 Jarosław Grytczuk 
Algorytmiczne Aspekty Kombinatoryki Fractions, Continued and Egyptian 
I will present some problems and results on continued fractions and Egyptian fractions. 
19.06.2013 Jean CardinalUniversité Libre de Bruxelles 
Informatyka Teoretyczna On Universal Point Sets for Planar Graphs and Related Problems 
A set S of points in the plane is said to be nuniversal if every planar graph on n vertices has a straightline plane embedding on a subset of S. Finding the minimum size f(n) of an nuniversal point set is a longstanding open problem, and the current upper and lower bounds differ by a linear factor. We will consider a lower bound technique that allowed us to prove that there is no nuniversal point set of size n for any n>14. We will also describe recent results on families of planar graphs on n vertices that cannot be embedded on a common npoint set. This is a joint work with Michael Hoffmann and Vincent Kusters. 
13.06.2013 Jakub Brzeski 
Algorytmiczne Aspekty Kombinatoryki The universal and canonically colored sequences 
12.06.2013 Marcin Ziemiński 
Informatyka Teoretyczna DAGGER: A Scalable Index for Reachability Queries in Large Dynamic Graphs 
With the ubiquity of largescale graph data in a variety of application domains, querying them effectively is a challenge. In particular, reachability queries are becoming increasingly important, especially for containment, subsumption, and connectivity checks. Whereas many methods have been proposed for static graph reachability, many realworld graphs are constantly evolving, which calls for dynamic indexing. In this paper, we present a fully dynamic reachability index over dynamic graphs. Our method, called DAGGER, is a lightweight index based on interval labeling, that scales to million node graphs and beyond. Our extensive experimental evaluation on realworld and synthetic graphs confirms its effectiveness over baseline methods. References: Hilmi Yildirim, Vineet Chaoji, Mohammed J.Zaki, DAGGER: A Scalable Index for Reachability Queries in Large Dynamic Graphs, arXiv:1301.0977 
06.06.2013 Marcin Dziaduś 
Algorytmiczne Aspekty Kombinatoryki The CaccettaHaggkvist Conjecture and Additive Number Theory 
05.06.2013 Patryk Zaryjewski 
Informatyka Teoretyczna Insitu associative permuting 
The technique of insitu associative permuting is introduced which is an association of insitu permuting and insitu inverting. It is suitable for associatively permutable permutations of {1,2,...,n} where the elements that will be inverted are negative and stored in order relative to each other according to their absolute values. Let K[1...n] be an array of n integer keys each in the range [1,n], and it is allowed to modify the keys in the range [n,n]. If the integer keys are rearranged such that one of each distinct key having the value i is moved to the i'th position of K, then the resulting arrangement (will be denoted by K^P) can be transformed insitu into associatively permutable permutation pi^P using only logn additional bits. The associatively permutable permutation pi^P not only stores the ranks of the keys of K^P but also uniquely represents K^P. Restoring the keys from pi^P is not considered. However, insitu associative permuting pi^P in O(n) time using logn additional bits rearranges the elements of pi^P in order, as well as lets to restore the keys of K^P in O(n) further time using the inverses of the negative ranks. This means that an array of n integer keys each in the range [1,n] can be sorted using only logn bits of additional space. References: A. Emre Cetin, Insitu associative permuting, arXiv:1301.2046 
05.06.2013 Łukasz Janiszewski 
Podstawy Informatyki Tetris is Hard, Even to Approximate by Erik D. Demaine, Susan Hohenberger and David LibenNowell 
In the popular computer game of Tetris, the player is given a sequence of tetromino pieces and must pack them into a rectangular gameboard initially occupied by a given configuration of filled squares; any completely filled row of the gameboard is cleared and all pieces above it drop by one row. We prove that in the offline version of Tetris, it is NPcomplete to maximize the number of cleared rows, maximize the number of tetrises (quadruples of rows simultaneously filled and cleared), minimize the maximum height of an occupied square, or maximize the number of pieces placed before the game ends. We furthermore show the extreme inapproximability of the first and last of these objectives to within a factor of p^{1−epsilon}, when given a sequence of p pieces, and the inapproximability of the third objective to within a factor of 2−epsilon, for any epsilon>0. Our results hold under several variations on the rules of Tetris, including different models of rotation, limitations on player agility, and restricted piece sets. 
23.05.2013 Wojciech Lubawski 
Algorytmiczne Aspekty Kombinatoryki Lovasz's original proof of Kneser conjecture 
In the last thirty years algebraic topology has become an important tool in combinatorics. We will show a classical proof of Kneser conjecture in which the author related ncolorability of a graph with kconnectedness of a neighbourhood simplicial complex. If time permits we will show some other applications of algebraic topology in combinatorics. 
