Seminars

28.03.2017 14:15
Piotr Wójcik
Cryptology
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 non-recycled 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)

29.03.2017 12:15
Szymon Stankiewicz
Computer science foundations
CANTOR POLYNOMIALS AND THE FUETER-POLYA 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.
The purpose of this paper is to present a beautiful elementary proof of Vsemirnov of the Fueter-Polya theorem. It is a century-old conjecture that the Cantor polynomials are the only packing polynomials on N^2.

04.04.2017 14:15
Mateusz Jachna
Cryptology
Secure Hash Algorithms family and the recently found collision for SHA-1
19.04.2017 16:15
Lech Duraj, Adam Polak
Theoretical computer science
Longest Common Strictly Increasing Subsequecnce
26.04.2017 16:15
Marcin Pilipczuk
University of Warsaw
Theoretical computer science
Subexponential Parameterized Algorithms for Planar Graphs, Apex-Minor-Free 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 O(√k log k), and

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 (2O(√k log2k)nO(1))−1, where n is the number of vertices of G.

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 2O(√k log2k)nO(1). The technique can be applied to problems expressible as searching for a small, connected pattern with a prescribed property in a large host graph; examples of such problems include Directed k-Path, Weighted k-Path, Vertex Cover Local Search, and Subgraph Isomorphism, among others. Up to this point, it was open whether these problems can be solved in subexponential parameterized time on planar graphs, because they are not amenable to the classic technique of bidimensionality. Furthermore, all our results hold in fact on any class of graphs that exclude a fixed apex graph as a minor, in particular on graphs embeddable in any fixed surface. We also provide a similar statement for graph classes of polynomial growth.

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.

31.05.2017 16:15
Piotr Micek
Theoretical computer science
Ramsey Theory for Binary Trees and the Separation of Tree-chromatic Number from Path-chromatic Number

We propose a Ramsey theory for binary trees and prove that for every
r-coloring 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 tree-chromatic number at most 2 while the path-chromatic number is bounded. This construction resolves a problem posed by Seymour.

 

Joint work with Fidel Barrera-Cruz, Stefan Felsner, Tamás Mészáros, Heather Smith, Libby Taylor, and Tom Trotter.

Poprzednie referaty

23.03.2017 16:15
Aleksandra Mędrek, Marcin Muszalski
Combinatorial Optimization
Planning for Fast Connectivity Updates
21.03.2017 14:15
Jan Szczepaniec
Cryptology
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.
Inclusive Block Chain Protocol is a alternative structure consists of a directed acyclic graph of blocks to the chain that allows for operation at much higher rates. It is showed that with this system the advantage of highly connected miners is greatly reduced. On the negative side, attackers that attempt to maliciously reverse transactions can try to use the forgiving nature of the DAG structure to lower the costs of their attacks.


References:
[1] Lewenberg Y., Sompolinsky Y., Zohar A., Inclusive Block Chain Protocols. In: Böhme R., Okamoto T. (eds) Financial Cryptography and Data Security, 2015. Lecture Notes in Computer Science, vol 8975. Springer, Berlin, Heidelberg (pdf)

16.03.2017 16:15
Patryk Urbański
Combinatorial Optimization
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 #P-complete. 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)).

Gara Pruesse, Frank Ruskey. Generating Linear Extensions Fast. SIAM J. Comput. Vol. 23, No. 2 (1994), pp. 373-386.

16.03.2017 14:15
Jakub Cisło, Grzegorz Jurdziński
Algorytmika
Tight Hardness Results for LCS and other Sequence Similarity Measures
15.03.2017 16:15
Manuel Bodirsky
TU Dresden
Theoretical computer science
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 Ramsey-theoretic assumptions that might hold in general for all reducts of finitely bounded homogeneous structures).
15.03.2017 12:15
Łukasz Lachowski
Computer science foundations
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.
14.03.2017 14:15
Marcin Briański
Cryptology
Non-Interactive 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 x1, ..., xk to one or more workers. The workers return the result of the function evaluation, e.g., yi = F(xi), as well as a proof that the computation of F was carried out correctly on the given value xi. The verification of the proof should require substantially less computational effort than computing F(xi) from scratch.

