Archiwum seminariów
19.12.73658 Krzysztof Barański 
Optymalizacja Kombinatoryczna A note on polynomials and ffactors of graphs 

24.08.73646 Demian Banakh 
Optymalizacja Kombinatoryczna Token sliding on graphs of girth five 
In the Token sliding problem, one starts with a graph and independent sets I_{s}, I_{t}. We put k tokens on vertices of I_{s} and ask whether it's possible to reach I_{t} after a finite sequence of moves, where 1 move is sliding 1 token along the edge so that no 2 tokens are adjacent at any point. It was shown in 2021 that this problem is W[1]hard for graphs of girth 4 or less. In this presentation, we will see how the problem becomes Fixedparameter tractable for the other graphs (girth 5 or more). 
30.12.73595 Grzegorz Gawryał, Szymon Salabura 
TSP in a Simple Polygon 
Problem komiwojażera (TSP) jest jednym z najbardziej popularnych problemów optymalizacyjnych w algorytmice. Jest on NPtrudny, nawet wtedy, gdy graf na wejściu jest grafem odległości euklidesowych między danymi punktami na płaszczyźnie. Autorzy wprowadzają nowy wariant tego problemu  TSP w wielokącie prostym, w którym to problemie należy znaleźć najkrótszą trasę nie wychodzącą poza wielokąt i odwiedzającą pewien zbiór punktów w tym wielokącie, w dowolnej kolejności. Autorzy najpierw pokazują, jak zastosować ogólniejszy i dość skomplikowany algorytm Marxa, Pilipczuka i Pilipczuka do tego problemu, uzyskując złożoność poly(n,m) + 2^{(O(sqrt(n) log n))}, a następnie prezentują własny, znacznie prostszy algorytm rozwiązujący ten wariant TSP w tej samej złożoności. 
05.11.70912 Andrzej Grzesik Jagiellonian 
Informatyka Teoretyczna Turántype problems for directed cycles 
A standard Turán problem for a graph F is to determine the maximal number of edges in a graph not containing F as a subgraph. This problem for directed cycles in oriented graphs is trivial, but its various generalizations, when one asks for minimum outdegree or number of other subgraphs, occurred to be hard problems. In particular, finding minimum outdegree (or semidegree) forcing an oriented graph to contain a directed triangle is a CaccettaHäggkvist conjecture, which is open for 45 years despite numerous partial results. During the talk we will present a solution (obtained with Jan Volec) to a conjecture of Kelly, Kühn and Osthus on the minimum semidegree forcing an oriented graph to contain a directed cycle of any given length at least four. We will also discuss results (obtained jointly with Justyna Jaworska, Bartłomiej Kielak and Tomasz Ślusarczyk) for the generalized Turán problem for directed cycles when one maximizes the number of directed cycles of some other length. 
21.03.70803 Krzysztof Barański 
Podstawy Informatyki A verified framework for higherorder uncurrying optimizations by Zaynah Dargaye and Xavier Leroy 
Function uncurrying is an important optimization for the efficient execution of functional programming languages. This optimization replaces curried functions by uncurried, multipleargument functions, while preserving the ability to evaluate partial applications. Firstorder uncurrying (where curried functions are optimized only in the static scopes of their definitions) is well understood and implemented by many compilers, but its extension to higherorder functions (where uncurrying can also be performed on parameters and results of higherorder functions) is challenging. This article develops a generic framework that expresses higherorder uncurrying optimizations as typedirected insertion of coercions, and prove its correctness. The proof uses stepindexed logical relations and was entirely mechanized using the Coq proof assistant. 
13.08.54493 Bartłomiej Błoniarz 
Optymalizacja Kombinatoryczna A Survey of the Game “Lights Out!" 

18.04.54481 Jakub Dziarkowski 
Optymalizacja Kombinatoryczna Note on Perfect Forests 

24.08.54430 Bartłomiej Wacławik, Krzysztof Ziobro 
Tiny Pointers 
Praca wprowadza nowe pojęcie: wskaźniczek. Wskaźniczek jest obiektem, który pozwala na dostęp do jednego z n miejsc w pamięci, jednocześnie używając znacząco mniej niż log(n) bitów. Jest to możliwe dzięki użyciu wprowadzonej w pracy tablicy dereferencyjnej, która pozwala dla danego klucza k (z dużym prawdopodobieństwem) zaalokować komórkę pamięci zwracając wskaźniczek, który razem z kluczem pozwalaja uzyskać dostęp do zaalokowanej komórki w czasie stałym. Dodatkowo autorzy podają przykłady zastosowań w popularnych strukturach danych, których rozmiar można zredukować dzięki zastąpieniu klasycznych wskaźników wskaźniczkami. Wśród tych przykładów znajdują się między innymi drzewa BST oraz słowniki o stałej pojemności. 
01.07.51747 Tuukka Korhonen University of Bergen 
Informatyka Teoretyczna An improved parameterized algorithm for treewidth 
Treewidth is a fundamental graph parameter that, informally, characterizes how treelike a graph is. We give a 2^{O(k^2)}·n^{O(1)} time algorithm for determining if the treewidth of a given nvertex graph is at most k and outputting the corresponding tree decomposition. This resolves the longstanding open problem of whether there is a 2^{o(k^3)}·n^{O(1)} time algorithm for treewidth. In particular, this is the first improvement on the dependency on k in fixedparameter algorithms for treewidth since the 2^{O(k^3)}·n^{O(1)} time algorithm given in 1991 by Bodlaender and Kloks, and independently, by Lagergren and Arnborg. We also give a k^{O(k/ε)}·n^{O(1)} time (1+ε)approximation algorithm for treewidth. Joint work with Daniel Lokshtanov. 
13.11.51637 Roman Madej 
Podstawy Informatyki Modular Construction of Fixed Point Combinators and Clocked Bohm Trees by Jorg Endrullis, Dimitri Hendriks and Jan Willem Klop 
Fixed point combinators (and their generalization: looping combinators) are classic notions belonging to the heart of λcalculus and logic. We start with an exploration of the structure of fixed point combinators (fpc’s), vastly generalizing the wellknown fact that if Y is an fpc, Y (SI) is again an fpc, generating the B ̈ohm sequence of fpc’s. Using the infinitary λcalculus we devise infinitely many other generation schemes for fpc’s. In this way we find schemes and building blocks to construct new fpc’s in a modular way. Having created a plethora of new fixed point combinators, the task is to prove that they are indeed new. That is, we have to prove their βinconvertibility. Known techniques via B ̈ohm Trees do not apply, because all fpc’s have the same Bohm Tree (BT). Therefore, we employ ‘clocked BT’s’, with annotations that convey information of the tempo in which the data in the BT are produced. BT’s are thus enriched with an intrinsic clock behaviour, leading to a refined discrimination method for λterms. The corresponding equality is strictly intermediate between =β and =BT, the equality in the classical models of λcalculus. An analogous approach pertains to L ́evy–Longo and Berarducci trees. Finally, we increase the discrimination power by a precision of the clock notion that we call ‘atomic clock’.

08.04.35328 Julia Biały 
Optymalizacja Kombinatoryczna Can a party represent its constituency? 
The paper focuses on the representation problem in political elections, using a theorem from number theory. A. Katz's work gives an answer to the question  of whether there exists a way to construct the election list so that it does not matter how many politicians are selected and the politically different groups of the party will be represented?

13.12.35315 Katzper Michno 
Optymalizacja Kombinatoryczna Internal Partitions of Regular Graphs 
We consider internal partitions of graphs, which is a partition of V into two sets, such that every vertex has at least half of its neighbors in its own set. Several investigators have raised the conjecture that dregular graphs always have an internal partition, assuming their set of vertices is big enough. Here we prove this conjecture for d=6. We also investigate the case when V=d+4, which leads to some new problems on cubic graphs, and find new families of graphs that don't have an internal partition.

18.04.35265 Ignacy Buczek, Tomasz Buczyński 
List Colouring Trees in Logarithmic Space 
Dla danego nwierzchołkowego grafu G = (V, E) oraz listy L(v) ⊆ {1, ..., n} dozwolonych kolorów dla każdego wierzchołka v ∊ V, kolorowanie listowe jest kolorowaniem wierzchołkowym c grafu G spełniającym c(v) ∊ L(v) dla każdego v. Autorzy pracy dowodzą, że problem kolorowania listowego nwierzchołkowych drzew może być rozwiązany za pomocą deterministycznej maszyny Turinga używającej O(log n) bitów na taśmie roboczej. 
23.02.32582 Jonathan Narboni Jagiellonian 
Informatyka Teoretyczna Vizing's Conjecture Holds 
In 1964 Vizing proved that to properly color the edges of a graph G, one need at most ∆+1 colors, where ∆ is the maximum degree of G. In his paper, Vizing actually proves that one can transform any proper edge coloring into a (∆+1)edgecoloring using only Kempe changes. Soon after his paper, he asked the following question: is an optimal edgecoloring always reachable from any proper edgecoloring using only Kempe changes? Bonamy & al. proved that the conjecture holds for triangle free graphs, following their work, we prove that it holds for all graphs. 