22.05.2013 Przemysław Derengowski 
Informatyka Teoretyczna Proper Interval Vertex Deletion 
The NPcomplete problem PROPER INTERVAL VERTEX DELETION is to decide whether an input graph on n vertices and m edges can be turned into a proper interval graph by deleting at most k vertices. Van Bevern et al. (In: Proceedings WG 2010. Lecture notes in computer science, vol. 410, pp.232–243, 2010) showed that this problem can be solved in O((14k+14)^{k+1}kn^6) time. We improve this result by presenting an O(6^kkn^6) time algorithm for PROPER INTERVAL VERTEX DELETION. Our fixedparameter algorithm is based on a new structural result stating that every connected component of a {claw, net, tent, C_4, C_5, C_6}free graph is a proper circular arc graph, combined with a simple greedy algorithm that solves PROPER INTERVAL VERTEX DELETION on {claw, net, tent, C_4, C_5, C_6}free graphs in O(n+m) time. Our approach also yields a polynomialtime 6approximation algorithm for the optimization variant of PROPER INTERVAL VERTEX DELETION. References: Pim van't Hof, Yngve Villanger, Proper Interval Vertex Deletion, Algorithmica, DOI 10.1007/s0045301296613 
22.05.2013 Aleksandra Piktus 
Podstawy Informatyki On the Additive Constant of the kServer Work Function Algorithm' by Yuval Emek, Pierre Fraigniaud, Amos Korman i Adi Rosen 
We consider the Work Function Algorithm for the kserver problem (Chrobak andr Larmore, 1991; Koutsoupias and Papadimitriou, 1995). We show that if the Work Function Algorithm is ccompetitive, then it is also strictly (2c)competitive. As a consequence of (Koutsoupias and Papadimitriou, 1995) this also shows that the Work Function Algorithm is strictly (4k2)competitive. 
16.05.2013 Grzegorz Stachowiak (UWr) 
Algorytmiczne Aspekty Kombinatoryki Counting and generating linear extensions 
I begin with the problem of computing two numbers related to a partial order: the number of linear extensions e(P) and the parity difference d(P). This second numer is the difference between the number of linear extensions being odd and even permutations. The number d(P) was considered because the condition d(P)=0,1 is a necessary for the existence of of an algorithm generating linear extensions by transpositions. Both e(P) and d(P) are comparability invariants. Computing both of them is #Phard. I will describe two simple algorithms to compute e(P) for special classes of posets. I will also formulate necessary and sufficient conditions for the possibility of generating permutations of a multiset by adjacent transpositions. 
15.05.2013 Paweł Komosa 
Informatyka Teoretyczna Multicut viewed through the eyes of vertex cover 
References: Jianer Chen, Jiahao Fany, Iyad A. Kanjz, Yang Liux, Fenghui Zhang, Multicut viewed through the eyes of vertex cover 
15.05.2013 Dawid Pustułka 
Podstawy Informatyki An alternate proof of Statman's finite completeness theorem by B. Srivathsan, Igor Walukiewicz 
Statman's finite completeness theorem says that for every pair of nonequivalent terms of simplytyped lambdacalculus there is a model that separates them. A direct method of constructing such a model is provided using a simple induction on the Böhm tree of the term. 
09.05.2013 Piotr Wójcik 
Algorytmiczne Aspekty Kombinatoryki On algebraic invariants of geometric graphs; the Colin de Verdiere number. 