We present a protocol that allows the worker to return a computationally sound, non-interactive proof that can be verified in O(m) time, where m is the bit-length of the output of F. The protocol requires a one-time pre-processing 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 xi or yi.

09.03.2017 16:15
Grzegorz Matecki
Combinatorial Optimization
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?
 
09.03.2017 14:00
Sylwester Klocek, Wojciech Kruk
Algorytmika
The Alternating Stock Size Problem and the Gasoline Puzzle
08.03.2017 12:15
Maciej Bendkowski
Computer science foundations
Boltzmann samplers: random generation of combinatorial structures with an application to lambda calculus
In their seminal paper, Duchon et al. proposed a surprisingly simple, general-purpose 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.
07.03.2017 14:15
Zygmunt Łenyk
Cryptology
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 pre-computations 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).
01.03.2017 12:15
Michał Zwonek
Computer science foundations
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 Feuter-Polya (jedyny kwadratowy i bijektywny wielomian N^2->N to funkcja cantore'a) https://arxiv.org/abs/1512.08261

2) Praca, w której autorzy pokazują nieistnienie wielomianów 3 i 4 stopnia.  http://www.sciencedirect.com/science/article/pii/0022314X78900367

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/1305.2538

4) W podobnej tematyce. http://www.sciencedirect.com/science/article/pii/0022314X78900355
 

 

28.02.2017
Michał Dyrek
Cryptology
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.
26.01.2017 16:15
Wojciech Kruk, Maciej Woźniak
Combinatorial Optimization
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
25.01.2017 16:15
01.03.2017 16:15
Grzegorz Guśpiel
Theoretical computer science
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

25.01.2017 12:00
Sylwester Klocek
Computer science foundations
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 proof-assistants – programs that assist the development of formal proofs by human-machine collaboration – has revived the interest in formal proofs and diminished considerably the value of these arguments. In this paper we discuss some challenges proof-assistants face in handling undecidable problems – the very results cited above – using for illustrations the generic proof-assistant Isabelle.
24.01.2017
Kamil Sałaś
Cryptology
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 Górniczo-Hutnicza
Combinatorial Optimization
Symmetry breaking polynomial
Let G be a graph, and let Γ= Aut G. A coloring c of G is symmetry-breaking if for every non-identity 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 symmetry-breaking coloring of G. We discuss here a different problem: counting the number of k-colorings 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 ψG. For positive integer k (number of colors), ψG(k) is the number of k-colorings that break all non-trivial symmetries of the graph G.
18.01.2017 16:15
Marian Mrozek
Theoretical computer science
The discrete charm of Morse theory
The lecture will start with recalling P.S. Alexandroff's Theorem (1937) on mutual equivalence of posets and T0 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.
18.01.2017 12:00
Michał Ziobro
Computer science foundations
Inhabitation in Simply-Typed Lambda-Calculus through a Lambda-Calculus for Proof Search by Jose Espırito Santo, Ralph Matthes, Luıs Pinto
Kontynuacja seminarium z 23.11.2016
17.01.2017
Grzegorz Bukowiec
Cryptology
A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic

Until recently, all the algorithms for computing discrete logarithm had a sub-exponential complexity of type L(1/3), similar to the factorization problem. In this talk we'll discuss a heuristic algorithm that provides quasi-polynomial 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 quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic (pdf)

11.01.2017 16:15
Patryk Mikos
Theoretical computer science
Online coloring of intervals with bandwidth
We study the online interval coloring problem with bandwidth. The input is a sequence of pairs Ji= (Ii,wi) where Ii is an interval on the real line and wi is a real number from (0,1]. In this setting a proper coloring is a function f:Ji →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.
11.01.2017 12:00
Patryk Mikos
Computer science foundations
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 k-letter alphabet that are accepted by deterministic finite automata (resp. nondeterministic finite automata) with n states.
10.01.2017
Szymon Policht
Cryptology
Faster operations on elliptic curves using Edwards curves
Elliptic curve cryptography is a broad and commonly used section of modern-day 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)
05.01.2017 14:15
Jan Derbisz, Jakub Łabaj
Algorytmika
How to sort by walking on a tree

We consider a tree with n vertices. On vertex number x there is a box with label p(x), with the function p being a permutation of {1,2,...,n}. A robot is walking on the tree, carrying at most one box at a time. If a box is placed where robot is standing, it can swap this box with the one being carried. The robot's goal is to sort the boxes, placing each one at the vertex with its number. The paper by D. Graf gives an algorithm computing the shortest possible robot's walk in quadratic time, as well as the proof that the problem becomes NP-complete if planar graphs are considered instead of trees.