08.07.32472 Rafał Loska 
Podstawy Informatyki Strict monotonic trees arising from evolutionary processes: combinatorial and probabilistic study by Olivier Bodini, Antoine Genitrini, Cécile Mailler and Mehdi Naima 
In this paper we study two models of labelled random trees that generalise the original unlabelled Schroder tree. Our new models can be seen as models for phylogenetic trees in which nodes represent species and labels encode the order of appearance of these species, and thus the chronology of evolution. One important feature of our trees is that they can be generated efficiently thanks to a dynamical, recursive construction. Our first model is an increasing tree in the classical sense (labels increase along each branch of the tree and each label appears only once). To better model phylogenetic trees, we relax the rules of labelling by allowing repetitions in the second model. For each of the two models, we provide asymptotic theorems for different characteristics of the tree (e.g. degree of the root, degree distribution, height, etc), thus giving extensive information about the typical shapes of these trees. We also provide efficient algorithms to generate large trees efficiently in the two models. The proofs are based on a combination of analytic combinatorics, probabilistic methods, and bijective methods (we exhibit bijections between our models and wellknown models of the literature such as permutations and Stirling numbers of both kinds). It turns out that even though our models are labelled, they can be specified simply in the world of ordinary generating functions. However, the resulting generating functions will be formal. Then, by applying Borel transforms the models will be amenable to techniques of analytic combinatorics. 
02.12.16162 Jakub Siuta 
Optymalizacja Kombinatoryczna On Induced Subgraphs with All Degrees Odd 
Gallai proved that the vertex set of any graph can be partitioned into two sets, each inducing a subgraph with all degrees even. We prove that every connected graph of even order has a vertex partition into sets inducing subgraphs with all degrees odd, and give bounds for the number of sets of this type required for vertex partitions and vertex covers. We also give results on the partitioning and covering problems for random graphs.

07.08.16150 Aleksander Katan 
Optymalizacja Kombinatoryczna A generalization of Konig's theorem 
König's theorem lets us determine the maximum number of pairwise independent edges in a bipartite graph. In the paper, L. Lovász focuses on critical graphs, meaning that if any of their edges are removed, the size of maximum matching diminishes. Considering a certain generalization of the abovementioned concept, Lovász gives a simple condition that is necessary and sufficient for a graph to be critical. The result is used to solve a conjecture by Erdős regarding strict hypergraph coloring. 
19.10.13416 Michał Pilipczuk University of Warsaw 
Informatyka Teoretyczna Flipper games for monadically stable classes of graphs 
We will provide a gentle introduction to the ongoing work on constructing a structural theory for graph classes defined by forbidding obstructions definable in logic. The focus will be on monadically stable classes of graphs: classes where one cannot define arbitrary long total orders using a fixed firstorder formula. We will review recent advances on characterizing these classes in a purely combinatorial manner, in particular through a game model: the Flipper game. 
04.03.13307 Sebastain Spyrzewski 
Podstawy Informatyki A characterization of lambdaterms transforming numerals by PAWEŁ PARYS 
It is well known that simply typed λterms can be used to represent numbers, as well as some other data types. We show that λterms of each fixed (but possibly very complicated) type can be described by a finite piece of information (a set of appropriately defined intersection types) and by a vector of natural numbers. On the one hand, the description is compositional: having only the finite piece of information for two closed λterms M and N, we can determine its counterpart for M N, and a linear transformation that applied to the vectors of numbers for M and N gives us the vector for M N. On the other hand, when a λterm represents a natural number, then this number is approximated by a number in the vector corresponding to this λterm. As a consequence, we prove that in a λterm of a fixed type, we can store only a fixed number of natural numbers, in such a way that they can be extracted using λterms. More precisely, while representing k numbers in a closed λterm of some type, we only require that there are k closed λterms M1, . . . , M k such that M i takes as argument the λterm representing the ktuple, and returns the ith number in the tuple (we do not require that, using λcalculus, one can construct the representation of the ktuple out of the k numbers in the tuple). Moreover, the same result holds when we allow that the numbers can be extracted approximately, up to some error (even when we only want to know whether a set is bounded or not). All the results remain true when we allow the Y combinator (recursion) in our λterms, as well as uninterpreted constants. 
04.04.62707 Ignacy Buczek 
Optymalizacja Kombinatoryczna K4free graphs have sparse halves 
In the extremal graph theory, there are many unsolved problems related to the finding of sparse subsets in graphs. The most famous one, stated by Erdos in 1976, asks whether every trianglefree graph contains n/2 vertices that span at most 1/50 n^{2} edges. In our work we consider, and successfully prove, a modified version of this theorem which conjectures that every K_{4}free graph has n/2 vertices spanning at most 1/18 n^{2} edges. This bound is tight, as the balanced blowup of a triangle is an extreme example. We achieve the proof by strengthening some of the previous results and by stating some new arguments which show that the only K_{4}free graph which has at least 1/18 n^{2} edges in every half is the blowup of a triangle. 
07.12.62694 Łukasz Selwa 
Optymalizacja Kombinatoryczna Isomorphic bisections of cubic graphs 
Ando conjecture states that we can partition vertices of any cubic graph into two parts that induce isomorphic subgraphs. We show that this conjecture is true for sufficiently large connected cubic graphs. In the proof, we use probabilistic methods with recoloring arguments. 
18.02.59961 Ross Kang University of Amsterdam 
Informatyka Teoretyczna Colouring graphs with sparse neighbourhoods 
Let us say that a graph of maximum degree Δ has local density at most η if the number of edges spanning any neighbourhood is at most η·(Δ choose 2), i.e. if the edge density is no more than an η fraction of the maximum possible. What is the largest chromatic number of such graphs? When η=0, this corresponds to asking about the largest chromatic number in trianglefree graphs of maximum degree Δ. This goes back to an old question of Vizing and is the objective of a recent breakthrough of Molloy. It is natural — and also connects to various other problems in the field — to consider other choices for η. We will broadly discuss this problem, including its classic origins in Ramsey theory, and some different ideas that have recently proven fruitful. This will touch on recent joint works with Davies, Hurley, de Joannis de Verclos, Pirot, and Sereni.

04.07.59851 Łukasz Grobelczyk  canceled 
Podstawy Informatyki Bijections between planar maps and planar linear normal \lambdaterms with connectivity condition by Wenjie Fang 
27.11.43541 Hubert Zięba 
Optymalizacja Kombinatoryczna The 3flow conjecture, factors modulo k, and the 123conjecture 
The 123 conjecture asserts that for every connected simple graph of order at least 3 edges can be weighted with 1,2 and 3 so that each pair of adjacent has different weighted degrees. We consider a modified version of this conjecture with 1,2 weights only. By using ffactors modulo k of the graph, we prove it for nonbipartite (6𝛘(G)5)edgeconnected graphs and completely characterize bipartite graphs having this property. 
02.08.43529 Tomasz Mazur 
Optymalizacja Kombinatoryczna Improved lower bound for the list chromatic number of graphs with no Kt minor 
Hadwiger's conjecture is an important conjecture in graph theory which states that every graph without a K_{t}minor is (t1)colorable. This conjecture does not extend to list colorings, but Kawarabayashi and Mohar (2007) conjectured that there exists a constant c such that every graph with no K_{t}minor has a list chromatic number at most c·t. More specifically, they conjectured that c = 3/2 is sufficient. Refuting the latter conjecture, we prove using the probabilistic method that there exist graphs with no K_{t}minor with list chromatic number at least (2o(1))·t, and hence c ≥ 2 is necessary. This improves the previous bestknown lower bound by Barát, Joret, and Wood (2011), who proved that c ≥ 4/3. 
07.12.43478 Roman Madej, Paweł Nowak 
Sinkless Orientation Made Simple 
Sinkless Orientation jest problemem grafowym, polegającym na skierowaniu krawędzi w grafie, aby każdy wierzchołek o stopniu co najmniej trzy miał krawędź wychodzącą. Problem ten odgrywa kluczową rolę w zrozumieniu teorii obliczeń rozproszonych. Tematem rozważań pracy będzie analiza lokalności problemu, jednej z podstawowej własności rozproszonych algorytmów grafowych, w modelach LOCAL i SLOCAL. Znane jest już dokładne ograniczanie w modelu LOCAL oraz ograniczenie górne w modelu SLOCAL, natomiast standardowe dowody wykorzystują zaawansowane techniki. W pracy autorzy prezentują jednak nowe, elementarne i samowystarczalne dowody obydwu ograniczeń. 
14.10.40795 Boris Bukh Carnegie Mellon 
Informatyka Teoretyczna Extremal graphs without exponentiallysmall bicliques 
In 1954 Kővári, Sós, and Turán showed that every nvertex graph not containing K_{s,t} has at most O(n^{2−1/s}) edges. We construct graphs matching this bound with t≈9^{s}, improving on factorialtype bounds. In this talk, I will explain probabilistic and geometric ideas behind the construction. 