08.05.2013 Sebastian Syta 
Informatyka Teoretyczna A Sublinear Time Algorithm for PageRank Computations 
In a network, identifying all vertices whose PageRank is more than a given threshold value $\Delta$ is a basic problem that has arisen in Web and social network analyses. In this paper, we develop a nearly optimal, sublinear time, randomized algorithm for a close variant of this problem. When given a directed network \graph, a threshold value $\Delta$, and a positive constant $c>3$, with probability $1o(1)$, our algorithm will return a subset $S\subseteq V$ with the property that $S$ contains all vertices of PageRank at least $\Delta$ and no vertex with PageRank less than $\Delta/c$. The running time of our algorithm is always $\tilde{O}(\frac{n}{\Delta})$. In addition, our algorithm can be efficiently implemented in various network access models including the Jump and Crawl query model recently studied by \cite{brautbar_kearns10}, making it suitable for dealing with large social and information networks. As part of our analysis, we show that any algorithm for solving this problem must have expected time complexity of ${\Omega}(\frac{n}{\Delta})$. Thus, our algorithm is optimal up to logarithmic factors. Our algorithm (for identifying vertices with significant PageRank) applies a multiscale sampling scheme that uses a fast personalized PageRank estimator as its main subroutine. For that, we develop a new local randomized algorithm for approximating personalized PageRank which is more robust than the earlier ones developed by Jeh and Widom \cite{JehW03} and by Andersen, Chung, and Lang \cite{AndersenCL06}. References: Christian Borgs, Michael Brautbar, Jennifer Chayes1, and ShangHua Teng, A Sublinear Time Algorithm for PageRank Computations, 
08.05.2013 Aneta Pawłowska 
Podstawy Informatyki TETRAVEX is NPcomplete by Yasuhiko Takenaga and Toby Walsh 
Tetravex is a widely played one person computer game in which you are given n^2 unit tiles, each edge of which is labelled with a number. The objective is to place each tile within a n by n square such that all neighbouring edges are labelled with an identical number. Unfortunately, playing Tetravex is computationally hard. More precisely, we prove that deciding if there is a tiling of the Tetravex board given n^2 unit tiles is NPcomplete. Deciding where to place the tiles is therefore NPhard. This may help to explain why Tetravex is a good puzzle. This result compliments a number of similar results for one person games involving tiling. For example, NPcompleteness results have been show for: the offline version of Tetris, KPlumber (which involves rotating tiles containing drawings of pipes to make a connected network), and shortest sliding puzzle problems. It raises a number of open questions. For example, is the infinite version Turingcomplete? How do we generate Tetravex problems which are truly puzzling as random NPcomplete problems are often surprising easy to solve? Can we observe phase transition behaviour? What about the complexity of the problem when it is guaranteed to have an unique solution? How do we generate puzzles with unique solutions? 
24.04.2013 Agnieszka Dymel 
Informatyka Teoretyczna A Simple 3EdgeConnected Component Algorithm 
A simple lineartime algorithm for finding all the 3edgeconnected components of an undirected graph is presented. The algorithm performs only one depthfirst search over the given graph. Previously best known algorithms perform multiple depthfirst searches in multiple phases. References: Yung H.Tsin, A Simple 3EdgeConnected Component Algorithm, Theory Comput. Systems 40(2007), 125142 
17.04.2013 Tomasz Kołodziejski 
Informatyka Teoretyczna 8/5 Approximation for TSP Paths 
We prove the approximation ratio 8/5 for the metric stPathTSP problem, and more generally for shortest connected Tjoins. The algorithm that achieves this ratio is the simple ``Best of Many'' version of Christofides' algorithm (1976), suggested by An, Kleinberg and Shmoys (2012), which consists in determining the best Christofides sttour out of those constructed from a family Fscr_{>0} of trees having a convex combination dominated by an optimal solution x^* of the fractional relaxation. They give the approximation guarantee sqrt{5}+1/2 for such an sttour, which is the first improvement after the 5/3 guarantee of Hoogeveen's Christofides type algorithm (1991). Cheriyan, Friggstad and Gao (2012) extended this result to a 13/8approximation of shortest connected Tjoins, for T≥4. The ratio 8/5 is proved by simplifying and improving the approach of An, Kleinberg and Shmoys that consists in completing x^*/2 in order to dominate the cost of "parity correction" for spanning trees. We partition the edgeset of each spanning tree in Fscr_{>0} into an stpath (or more generally, into a Tjoin) and its complement, which induces a decomposition of x^*. This decomposition can be refined and then efficiently used to complete x^*/2 without using linear programming or particular properties of T, but by adding to each cut deficient for x^*/2 an individually tailored explicitly given vector, inherent in the problem. A simple example shows that the Best of Many Christofides algorithm may not find a shorter sttour than 3/2 times the incidentally common optima of the problem and of its fractional relaxation. References: András Sebö, EightFifth Approximation for TSP Paths, Integer Programming and Combinatorial Optimization, LNCS7801, 2013, pp 362374 
17.04.2013 Monika Krupnik 
Podstawy Informatyki Inclusion problems for patterns with a bounded number of variables by Joachim Bremer, Dominik D. Freydenberger 
We study the inclusion problems for pattern languages that are generated by patterns with a bounded number of variables. This continues the work by Freydenberger and Reidenbach (Information and Computation 208 (2010)) by showing that restricting the inclusion problem to significantly more restricted classes of patterns preserves undecidability, at least for comparatively large bounds. For smaller bounds, we prove the existence of classes of patterns with complicated inclusion relations, and an open inclusion problem, that are related to the Collatz Conjecture. In addition to this, we give the first proof of the undecidability of the inclusion problem for NEpattern languages that, in contrast to previous proofs, does not rely on the inclusion problem for Epattern languages, and proves the undecidability of the inclusion problem for NEpattern languages over binary and ternary alphabets. 