04.01.2017 12:00
Konrad Kalita
Computer science foundations
ANALYTIC MODELS AND AMBIGUITY OF CONTEXT-FREE LANGUAGES by Philippe Flajolet
We establish that several classical context-free 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 context-free languages.
03.01.2017

Cryptology
(Cancelled)
22.12.2016 16:15
Łukasz Majcher, Jan Szczepaniec
Combinatorial Optimization
Convex p-partitions 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.
21.12.2016 16:15
Maciej Bendkowski
Theoretical computer science
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, general-purpose 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.
20.12.2016 12:00
Bartłomiej Puget
Cryptology
An introduction to quantum computing and cryptography II
15.12.2016 14:15
Michał Glapa, Franciszek Stokowacki
Algorytmika
Maximum matching with algebraic methods

In 2006, a celebrated result by Mucha and Sankowski stated that the maximum matching problem can be done by Gaussian elimination. The complexity of this algorithm depends on matrix multiplication, but certainly beats O(n2.5) long-standing record of Micali-Vazirani algorithm.

15.12.2016
Anna Kobak
Combinatorial Optimization
Open problems in graph theory concerning minors.
We mentioned following open problems in graph theory:
  1. Hadwiger's Conjecture
  2. Seagull Conjecture
  3. Jorgensen's Conjecture
  4. Unfriendly partitions
  5. and a few more conjectures concerning minors.
14.12.2016 16:15
Grzegorz Matecki
Theoretical computer science
Two-Dimensional Irregular Packing Problem
We present results on packing irregular shapes onto given sheets of material.
14.12.2016 12:00
Piotr Wójcik
Computer science foundations
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 k-letters alphabet and some diagrams, which can themselves be represented as partitions of a set of kn + 1 elements into n non-empty 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.
13.12.2016 12:00
Krzysztof Kleiner
Cryptology
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 polynomial-time 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.


References:

[1] M. Hirvensalo, Quantum Computing (http://link.springer.com/book/10.1007/978-3-662-09636-9)
[2] F. Benatti, M. Fannes, R. Floreanini, D. Petritis, Quantum Information, Computation and Cryptography (http://link.springer.com/book/10.1007/978-3-642-11914-9)
[3] D. Deutsc, Lectures on Quantum Computation (http://www.daviddeutsch.org.uk/videos/)
[4] U. Vazirani, BerkeleyX's Lectures: Quantum Mechanics and Quantum Computation (https://www.edx.org/course/quantum-mechanics-quantum-computation-uc-berkeleyx-cs-191x)

08.12.2016
Lech Duraj
Algorytmika
A short tale of matrix multiplication

In recent years, some new algorithms for matrix multiplication problem were presented. Each of them is, however, only slightly faster than previous ones, while requiring substantially more complex analysis. Because of this, the long-standing question of optimal matrix multiplication algorithm seems even harder.

In my presentation, a short survery of the matrix multiplication algorithm is given. The presentation is based on François Le Gall's survey lecture of 2014.

08.12.2016
Zygmunt Łenyk
Combinatorial Optimization
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.
  1.  
  2.  
  3. www.openproblemgarden.org/op/rendezvous_on_a_line
  4. Improved bounds for the symmetric rendezvous value on the line. Qiaoming Han, Donglei Du, Juan Vera, Luis F. Zuluaga. SODA 2007
07.12.2016 12:00
Jakub Brzeski
Computer science foundations
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 context-free languages and more general structures.
06.12.2016
Marek Rusinowski
Cryptology
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 protocols---OTR and Signal Protocol in particular---that provide security features desired by users.
01.12.2016
Aleksandra Mędrek, Krzysztof Maziarz
Algorytmika
Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back

The paper by Aleksander Mądry describes a new approach to the maximum flow problem. We define an electrical flow by assigning resistances to every edge and minimizing total energy instead of maximizing flow. Any flow network can be reduced to some electrical flow problem, using auxiliary reductions to some bipartite matching problems. The main result is a new maximum flow algorithm, working in O(m10/7). The presentation will cover a simpler, O(m3/2) version of the algorithm.