26.02.40686 Filip Jasiński 
Podstawy Informatyki A Universal Skolem Set of Positive Lower by Density Florian Luca, Joël Ouaknine and James Worrell 
The Skolem Problem asks to decide whether a given integer linear recurrence sequence (LRS) has a zero term. Decidability of this problem has been open for many decades, with little progress since the 1980s. Recently, a new approach was initiated via the notion of a Skolem set – a set of positive integers relative to which the Skolem Problem is decidable. More precisely, S is a Skolem set for a class L of integer LRS if there is an effective procedure that, given an LRS in L, decides whether the sequence has a zero in S. A recent work exhibited a Skolem set for the class of all LRS that, while infinite, had density zero. In the present work we construct a Skolem set of positive lower density for the class of simple LRS. 
22.07.24376 Grzegorz Gawryał 
Optymalizacja Kombinatoryczna On topological aspects of orientations 
Constrained graph orientation problem deals with directing graph edges such that graph vertices fulfills some conditions. Here, we are focusing on contant indegree orientations of maximal planar and similar classes of graphs. We analyse the relationship between such orientations and other combinatorial properties of these graphs, including the existence of particular decompositions into trees given by the famous Nash William's theorem. 
27.03.24364 Rafał Kilar 
Optymalizacja Kombinatoryczna Minimal NonTwoColorable Hypergraphs and Minimal Unsatisfiable Formulas 
It is known that the number of edges in a minimal non2colorable hypergraph is at least as high as the number of its vertices. We show the link between this and the fact that a minimal unsatisfiable CNF formula with n variables must contain at least n + 1 clauses. We show different proof of these facts and give infinite versions. We also analyze the structure of minimal unsatisfiable CNF formulas with exactly n variables and n + 1 clauses. 
08.06.21630 László Végh London School of Economics 
Informatyka Teoretyczna Interior point methods are not (much) worse than Simplex 
Whereas interior point methods provide polynomialtime linear programming algorithms, the running time bounds depend on bitcomplexity or condition measures that can be unbounded in the problem dimension. This is in contrast with the simplex method that always admits an exponential bound. We introduce a new polynomialtime pathfollowing interior point method where the number of iterations also admits a combinatorial upper bound O(2^{n} n^{1.5} log n) for an nvariable linear program in standard form. This complements previous work by Allamigeon, Benchimol, Gaubert, and Joswig (SIAGA 2018) that exhibited a family of instances where any pathfollowing method must take exponentially many iterations. The number of iterations of our algorithm is at most O(n^{1.5} log n) times the number of segments of any piecewise linear curve in the wide neighbourhood of the central path. In particular, it matches the number of iterations of any pathfollowing interior point method up to this polynomial factor. The overall exponential upper bound derives from studying the ‘max central path’, a piecewiselinear curve with the number of pieces bounded by the total length of 2n shadow vertex simplex paths. This is joint work with Xavier Allamigeon (INRIA/Ecole Polytechnique), Daniel Dadush (CWI Amsterdam), Georg Loho (U Twente), and Bento Natura (LSE/Georgia Tech). 
22.10.21520 Katarzyna Król 
Podstawy Informatyki Universal Skolem Sets by Florian Luca, Joel Ouaknine, and James Worrell 
It is a longstanding open problem whether there is an algorithm to decide the Skolem Problem for linear recurrence sequences, namely whether a given such sequence has a zero term. In this paper we introduce the notion of a Universal Skolem Set: an infinite subset S of the positive integers such that there is an effective procedure that inputs a linear recurrence sequence u = (u(n))n≥0 and decides whether u(n) = 0 for some n ∈ S . The main technical contribution of the paper is to exhibit such a set 
17.03.5211 Szymon Salabura 
Optymalizacja Kombinatoryczna Farey sequence and Graham’s conjectures 
The Farey sequence F_{n} is the set of rational numbers a/b with 0 ≤ a ≤ b ≤ n and gcd(a,b) = 1. In 1970, Graham proposed the following conjecture. Let a_{1}, a_{2}, ..., a_{n} be distinct positive integers. There exist indices i ≠ j, such that we have a_{i}/gcd(a_{i},a_{j}) ≥ n. In the paper, the authors show interesting properties of Farey sequence sets and how they are closely related to Graham's problems. 
20.11.5198 Katarzyna Kępińska 
Optymalizacja Kombinatoryczna ColorCritical Graphs on a Fixed Surface 
A graph G is kcolorcritical if G is not (k1)colorable, but every proper subgraph is. For S, an orientable surface other than the sphere, there are infinitely many kcolorcritical graphs if and only if 2<k<6. For k>4 there is the polynomial algorithm for deciding if a graph can be colored with k colors. In this paper, the authors prove those theorems and show some results for list coloring. 
27.03.5148 Tomasz Mazur, Katzper Michno 
Constrained Backward Time Travel Planning is in P 
Tematem rozważań będą sieci transportowe modelowane przez dynamiczne grafy, w których wierzchołkach dopuszczalne jest cofanie się w czasie, przy czym nie można cofnąć się o więcej niż pewną liczbę jednostek oraz jest ono obarczone kosztem wyrażonym pewną funkcją kosztu. Skupiamy się na dynamicznych grafach będącymi podgrafami ścieżki. W szczególności podajemy algorytmy wielomianowe dla różnych wariantów szukania trasy z jednego wierzchołka do drugiego minimalizującej w pierwszej kolejności opóźnienie (różnicę między czasem dotarcia a wyruszenia), a drugiej sumaryczny koszt cofania się w czasie. Warianty różnią się ograniczeniami na to, jak możemy cofać się w czasie. Badamy wpływ wyboru funkcji kosztu cofania na problem obliczania optymalnej trasy oraz podajemy warunki konieczne dla funkcji kosztu, aby optymalna trasa istniała. Na koniec podajemy optymalny algorytm online na szukanie optymalnej trasy dla funkcji kosztu będącej identycznością, w przypadku, gdy możemy cofać się dowolnie daleko w czasie. 
20.03.84602 Małgorzata Sulkowska Wrocław University of Technology 
Informatyka Teoretyczna Modularity of minorfree graphs 
Modularity is a wellestablished parameter measuring the presence of community structure in the graph. It was introduced by Newman and Girvan in 2004. Nowadays it is widely used as a quality function for community detection algorithms. The popular heuristic clustering algorithms (e.g., Louvain algorithm or Leiden algorithm) find a partition using modularitybased approach. We prove that a class of graphs with an excluded minor and with the maximum degree sublinear in the number of edges is maximally modular, that is, for every ε>0, the modularity of any graph in the class with sufficiently many edges is at least 1−ε. This completes the classification of maximally modular classes among all commonly considered subclasses of nowhere dense graphs with maximum degree sublinear in the number of edges.
Joint work with Michał Lasoń 
01.08.84492 Tomasz Buczyński 
Podstawy Informatyki The Variable Containment Problem by Stefan Kahrs 
The essentially free variables of a term t in some lambda calculus $FV(t)$ form the set $\{x : \forall t =_{beta} u \rightarrow x\in FV(u) \}. This set is signicant once we consider equivalence classes of \lambda terms rather than \lambda terms themselves as for instance in higher order rewriting. An important problem for (generalised) higher order rewrite systems is the variable containment problem. This property is important when we want to consider $t \rightarrow u$ as a rewrite rule and keep nstep rewriting decidable. Variable containment is in general not implied by $FV(t) \supseteq FV(u)$. We give a decision procedure for the variable containment problem of the second order fragment of $\lambda^\rightarrow$. For full $\lambda^\rightarrow$ we show the equivalence of variable containment to an open problem in the theory of PCF; this equivalence also shows that the problem is decidable in the third order case. 
26.12.68182 Filip Konieczny 
Optymalizacja Kombinatoryczna Factorizing regular graphs 
A qfactor of a kregular graph is its qregular subgraph covering all vertices. qfactorization is a partition of edges of a graph into disjoint qfactors. For qfactorization to exist it is necessary that q\mid k. It was proven that for even q the converse is also true  qdregular graph has a qfactorization. The paper investigates when qdregular graph with odd q admits qfactorization, given additional assumptions like planarity and/or high connectivity. 
31.08.68170 Hubert Dej 
Optymalizacja Kombinatoryczna On the Gap Structure of Sequences of Points on a Circle 
The problem of determining a sequence of points on the unit circle is considered, such that at any time t the lengths of the segments (sticks) resulting from splitting the circle at the locations set by the first t points are as equal as possible. The authors consider the sequence x_{k}=lg(2k1) mod 1 discovered and analyzed by De Brujin and Erdos in 1949 called the log stickbreaking strategy, proven to be optimal under 3 selected measures. The analysis of this sequence is extended by showing an interpretation in which log stickbreaking is a uniquely optimal strategy, and a more general framework is designed in which the optimality of this strategy can be explored. 
06.01.68120 Dominik Chmura, Jan Klimczak 
Derandomized Squaring of Graphs 
Praca opisuje "zderandomizowany" odpowiednik podnoszenia grafu do kwadratu. Nowa operacja zwiększa spójność grafu (mierzoną jako druga co do wielkości wartość własna macierzy sąsiedztwa) prawie tak dobrze jak potęgowanie grafu, zwiększając stopień grafu nie kwadratowo, a jedynie o stałą. Przedstawiono również kilka zastosowań tej konstrukcji, m.in. algorytm alternatywny do wyniku O. Reingolda, który pozwala deterministycznie badać osiągalność w grafach nieskierowanych w logarytmicznej pamięci. 
12.11.65436 Sophie Spirkl University of Waterloo 
Informatyka Teoretyczna Induced subgraphs and treewidth: Hfree graphs 
Treewidth is an important measure of the “complexity” of a graph, and as part of the Graph Minors project, Robertson and Seymour characterized unavoidable subgraphs of graphs with large treewidth. Here we are interested in unavoidable induced subgraphs instead. In this context, Lozin and Razgon characterized all finite families F of graphs such that Ffree graphs have bounded treewidth. I will talk about related result, characterizing which graphs H have the property that excluding H as well as four families of large treewidth (a complete graph, a complete bipartite graph, all subdivisions of a wall, and their line graphs) as induced subgraphs leads to a class of bounded treewidth. Joint work with Tara Abrishami, Bogdan Alecu, Maria Chudnovsky, and Sepehr Hajebi 
28.03.65327 Piotr Kubaty 
Podstawy Informatyki Decision Problems for SecondOrder Holonomic Recurrences by Eike Neumann, Joel Ouaknine and James Worrel 
We study decision problems for sequences which obey a secondorder holonomic recurrence of the form $f (n + 2) = P (n)f (n + 1) + Q(n)f (n)$ with rational polynomial coefficients, where P is nonconstant, Q is nonzero, and the degree of Q is smaller than or equal to that of P . We show that existence of infinitely many zeroes is decidable. We give partial algorithms for deciding the existence of a zero, positivity of all sequence terms, and positivity of all but finitely many sequence terms. If Q does not have a positive integer zero then our algorithms halt on almost all initial values (f (1), f (2)) for the recurrence. We identify a class of recurrences for which our algorithms halt for all initial values. We further identify a class of recurrences for which our algorithms can be extended to total ones. 
21.08.49017 Kamil Galewski 
Optymalizacja Kombinatoryczna Majority colorings of sparse digraphs 
A Majority kcoloring of a directed graph is an assignment of k colors to its vertices in such a way that every vertex has the same color as at most half of its outneighbors. It is known that every digraph is majority 4colorable, but it remains an open question whether every digraph is majority 3colorable. The authors of the paper validate this conjecture for digraphs with a chromatic number at most 6 and digraphs with a dichromatic number at most 3. They also prove analogous theorems for list coloring: digraphs with a list chromatic number at most 6 or list dichromatic number at most 3 are majority 3choosable. The paper also investigates which digraphs are majority 2colorable: the authors show that digraphs without directed odd cycles are majority 2colorable, but in general deciding whether a given digraph is majority 2colorable is NPcomplete. The last result proposed in this paper is proof that every digraph has a fractional majority of 3.9602coloring. 
26.04.49005 Piotr Kaliciak 
Optymalizacja Kombinatoryczna A counterexample to the lights out problem 
In the basic Lights Out problem, we are given the undirected graph of turnedoff lights, and our goal is to turn on all the lights. In the generalized version of this problem, our mission is to assign every vertex a value from 0 to p, such that for every vertex, the sum of values in its neighbors is equal to 0 mod p. The authors not only prove that a generalized version of this problem isn't always solvable but also they show conditions, under which the problem has a solution. 
31.08.48954 Bartłomiej Błoniarz, Hubert Dej 
More on ChangeMaking and Related Problems 
Mając do dyspozycji zbiór n typów monet o wartościach całkowitych oraz wartość docelową t, w problemie wydawania reszty (changemaking) szukamy minimalnej liczby monet, które sumują się do t, zakładając możliwość wykorzystania dowolnej liczby monet każdego typu. W bardziej ogólnej wersji tego problemu (w wersji alltargets), chcemy obliczyć wyniki dla wszystkich wartości docelowych 0, 1, ..., t. Klasyczny algorytm dynamiczny rozwiązuje ten problem w czasie O(nt). W publikacji autorzy przedstawiają szereg nowych wyników dotyczących problemu wydawania reszty i innych pokrewnych problemów. Dla u – wartości największej z monet (wagi najcięższego przedmiotu w przypadku problemu plecakowego) pokażemy algorytmy o złożoności: 
08.07.46271 Hoang La Jagiellonian 
Informatyka Teoretyczna On Barnette's Conjecture for directed graphs 
Knauer and Valicov showed that multiples conjectures from seemingly different problems all fit into the same framework of cuts in matchings of 3connected cubic graphs. They unite Tait's, Barnette's, and Tutte's conjectures on Hamiltonicity in cubic graphs, NeumannLara's on the dichromatic number of planar graphs, and Hochstättler's on contraction of even digraphs. More precisely, these are all equivalent to conjectures of the form ''Every 3connected, cubic, bipartite/planar/directed graph contains a perfect matching without (directed) cut''. If you drop two of these restrictions (bipartite, planar, directed), then the conjecture is false. If you drop one or none, then the conjecture remains open. We are investigating the dual version of the conjecture with all three restrictions, namely ''Every directed planar Eulerian triangulation can be vertexpartitioned into two acyclic sets''. This new framework can be useful as a planar Eulerian triangulation has an unique partition into three independent sets. 
20.11.46161 Aleksander Katan 
Podstawy Informatyki The combinator M and the Mockingbird lattice by Samuele Giraudo 
We study combinatorial and order theoretic structures arising from the fragment of combinatory logic spanned by the basic combinator M. This basic combinator, named as the Mockingbird by Smullyan, is defined by the rewrite rule Mx_1 → x_1x_1. We prove that the reflexive and transitive closure of this rewrite relation is a partial order on terms on M and that all connected components of its rewrite graph are Hasse diagram of lattices. This last result is based on the introduction of new lattices on duplicative forests, which are sorts of treelike structures. These lattices are not graded, not selfdual, and not semidistributive. We present some enumerative properties of these lattices like the enumeration of their elements, of the edges of their Hasse diagrams, and of their intervals. These results are derived from formal power series on terms and on duplicative forests endowed with particular operations. 
15.04.29852 Rafał Pyzik 
Optymalizacja Kombinatoryczna Every graph contains a linearly sized induced subgraph with all degrees odd 
It was proven by Gallai, that every undirected graph on n vertices contains an induced subgraph on at least n/2 vertices with all degrees even. It is natural to ask a similar question for odd degrees. It was conjectured, that in every graph on n vertices, without isolated vertices, we can find an induced subgraph on at least cn vertices with all degrees odd for some constant c>0. We will prove this conjecture for c=1/10000. 
20.12.29839 Justyna Jaworska 
Optymalizacja Kombinatoryczna The Lovász Local Lemma is Not About Probability 
Since the original statement of Lovas Local Lemma in 1973, multiple variants of the lemma with different levels of complexity have been formulated. We will present a general theorem from which most known variants of LLL follow. Additionally, the results will be generalized to supermodular functions rather than probability measures, allowing a wider range of applications. 
03.03.27106 Wojciech Czerwiński University of Warsaw 
Informatyka Teoretyczna Reachability problem in Vector Addition Systems 
Recently we managed with coauthors to settle the complexity of the reachability problem for Vector Addition Systems (VASes) to be Ackermanncomplete. Despite of that the combinatorics of VASes still remains mysterious and there is a bunch of very natural problems about which we know shockingly little. The focus of my talk will be on tools. I will present techniques, which led to the proof of Ackermannhardness for the reachability problem and which hopefully may help in solving the remaining challenges. 
09.12.10686 Jędrzej Kula 
Optymalizacja Kombinatoryczna Complete minors and average degree – a short proof 
We call graph H a minor of graph G, if there exists such a sequence of deletions of vertices, deletions of edges, or contradictions of edges, which transforms G into H. The authors of the paper created a short proof of the result of Kostochka and of Thomasen. The proven theorem states that for every graph whose vertices have the average degree d the graph itself also contains a complete minor of order Ω(d/sqrt(log(d))). 
14.08.10674 Krzysztof Ziobro 
Optymalizacja Kombinatoryczna Note on the Lamp Lighting Problem 
In the most basic version of the Lamp Lighting Problem, we are given an undirected graph G. We can toggle light in a chosen vertex and all of its neighbors. Our goal is to decide if it is possible to turn on the light in all vertices by performing only moves as described. Authors prove that it is always possible and explore other variants of the problem such as the directed case or the problem of checking if all lighting configurations are possible to achieve. 