01.12.2016
Patryk Urbański
Combinatorial Optimization
Coloring Ordinary Maps, Maps of Empires and Maps of the Moon
A short review of generalized map coloring problems:
  • Heawood's empire coloring problem in the plane - 6M colors are sufficient to color a map of empires each consisting of at most M connected regions.
  • Earth-Moon map coloring Mathematics Magazine Vol. 66, No. 4 (Oct., 1993), pp. 211-226problem - it is known that the chromatic number of thickness-2 graphs is between 9 and 12. It is an open problem to find the exact value.
Coloring Ordinary Maps, Maps of Emipres, and Maps of the Moon. Joan P. Hutchinson. Mathematics Magazine. Vol. 66, No. 4 (Oct., 1993), pp. 211-226.
01.12.2016
Mateusz Twaróg
Combinatorial Optimization
Second Neighborhood via First Neighborhood in Digraphs

Second Neighborhood via First Neighborhood in Digraphs. Guantao Chen, Jian Shen, Raphael Yuster. Annals of Combinatorics. June 2003, Volume 7, Issue 1, pp 15–20.

30.11.2016 18:15
Bartosz Walczak
Theoretical computer science
Coloring curves that cross a fixed curve
A class of graphs is χ-bounded 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 χ-bounded. In particular, it is known since 2012 that the class of all string graphs is not χ-bounded. 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 χ-bounded. 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 so-called k-quasi-planar topological graphs. This is joint work with Alexandre Rok.
30.11.2016 12:00
Yauheni Ananchuk
Computer science foundations
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 non-associative 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 non-associative algebras is NP-complete; the network satisfaction problem over a finite qualitatively representable algebra is always ; the validity of equations over qualitative representations is co-NP-complete. On the other hand we prove that there is no finite axiomatisation of the class of qualitatively representable algebra
29.11.2016
Anna Kobak
Cryptology
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 non-generic and hence will have to manipulate the particular bit-representation 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
Combinatorial Optimization
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.
Wikipedia: Book embedding
Wikipedia: Mechanism design

24.11.2016
Dominika Salawa, Jakub Cisło
Algorytmika
Greedy algorithms for Steiner forest

The paper, resolves a long-standing open question: is the greedy approach for Steiner forest problem optimal up to multiplicative constant? The result by Anupam Gupta and Amit Kumar proves that in fact it is, with constant being at most 96. While some approximation algorithms for this problem, using linear programming, were previously known, this is the first known bound for a greedy algorithm.

23.11.2016
Piotr Danilewski
Theoretical computer science
Functional Code Building

 
A typical language translator uses a parser to convert an input string into some internal representation, usually in a form of an AST. The AST is then analyzed and transformed in passes. In the final pass, the AST is converted into the output, be it a machine code or source code of another language.
 
However, if we try to combine different languages, e.g. for a purpose of a multi-domain project, we may have a problem: each language uses different kinds of AST nodes, has different assumptions on the AST structure and features different pass algorithms. Settling for the common ground by limiting the node types, assumptions, and algorithms limits how the languages may reason about their code. Any high-level information is lost in such representation and high-level transformations cannot be defined.
 
Working on the common AST is similar to unstructured programming: AST acts as a global machine state. Any change to the state, e.g. introduced by a new language, may inadvertely affect the behavior of the existing languages. In regular programming we have moved away from unstructured programming towards higher abstraction levels, e.g. through functional programming. If it can be done to regular programming, can it be done to AST and code builders as well?
 
Our solution treats AST nodes not as objects of a fixed type. Instead, it is a function with its body describing entirely the behavior of such node. Even the connection between the nodes is represented internally by the function, in a form of continuations. 
The passes over the AST are replaced by a single invocation of these functions. The node functions may contain code for multiple stages of code analysis. In order to reduce the run time these additional stages are scheduled through dynamic staging.
 
This gives the power of abstraction to code building. Even nodes come from different languages may interact, as long as they understand the passed arguments.
 
This major change on how a code is represented requires changes in how we think about common basic operations during language interpretation:
- how do we link two nodes/functions together?
- how do we create control flow structures?
- how do we perform name lookups, even across different languages?
- how do we optimize the code so that the AST layer dissapears when generating code?
- what language-specific optimizations can be performed and how do we specify them?
 