26.10.7940 Jędrzej Hodor Jagiellonian 
Informatyka Teoretyczna Dimension of planar posets 
It is a longstanding open problem if posets with a planar cover graph are dimbounded (meaning that large dimension yields a large standard example as a subposet). This notion is the posets' counterpart of the wellstudied χboundedness in the graph theory. In my talk, I will focus on summarizing the new progress in this area. The dimboundedness was recently proved for posests with planar diagram and for posets with planar cover graph and a zero. I will try to sketch some ideas standing behind these results. The other interesting related question in the area is the following. Suppose that a planar poset has a large standard example as a subposet, then, how does this standard example look like? There are two canonical constructions of planar posets with large standard example contained, namely, Kelly's example and Trotter's wheel. We believe that these are (in a structural sense) the only ways to draw a standard example on the plane. For example, we proved that a poset with a planar cover graph, a zero, and large dimension contains a large Trotter's wheel. The list of coauthors of substantial results that are going to be discussed in my talk: P.Micek, M.Seweryn, H.S.Blake, W.T.Trotter 
20.04.76384 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna On a Problem of Steinhaus 
Let N be a positive integer. A sequence X=(x_{1},x_{2},…,x_{N}) of points in the unit interval [0,1) is piercing if {x_{1},x_{2},…,x_{n}}∩[i/n,(i+1)/n)≠∅ holds for every n=1,2,…,N and every i=0,1,…,n−1. In 1958 Steinhaus asked whether piercing sequences can be arbitrarily long. A negative answer was provided by Schinzel, who proved that any such sequence may have at most 74 elements. This was later improved to the best possible value of 17 by Warmus, and independently by Berlekamp and Graham. We study a more general variant of piercing sequences. Let f(n)≥n be an infinite nondecreasing sequence of positive integers. A sequence X=(x_{1},x_{2},…,x_{f(N)}) is fpiercing if {x_{1},x_{2},…,x_{f(n)}}∩[i/n,(i+1)/n)≠∅ holds for every n=1,2,…,N and every i=0,1,…,n−1. A special case of f(n)=n+d, with d a fixed nonnegative integer, was studied by Berlekamp and Graham. They noticed that for each d≥0, the maximum length of any (n+d)piercing sequence is finite. Expressing this maximum length as s(d)+d, they obtained an exponential upper bound on the function s(d), which was later improved to s(d)=O(d^{3}) by Graham and Levy. Recently, Konyagin proved that 2d⩽s(d)<200d holds for all sufficiently big d. Using a different technique based on the Farey fractions and stickbreaking games, we prove here that the function s(d) satisfies ⌊c_{1}d⌋⩽s(d)⩽c_{2}d+o(d), where c_{1}=ln2/(1−ln2)≈2.25 and c_{2}=(1+ln2)/(1−ln2)≈5.52. We also prove that there exists an infinite fpiercing sequence with f(n)=γn+o(n) if and only if γ≥1/ln2≈1.44. This is joint work with Marcin Anholcer, Jarosław Grytczuk, Grzegorz Gutowski, Jakub Przybyło, Rafał Pyzik, and Mariusz Zając. 
26.08.76333 Łukasz Selwa, Juliusz Wajgelt 
Token sliding on graphs of girth five 
Intuicyjnie problem Token Sliding możemy rozumieć jako grę, w której otrzymujemy graf oraz żetony ustawione na jego wierzchołkach. Pytamy, czy da się uzyskać zadany stan końcowy poprzez przesuwanie żetonów wzdłuż krawędzi grafu tak, że w żadnym momencie dwa żetony nie łączyła wspólna krawędź. Formalnie mamy na wejściu graf G oraz zbiory niezależne wierzchołków I_{s}, I_{t} i chcemy stwierdzić czy istnieje sekwencja I_{1}, …, I_{s} zbiorów niezależnych w G taka, że I_{1} = I_{s}, I_{l} = I_{t} oraz I_{i} ∆ I_{i+1} = {u, v} \in E(G). Wykazano wcześniej, że dla grafów o talii (ang. girth) 4 lub mniejszej problem Token Sliding jest W[1]trudny. Prezentujemy dowód z pracy „Token sliding on graphs of girth five”, że dla grafów o talii 5 lub większej problem Token Sliding jest fixedparameter tractable (FPT). 
02.07.73650 Dömötör Pálvölgyi Eötvös Loránd University 
Informatyka Teoretyczna At most 3.55^n stable matchings 
We improve the upper bound for the maximum possible number of stable matchings among n jobs and n applicants (formerly known as n men and n women) from 131072^{n} to 3.55^{n}. To establish this bound, we state a novel formulation of a certain entropy bound that is easy to apply and may be of independent interest in counting other combinatorial objects. Joint work with Cory Palmer 
15.11.73540 Julian Leśniak 
Podstawy Informatyki Tight rank lower bounds for the Sherali–Adams proof system by Stefan Dantchev, Barnaby Martin and Mark Rhodes 
We consider a proof (more accurately, refutation) system based on the Sherali–Adams (SA) operator associated with integer linear programming. If F is a CNF contradiction that admits a Resolution refutation of width k and size s, then we prove that the SA rank of F is ≤ k and the SA size of F is \leq (k + 1)s + 1. We establish that the SA rank of both the Pigeonhole Principle PHP_n^{n1} and the Least Number Principle LNP_n is n − 2. Since the SA refutation system rank simulates the refutation system of Lovász–Schrijver without semidefinite cuts (LS), we obtain as a corollary linear rank lower bounds for both of these principles in LS. 
14.12.57218 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna A Note on Generalized Majority Colorings 
A majority coloring of a directed graph is a vertex coloring in which each vertex has the same color as at most half of its outneighbors. In this note we simplify some proof techniques and generalize previously known results on various generalizations of majority coloring. In particular, our unified and simplified approach works for paintability  an online analog of list coloring. This is joint work with Marcin Anholcer, Jarosław Grytczuk, Grzegorz Gutowski, Jakub Przybyło, Mariusz Zając. 
20.04.57168 Julia Biały, Zofia Glapa 
All Paths Lead to Rome 
Roma to łamigłówka rozgrywana na składającej się z kwadratowych pól planszy rozmiaru n x n. Pola pogrupowane są w obszary składające się z co najwyżej 4 sąsiadujących ze sobą komórek, z których każda albo jest wypełniona, albo ma zostać wypełniona strzałką w jednym z 4 kierunków. Celem gry jest wypełnienie wszystkich komórek strzałkami tak by w każdym obszarze była co najwyżej jedna strzałka w danym kierunku i by podążając zgodnie ze strzałkami można było dojść do wyróżnionego pola Roma z każdego pola na planszy. Autorzy pracy rozważają złożoność obliczeniową gry i pokazują, że uzupełnienie planszy zgodnie z zasadami jest problemem NPzupełnym, zliczenie możliwych rozwiązań jest #P zupełne oraz wyznaczenie liczby zadanych z góry strzałek koniecznych by gra miała tylko jedno rozwiązanie jest Σ^{P2}  zupełne. Praca dowodzi też, że zakładając prawdziwość ETH problem uzupełnienia planszy dla danej instancji gry nie może być rozwiązany w czasie O(2^{o(n)}). Omawia także algorytm programowania dynamicznego rozwiązujący planszę gry, opierający się na strukturach Catalana. 
24.02.54485 Vida Dujmović University of Ottawa 
Informatyka Teoretyczna Stack and Queue layouts 
This talk will focus on two graph parameters: stack layouts (aka. book embeddings) and queue layouts of graphs. I will talk about the history of these two graph parameters, their still not fully understood relationship and some recent breakthroughs. 
11.07.54375 Juliusz Wajgelt 
Podstawy Informatyki Short Proofs of Normalization for the simplytyped λcalculus, permutative conversions and Godel’s T by Felix Joachimski and Ralph Matthes 
Inductive characterizations of the sets of terms, the subset of strongly normalizing terms and normal forms are studied in order to reprove weak and strong normalization for the simply typed λcalculus and for an extension by sum types with permutative conversions. The analogous treatment of a new system with generalized applications inspired by generalized elimination rules in natural deduction, advocated by von Plato, shows the flexibility of the approach which does not use the strong computability/candidate style `a la Tait and Girard. It is also shown that the extension of the system with permutative conversions by (\eta) rules is still strongly normalizing, and likewise for an extension of the system of generalized applications by a rule of “immediate simplification”. By introducing an infinitely branching inductive rule the method even extends to Godel’s T 
08.08.38053 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna Recoloring Unit Interval Graphs with Logarithmic Recourse Budget 
We study the problem of coloring a unit interval graph that changes dynamically. In our model the unit intervals are added or removed one at a time and have to be colored immediately so that no two overlapping intervals share the same color. After each update, only a limited number of intervals are allowed to be recolored. The limit on the number of recolorings per update is called the recourse budget. In this paper, we show, that if the graph remains kcolorable at all times, and the updates consist of insertions only, then we can achieve the amortized recourse budget of O(k^{7}logn) while maintaining a proper coloring with k colors. This is an exponential improvement over the result in [Bosek et al., Recoloring Interval Graphs with Limited Recourse Budget. SWAT 2020] in terms of both k and n. We complement this result by showing the lower bound of Ω(n) on the amortized recourse budget in the fully dynamic setting. Our incremental algorithm can be efficiently implemented. As a byproduct of independent interest, we include a new result on coloring proper circulararc graphs. Let L be the maximum number of arcs intersecting in one point for some set of unit circular arcs A. We show that if there is a set A′ of nonintersecting unit arcs of size L^{2}−1 such that A∪A′ does not contain L+1 arcs intersecting in one point, then it is possible to color A with L colors. This complements the work on unit circular arc coloring, which specifies sufficient conditions needed to color A with L+1 colors or more. This is joint work with Anna ZychPawlewicz. 
21.10.35319 Friedrich Eisenbrand École Polytechnique Fédérale de Lausanne 
Informatyka Teoretyczna Integer programming with few constraints 
The talk features a survey as well as recent new results on two independent approaches to derive efficient algorithms for integer programming, namely algorithms based on the geometry of numbers and dynamic programming techniques, with an extra spotlight on the case in which the number of constraints (apart from bounds on the variables) is small. We will highlight open problems and possible future directions. The presented results of the speaker have been jointly achieved with Daniel Dadush, Thomas Rithvoss and Robert Weismantel. 
05.03.35210 Mateusz Olszewski 
Podstawy Informatyki Implicit computation complexity in higherorder programming languages (A Survey in Memory of Martin Hofmann) by Ugo Dal Lago 
This paper is meant to be a survey about implicit characterizations of complexity classes by fragments of higherorder programming languages, with a special focus on type systems and subsystems of linear logic. Particular emphasis will be put on Martin Hofmann’s contributions to the subject, which very much helped in shaping the field. 
02.04.18888 Jędrzej Hodor 
Optymalizacja Kombinatoryczna Dimension of planar posets 
It is a longstanding open problem if planar posets are dimbounded (an analog of chibounded in the graph theory). I summarize recent progress on this problem. We explore different notions of what does it mean for posets to be planar. Finally, I will sketch the proof of dimboundedness in the case of posets with planar cover graphs and a zero. 
15.06.16154 Paul Seymour Princeton University 
Informatyka Teoretyczna Getting closer to the ErdősHajnal conjecture 
A general nvertex graph may not have a clique or stable set larger than O(log n), but excluding an induced subgraph makes a significant difference. The ErdősHajnal conjecture (from 1977) says that for every graph H, there exists c such that every Hfree graph G (that is, not containing H as an induced subgraph) has a clique or stable set of size at least G^{c}. This is still open, and is notoriously intractable.

11.03.43533 Piotr Micek Jagiellonian 
Informatyka Teoretyczna Boolean dimension and dimboundedness of posets with a unique minimal element whose cover graphs are planar 
In 1989, Nešetřil and Pudlák posed the following challenging question: Do planar posets have bounded Boolean dimension? We show that every poset with a planar cover graph and a unique minimal element has Boolean dimension at most 13. As a consequence, we are able to show that there is a reachability labeling scheme with labels consisting of O(log n) bits for planar digraphs with a single source. The best known scheme for general planar digraphs uses labels with O(log^{2}n) bits [Thorup, JACM 2004], and it remains open to determine whether a scheme using labels with O(log n) bits exists. The Boolean dimension result is proved in tandem with a second result showing that the dimension of a poset with a planar cover graph and a unique minimal element is bounded by a linear function of its standard example number. However, one of the major challenges in dimension theory is to determine whether dimension is bounded in terms of standard example number for all posets with planar cover graphs. 
01.10.27105 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna The 1/3  2/3 conjecture 
A given pair of two incomparable elements x, y in poset P is called balanced if, of all line extensions P, the element x lies above y by at most 2/3 and on at least 1/3 of all extensions of the poset P. The 1/3  2/3 conjecture says that any poset that is not linear has a balanced pair. The talk presents basic definitions and an overview of the most important results in this field. 
04.11.24367 Michał Wrona Jagiellonian 
Informatyka Teoretyczna Local consistency methods in Solving CSPs and CSPlike problems over omegacategorical structures 
FederVardi conjecture has been settled independently by Dmitriy Zhuk and Andrei Bulatov. What is perhaps even more interesting, though, is that they not only confirmed the complexity (FederVardi) conjecture, i.e., CSP(B) for a finite structure B is either in P or it is NPcomplete, but they also confirmed the algebraic dichotomy conjecture describing tractable B in terms of operations preserving B. A similar algebraic dichotomy conjecture called an infinite algebraic dichotomy conjecture has been established for CSP(B) over firstorder reducts B of finitely bounded homogeneous structures, all of which are in particular omegacategorical. Despite recent advances towards solving this dichotomy, it still seems to be wide open. One of the reasons is probably that local consistency and similar algorithmic techniques are in this context not yet fully understood. This step seems to be crucial since the characterization of finitedomain CSP solvable by local consistency is considered as a major step towards the resolution of the dichotomy. In this talk, I will survey the results on the local consistency methods in solving CSP and CSPlike problems over omegacategorical structures. 
29.04.24258 Karolina Gontarek 
Podstawy Informatyki THE TU–DENG CONJECTURE HOLDS ALMOST SURELY by LUKAS SPIEGELHOFER AND MICHAEL WALLNER 
The Tu–Deng Conjecture is concerned with the sum of digits w(n) of n in base 2 (the Hamming weight of the binary expansion of n) and states the following: assume that k is a positive integer and t \in {1, . . . , 2^k − 2}. Then #\{ (a, b) ∈ {0, . . . , 2k − 2}^2 : a + b ≡ t mod 2^k − 1, w(a) + w(b) < k \} \leq ≤ 2^{k1}

03.09.7963 Krzysztof Pióro 
Optymalizacja Kombinatoryczna Brooks' Theorem via the AlonTarsi Theorem 
Brooks' Theorem states that every connected graph G with maximum degree d is dcolorable unless G is an odd cycle or a complete graph. It is one of the most famous theorem on graph colorings. In the paper, the author presents yet another proof of this theorem. This proof is based on AlonTarsi Theorem and it remains valid in a more general choosability version of Brooks' theorem. 
26.05.7940 Demian Banakh 
Optymalizacja Kombinatoryczna Separating polynomial χboundedness from χboundedness 
A class of graphs is hereditary χbounded if it is closed under taking induced subgraphs and every graph’s chromatic number is bounded by some function of its clique number. A wellknown recently stated open question has been whether for every hereditary χbounded class that function can be chosen to be a polynomial. We provide a counterexample for it; namely, for any function f, we construct a hereditary χbounded class containing graphs of large chromatic number. In particular, for any polynomial f, such a class exists, which answers the aforementioned question negatively. 
22.08.7885 Jędrzej Kula, Maciej Nemś 
Towards SubQuadratic Diameter Computation in Geometric Intersection Graphs 
Grafy przecięć geometrycznych to grafy, gdzie wierzchołki odpowiadają figurom geometrycznym w dwymiarowej przestrzeni euklidesowej. Mogą do to być na przykład kule, kwadraty, hiperkostki. Krawędź między dwoma wierzchołkami istnieje, jeśli dwie figury przecinają się. Jest to typowy sposób modelowania na przykład komunikacji bezprzewodowej. W pracy autorzy zajmują się obliczaniem średnicy tego typu grafów. Dokładniej rozważają to, czy da się ten problem rozwiązać w czasie poniżej kwadratowym względem liczby wierzchołków. Na referacie zostanie pokazany dowód algorytmu o czasie działania O(n logn) dla sprawdzania, czy średnica jest mniejsza bądź równa 2 dla grafów przecięć kwadratów jednostkowych równoległych do osi. Następnie zostanie pokazane dolne ograniczenie szukania średnicy dla kul jednostkowych na bazie Orthogonal Vectors Hypothesis. Ograniczenie to pokazuje, że nie ma algorytmów pod kwadratowych przy założeniu Orthogonal Vectors Hypothesis. 
22.12.5092 Juliusz Wajgelt 
Podstawy Informatyki EFFICIENT FULL HIGHERORDER UNIFICATION by PETAR VUKMIROVIC, ALEXANDER BENTKAMP, AND VISA NUMMELIN 
We developed a procedure to enumerate complete sets of higherorder unifiers based on work by Jensen and Pietrzykowski. Our procedure removes many redundant unifiers by carefully restricting the search space and tightly integrating decision procedures for fragments that admit a nite complete set of uni ers. We identify a new such fragment and describe a procedure for computing its uni ers. Our uni cation procedure, together with new higherorder term indexing data structures, is implemented in the Zipperposition theorem prover. Experimental evaluation shows a clear advantage over Jensen and Pietrzykowski's procedure. 