We will address these questions in the upcoming talk.

23.11.2016
Michał Ziobro
Computer science foundations
Inhabitation in Simply-Typed Lambda-Calculus through a Lambda-Calculus for Proof Search by Jos´e Espırito Santo, Ralph Matthes, Luıs Pinto
A new, comprehensive approach to inhabitation problems in simply-typed lambda-calculus 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 lambda-calculus for proof search that the authors developed recently. The representation may be seen as extending the Curry-Howard representation of proofs by lambda-terms, staying within the methods of lambda-calculus and type systems. Our methodology reveals inductive descriptions of the decision problems, driven by the syntax of the proof-search expressions, and the end products are simple, recursive decision procedures and counting functions.
22.11.2016
Aleksandra Nowak
Cryptology
Lattice Cryptography and The Learning With Errors Problem
17.11.2016
Paweł Kubiak
Combinatorial Optimization
Succinct Data Structures
17.11.2016
Patryk Gołębiowski, Wojciech Kruk
Algorytmika
Lower Bounds in the Preprocessing and Query Phases of Routing Algorithms
In the last decade, there has been a substantial amount of research in finding routing algorithms designed specifically to run on real-world graphs. The paper by Colin White analyzes some of these algorithms and gives lower bounds for their complexity.
16.11.2016
Bartłomiej Bosek
Theoretical computer science
Every digraph is majority 4-choosable
A majority coloring of a digraph is a coloring of its vertices such that for each vertex at most half of its out-neighbors has the same color as that vertex. A digraph D is majority k-choosable 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.
  1. S. Kreutzer, S. Oum, P. Seymour, D. van der Zypen, D. R. Wood, Majority Colourings of Digraphs, Arxiv.
  2. Marcin Anholcer, Bartłomiej Bosek, Jarosław Grytczuk Every digraph is majority 4-choosable, Arixv.
16.11.2016
Michał Zieliński
Computer science foundations
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 non-quantum, 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 N-bit 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 N-bit 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 N-bit program can stop after the time 2^{N+constant} has effectively zero density.
15.11.2016
Piotr Kawałek
Cryptology
Teoretyczne podstawy kryptoanalizy
Celem referatu jest przedstawienie teoretycznych modeli ataków kryptoanalitycznych oraz tematów pokrewnych wraz z przykładami.
10.11.2016
Magdalena Gargas, Mateusz Jachna
Algorytmika
Max flows in O(nm) time, or better
A new max-flow algorithm with O(nm + m16/15 logn) time complexity is presented. By combining this with previous results, an O(nm) algorithm may be obtained, resolving a long-standing open question. This work is due to James B. Orlin.
10.11.2016
Grzegorz Bukowiec
Combinatorial Optimization
On more variants of the Majority Problem
09.11.2016
26.10.2016
Adam Polak
Theoretical computer science
Open problems in on-line and approximation algorithms
During the talk I will present several promising open problems including:
  • Online Deadline Scheduling with Machine Augmentation
  • Scheduling with Precedence Constraints
  • Multiway Cut
  • Traveling Repairman Problem
09.11.2016
Wojciech Kruk
Computer science foundations
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 one-way tape on a set of asymptotic probability one (on a so-called 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 one-way and two-way tape. It also implies that the Hamkins-Miasnikov algorithm is not generic for normalized Turing machines.
08.11.2016
Patryk Gołębiowski
Cryptology
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
Combinatorial Optimization
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 polynomial-time 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 2-6, sep 2016.
03.11.2016
Krzysztof Francuz, Szymon Łukasz
Algorytmika
Fast and simple connectivity in graph timelines

The presented paper (by J. Łącki and A. Karczmarz) deals with graph timelines - graphs with edges being created and destroyed over time. There is an effective algorithm for answering queries about reachability (finding a path between two given vertices) and biconnectivity (two disjoint paths) over some given time intervals.

27.10.2016
Dawid Pyczek, Jakub Rówiński
Algorytmika
Faster deterministic sorting and priority queues in linear space

The O(n log n) lower bound for sorting is valid only if the sorted objects allow no operations except comparing. For sorting integers, the bound can be broken - Mikkel Thorup's result of 1997 shows an O (n (log log n)2) algorithm for sorting arbitrary integers.