09.05.73673 Bartosz Podkanowicz 
Optymalizacja Kombinatoryczna Digraphs are 2weight choosable 
Consider following problem. We are given a digraph. For every edge, there are 2 options to choose a weight for this edge. We want to pick the weights of edges in a specific way. After picking weights we color vertices. The color of the vertex will be the sum of incoming edges minus the sum of outgoing edges from that vertex. We show that it is always possible to choose weights of edges such that the resulting coloring will be proper. This property is called 2weightchoosability. 
30.01.73650 Łukasz Selwa 
Optymalizacja Kombinatoryczna A better lower bound on average degree of 4listcritical graphs 
A graph G is klistcritical if it is not (k1)choosable, but every proper subgraph of G is (k1)choosable. We give a new lower bound for the average degree of incomplete klistcritical graphs and online klistcritical graphs. The presented bound improves the earlier known lower bounds for k = 4,5,6.

29.04.73595 Grzegorz Gawryał, Rafał Kilar 
Dynamic Time Warping Under Translation: Approximation Guided by SpaceFilling Curves 
05.03.70912 Szymon Toruńczyk University of Warsaw 
Informatyka Teoretyczna Ordered graphs of bounded twinwidth and monadically NIP graph classes 
We establish a list of characterizations of bounded twinwidth for hereditary classes of totally ordered graphs: as classes of at most exponential growth studied in enumerative combinatorics, as monadically NIP classes studied in model theory, as classes that do not transduce the class of all graphs studied in finite model theory, and as classes for which model checking firstorder logic is fixedparameter tractable studied in algorithmic graph theory. This has several consequences.First, it allows us to show that every hereditary class of ordered graphs either has at most exponential growth, or has at least factorial growth. This settles a question first asked by Balogh, Bollobás, and Morris [Eur. J. Comb. '06] on the growth of hereditary classes of ordered graphs, generalizing the StanleyWilf conjecture/MarcusTardos theorem. Second, it gives a fixedparameter approximation algorithm for twinwidth on ordered graphs. Third, it yields a full classification of fixedparameter tractable firstorder model checking on hereditary classes of ordered binary structures. Fourth, it provides a modeltheoretic characterization of classes with bounded twinwidth. Those results are joint work with Bonnet, Giocanti, Ossona de Mendez, Simon, Thomasse, accepted to STOC'22. Time permitting, I will also discuss the more general landscape of monadically NIP graph classes, generalizing both nowhere dense classes and classes of bounded twinwidth. 
29.08.70802 Vitaliy Mysak 
Podstawy Informatyki An Introduction to the Clocked Lambda Calculus byJörg Endrullis, Dimitri Hendriks, Jan Willem Klop, and Andrew Polonsky 
We give a brief introduction to the clocked λcalculus, an extension of the classical λcalculus with a unary symbol τ used to witness the βsteps. In contrast to the classical λcalculus, this extension is infinitary strongly normalising and infinitary confluent. The infinitary normal forms are enriched Lévy–Longo Trees, which we call clocked Lévy–Longo Trees. 
03.01.54508 Rafał Kilar 
Optymalizacja Kombinatoryczna Lower Bounds on the Online Chain Partitioning of Semiorders with Representation 
An online chain partitioning algorithm is presented with one element of a poset at a time and has to assign it to a chain, partitioning the poset. We consider posets with elements represented by unit length intervals. The paper slightly improves the lower bound for the minimum number of chains needed by an online algorithm to partition these posets from ⌊3/2 w⌋ to ⌈3/2 w⌉. 
24.09.54484 Krzysztof Potępa 
Optymalizacja Kombinatoryczna UnitMonge matrices and seaweed braids 
Simple unitMonge matrices form a special subclass of square matrices, which can be represented implicitly in linear space by permutations. Somewhat surprisingly, the subclass is closed under distance multiplication. We will show connection between simple unitMonge matrices and seaweed braids: braids in which each pair of strings crosses at most once. In particular, distance multiplication is equivalent to a "combing procedure", where doublecrossings in braid are removed. We will discuss applications of these methods to a few subsequence problems. In particular, the combing procedure can be exploited to obtain an elegant algorithm for allsubstring LCS problem. 
22.12.54429 Andrii Orap, Maksym Zub 
Grundy Distinguishes Treewidth from Pathwidth 
Strukturalne parametry grafów, takie jak treewidth, pathwidth i cliquewidth, są głównym tematem badań sparametryzowanej złożoności. Głównym celem badań w tej dziedzinie jest zrozumienie „ceny ogólności” tych szerokości: kiedy przechodzimy od pojęć bardziej restrykcyjnych do bardziej ogólnych, jakie są problemy, w których złożoność pogarsza się z fixedparameter tractable do intractable? Ten rodzaj pytania jest już bardzo dobrze zbadany, ale, co jest dość uderzające, algorytmiczna granica między dwoma (prawdopodobnie) najbardziej centralnymi pojęciami szerokości (notacjami), treewidth i pathwidth, jest nadal niezrozumiała: obecnie nie jest znany żaden naturalny problem na grafie, który byłby Wtrudny dla jednego, ale FPT dla drugiego. Rzeczywiście, zaskakującym rozwojem ostatnich kilku lat była obserwacja, że: w przypadku wielu najbardziej paradygmatycznych problemów ich złożoność dla tych dwóch parametrów w rzeczywistości dokładnie się pokrywają, pomimo faktu, że szerokość drzewa jest parametrem o wiele bardziej ogólnym. W ten sposób wydaje się, że dodatkowa ogólność szerokości drzewa nad szerokością ścieżki często przychodzi „za darmo”. Naszym głównym wkładem w ten artykuł jest odkrycie pierwszego naturalnego przykładu, w którym ta ogólność ma wysoką cenę. Rozważamy Grundy Coloring, wariację kolorowania, w której próbujemy obliczyć najgorsze możliwe kolorowanie, które można przypisać do grafu przez zachłanny algorytm FirstFit . Pokazujemy, że ten dobrze zbadany problem jest parametryzowany (FPT) przez pathwidth; jednakże to staje się znacznie trudniejsze (W[1]hard), gdy jest sparametryzowany przez treewidth. Ponadto pokazujemy, że Grundy Coloring sprawia, że jest drugi skok złożoności dla bardziej ogólnych szerokości, gdy staje się paraNPhard dla cliquewidth. Dlatego Grundy Coloring ładnie oddaje złożoność kompromisów między trzema najlepiej zbadanymi parametrami. Uzupełniając obraz, pokazujemy, że Grundy Coloring jest parametryzowane przez FPT według modularwidth. 
29.10.51746 Rose McCarty University of Warsaw 
Informatyka Teoretyczna Circuit decompositions of grouplabelled graphs 
This talk focuses on Eulerian graphs whose arcs are directed and labelled in a group. Each circuit yields a word over the group, and a circuit is nonzero if this word does not evaluate to 0. We give a precise minmax theorem for the following problem. Given a vertex v, what is the maximum number of nonzero circuits in a circuitdecomposition where each circuit begins and ends at v? This is joint work with Jim Geelen and Paul Wollan. Our main motivation is a surprising connection with vertexminors which is due to Bouchet and Kotzig. 
23.04.51637 Jan Koscisz 
Podstawy Informatyki Functionsasconstructors higherorder unification: extended pattern unification by Tomer Libal and Dale Miller 
Unification is a central operation in constructing a range of computational logic systems based on firstorder and higherorder logics. Firstorder unification has several properties that guide its incorporation in such systems. In particular, firstorder unification is decidable, unary, and can be performed on untyped term structures. None of these three properties hold for full higherorder unification: unification is undecidable, unifiers can be incomparable, and termlevel typing can dominate the search for unifiers. The socalled pattern subset of higherorder unification was designed to be a small extension to firstorder unification that respects the laws governing λbinding (i.e., the equalities for α, β, and ηconversion) but which also satisfied those three properties. While the pattern fragment of higherorder unification has been used in numerous implemented systems and in various theoretical settings, it is too weak for many applications. This paper defines an extension of pattern unification that should make it more generally applicable, especially in proof assistants that allow for higherorder functions. This extension’s main idea is that the arguments to a higherorder, free variable can be more than just distinct bound variables. In particular, such arguments can be terms constructed from (sufficient numbers of) such bound variables using term constructors and where no argument is a subterm of any other argument. We show that this extension to pattern unification satisfies the three properties mentioned above. 
28.08.35342 Jacek Salata 
Optymalizacja Kombinatoryczna A Short Proof of NashWilliams' Theorem for the Arboricity of a Graph 
NashWilliams theorem (treepacking theorem) is a classical result due to NashWilliams (1961) that characterizes graphs with k edgedisjoint spanning trees. In the seminar, I will present a short and elegant proof of the theorem. 
21.05.35319 Kamil Galewski 
Optymalizacja Kombinatoryczna Bears with Hats and Independence Polynomials 
The hat guessing game is a game in which bears sit in the vertices of an undirected graph. A demon puts hats on the bears' heads. Each hat has one of the h available colors. Each bear sees only the hat colors of his neighbors. The goal of the bears is to guess the color of their hats  each bear has g tries to guess his hat color. The bears win if at least one of them has guessed the color of his hat correctly. This paper describes the relationship between the hat guessing game and the independence polynomial of graphs. 