27.10.2016
Magdalena Gargas
Combinatorial Optimization
The geometry of nesting problems: A tutorial
26.10.2016
Wojciech Łopata
Computer science foundations
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
Cryptology
Unifying Zero-knowledge Proofs of Knowledge

We present a simple zero-knowledge 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 Fiat-Shamir and Guillou-Quisquater 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 Diffie-Hellman key, protocols for proving the multiplicative relation of three commitments (as required in secure multi-party 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 Zero-knowledge Proofs of Knowledge, Progress in Cryptology – AFRICACRYPT 2009, Vol. 5580 LNCS, pp 272-286

 

 

20.10.2016
Helena Borak
Combinatorial Optimization
Exact algorithms for the two-dimensional strip packing problem with and without rotations
We propose exact algorithms for the two-dimensional 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 branch-and-bound 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
Algorytmika
Disjoint Set Union with randomized linking

The most popular version of Find-Union algorithm uses path compression and linking by rank. The presented work of Goel, Khanna, Larkin and Tarjan gives an analysis of the same algorithm, but with arbitrary (randomized) linking.

19.10.2016
Bartosz Walczak
Theoretical computer science
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 linear-time constant-workspace algorithm to compute all common tangents of two disjoint polygons, each given by a read-only array of its corners in a cyclic order. This is joint work with Mikkel Abrahamsen.
19.10.2016
Pola Kyzioł
Computer science foundations
The domino problem for self-similar structures by Sebastian Barbieri and Mathieu Sablik
We defne the domino problem for tilings over self-similar structures of $Z^d$ given by forbidden patterns. In this setting we exhibit non-trivial families of subsets with decidable and undecidable domino problem.
18.10.2016
Grzegorz Jurdzinski
Cryptology
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.


References:
[1] Paul C. Kocher, Timing Attacks on Implementations of Diffe-Hellman, RSA, DSS and Other Systems (http://www.cryptography.com/public/pdf/TimingAttacks.pdf)
[2] David Brumley, Dan Boneh, Remote Timing Attacks are Practical (https://crypto.stanford.edu/~dabo/papers/ssl-timing.pdf)
[3] Daniel J. Bernstein, Cache-timing attacks on AES (http://cr.yp.to/antiforgery/cachetiming-20050414.pdf)

13.10.2016
Krzysztof Barański
Combinatorial Optimization
Level-Oriented Two-Dimensional Packing Algorithms
The paper includes an overview of several algorithms, their complexities and approximation ratios solving two-dimensional strip packing problem:
1) First-Fit Decreasing Height (FFDH) - time complexity: O(nlgn), approximation ratio: <= 17/10 OPT(I) + 1 [with proof]
2) Next-Fit Decreasing Height (NFDH) - time complexity: O(nlgn), approximation ratio: <= 17/10 OPT(I) + 1 [with proof]
3) Best-Fit Decreasing Height (BFDH), Bottom-Left (BL), Steinberg's algorithm, Split-Fit (SF)
13.10.2016
G. Bukowiec, S.Klocek
Algorytmika
FKT algorithm

Counting all matchings in a given graph is a #P-complete problem. However, for planar graphs it can be done in polynomial time. The FKT algorithm does it by exploiting the connection between the notions of matrix determinant and matrix permanent.

12.10.2016
Adam Polak
Theoretical computer science
Why is it hard to beat O(n^2) for Longest Common Weakly Increasing Subsequecnce?
 
For many years the classic Longest Common Subsequecnce problem (LCS) have not seen any significant improvement over the simple quadratic time dynamic programming algorithm, with the current fastest algorithm by Masek and Paterson dating back to 1980. In the meantime numerous related problems were studied, among them the Longest Common (Weakly) Increasing Subsequecnce problem, for which Yang, Huang, and Chao found a quadratic time dynamic programming algorithm. Despite some attempts, their result have not been improved for over a decade. In a recent line of research Abboud, Backurs, and Vassilevska Williams show a reduction from SAT to LCS, proving that LCS cannot be solved in strongly subquadratic time unless the Strong Exponential Time Hypothesis is false. During the talk I will present an analogous hardness result for the Longest Common Increasing Subsequecnce problem.