23.06.32581 Michał Seweryn Jagiellonian 
Informatyka Teoretyczna Forcing walls with divisibility constraints 
An nwall is a graph obtained from the square grid with n rows and 2n columns by deleting every odd vertical edge in every odd row and even vertical edge in every even row, then deleting the two resulting vertices of degree 1, and finally subdividing each edge any number of times. Thomassen showed that there exists a function f(n,m) such that every f(n,m)wall contains an nwall such that every path between two branch vertices has length divisible by m. We study the asymptotics of the optimal such function f(n,m). For odd m we show that f(n,m) = O(n·poly(m)). In the case m=2, we obtain a bound f(n, 2) = O(n·log n). This is joint work with Piotr Micek, Raphael Steiner and Sebastian Wiederrecht. 
28.10.32471 Roch Wójtowicz 
Podstawy Informatyki SHARP THRESHOLDS OF GRAPH PROPERTIES, AND THE kSAT PROBLEM by EHUD FRIEDGUT AND AN APPENDIX BY JEAN BOURGAIN 
Consider G(n, p) to be the probability space of random graphs on n vertices with edge probability p. We will be considering subsets of this space defined by monotone graph properties. A monotone graph property P is a property of graphs such that
A monotone symmetric family of graphs is a family defined by such a property. One of the first observations made about random graphs by Erdos and Renyi in their seminal work on random graph theory [12] was the existence of threshold phenomena, the fact that for many interesting properties P , the probability of P appearing in G(n, p) exhibits a sharp increase at a certain critical value of the parameter p. Bollob ́as and Thomason proved the existence of threshold functions for all monotone set properties ([6]), and in [14] it is shown that this behavior is quite general, and that all monotone graph properties exhibit threshold behavior, i.e. the probability of their appearance increases from values very close to 0 to values close to 1 in a very small interval. More precise analysis of the size of the threshold interval is done in [7]. This threshold behavior which occurs in various settings which arise in combinatorics and computer science is an instance of the phenomenon of phase transitions which is the subject of much interest in statistical physics. One of the main questions that arises in studying phase transitions is: how “sharp” is the transition? For example, one of the motivations for this paper arose from the question of the sharpness of the phase transition for the property of satisfiability of a random kCNF Boolean formula. Nati Linial, who introduced me to this problem, suggested that although much concrete analysis was being performed on this problem the best approach would be to find general conditions for sharpness of the phase transition, answering the question posed in [14] as to the relation between the length of the threshold interval and the value of the critical probability. 
22.04.16177 Szymon Salabura 
Optymalizacja Kombinatoryczna Contact graphs of ball packings 
A contact graph of a ball packing is a graph with nonintersecting balls as vertices and edges between pairs of tangent balls. In the seminar, we will focus on the upper bounds for the average degree of such graphs in any number of dimensions. 
13.01.16154 Mateusz Pach 
Optymalizacja Kombinatoryczna Exponentially many 3colorings of planar trianglefree graphs with no short separating cycles 
It has been conjectured that every planar trianglefree graph G has exponentially many proper vertex3colorings. In this paper, the conjecture is disproved. It is also shown that the conjecture holds if we add an assumption about the nonexistence of separating cycles of lengths 4 and 5. Specifically, it is proved that the number of proper vertex3colorings of every trianglefree planar graph with n vertices and with no separating cycle of length 4 or 5 is at least 2^{n/17700000}. 
11.04.16099 Krzysztof Pióro, Krzysztof Potępa 
Breaking the Cubic Barrier for (Unweighted) Tree Edit Distance 
W problemie odległości między drzewami dane są dwa ukorzenione drzewa z etykietami na krawędziach. Dodatkowo dla każdego wierzchołka jego dzieci mają ustalony porządek. Naszym celem jest znalezienie minimalnej liczby operacji kontrakcji krawędzi i zmiany etykiety krawędzi, tak aby doprowadzić oba drzewa do takiego samego drzewa. Autor pracy pokazuje algorytm o złożoności O(n^{2.9546}) dla wariantu tego problemu, w którym operacje mają koszty jednostkowe. Jest to pierwszy podsześcienny algorytm dla problemu odległości edycyjnej między drzewami. Warto tutaj zwrócić uwagę, że dla wariantu o dowolnych kosztach operacji istnieje warunkowe ograniczenie dolne, które mówi, że nie istnieje dla tego problemu algorytm podsześcienny. Zatem autor pokazuje, że wariant z jednostkowymi kosztami najprawdopodobniej jest istotnie prostszy od wariantu ogólnego. Aby złamać granicę O(n^{3}) autor redukuje problem do mnożenia macierzy maxplus, w których sąsiednie elementy różnią się co najwyżej o stałą. O takim problemie zostało już udowodnione wcześniej, że może zostać rozwiązany w czasie podsześciennym. 
17.02.13416 Jakub Kozik Jagiellonian 
Informatyka Teoretyczna Deterministic Constructions of 3Chromatic Hypergraphs with Few Edges 
How many edges do we need to build a kuniform hypergraph that cannot be properly two colored? Using the probabilistic argument Erdös proved in 1964, that there exist such hypergraphs with roughly k^{2}·2^{k} edges. However, without a random source at hand, the sizes that we can achieve by efficient procedures are much larger. The first and only known explicit construction with 2^{k+o(k)} edges was proposed by Gebauer in 2013. We will discuss how it can be improved first by randomizing and then derandomizing it once more. 
01.02.79149 Karolina Gontarek 
Optymalizacja Kombinatoryczna On topological aspects of orientations 
The paper considers two classes of planar graphs: maximal planar graphs and maximal bipartite planar graphs. The authors describe how these graphs can be oriented in the way that each vertex has prescribed indegree. Then the relation of such orientations to specific graph decompositions and orderings on the vertex set is provided. Discussed orientations can be used to characterize some of the planar graphs. Described properties have applications e.g. in graph drawing and planar augmentation problems.

25.10.79125 Ruslan Yevdokymov 
Optymalizacja Kombinatoryczna Flexible Color Lists in Alon and Tarsi’s Theorem, and Time Scheduling with Unreliable Participants 
By describing a winning strategy for Mrs. Correct in the coloring game of Mr. Paint and Mrs. Correct author presents a purely combinatorial proof of a strengthening of Alon and Tarsi's Theorem. Strengthening of the theorem also leads to the strengthening of its applications, for example, upper bounds for list chromatic numbers of bipartite graphs, list chromatic indices of complete graphs, and chess tournament time scheduling problem with unreliable participants. 
21.01.79071 Jakub Fedak, Mateusz Golonka 
Wordle is NPhard 
Wordle jest grą dla jednego gracza, której celem jest zgadnięcie pewnego słowa x wybranego ze słownika D. Aby zgadnąć słowo x gracz może wykonać co najwyżej k prób, przy czym w każdej próbie gracz musi podać słowo, które również znajduje się w słowniku D. Wszystkie słowa w słowniku mają długość n. Po każdej próbie zgadnięcia gracz otrzymuje informację o pozycjach, na których jego słowo zgadza się z rozwiązaniem oraz o literach z podanego słowa, które znajdują się w rozwiązaniu, lecz na innej pozycji. Autorzy udowadniają, że następujący problem jest NPtrudny: mając dany słownik D oraz liczbę naturalną k powiedzieć, czy gracz może zagwarantować zgadnięcie słowa w k próbach. Ponadto autorzy dowodzą, że dla słów długości 5 ten problem pozostaje trudny, a nawet w tym przypadku przybliżenie najmniejszej liczby prób potrzebnej do zagwarantowania zgadnięcia słowa jest NPtrudne. W pracy znajdują się również wyniki dotyczące złożoności parametryzowanej oraz kilka pytań otwartych związanych z tym tematem. 
28.11.76387 Andrew Suk University of California at San Diego 
Informatyka Teoretyczna Unavoidable patterns in simple topological graphs 
A simple topological graph is a graph drawn in the plane so that its vertices are represented by points, and its edges are represented by nonselfintersecting arcs connecting the corresponding points, with the property that any two edges have at most one point in common. In 2003, PachSolymosiTóth showed that every nvertex complete simple topological graph contains a topological subgraph on m = Ω(log n) vertices that is weakly isomorphic to the complete convex geometric graph or to the complete twisted graph on m vertices. Here, we improve this bound to (log n)^{1/4−o(1)}. I will also discuss other related problems as well. This is joint work with Ji Zeng. 
23.05.76278 Roch Wójtowicz 
Podstawy Informatyki SEMINARIUM i WYSTĄPIENIE ROCHA WÓJTOWICZA PRZENIESINE NA 11.05.2022 
Consider G(n, p) to be the probability space of random graphs on n vertices with edge probability p. We will be considering subsets of this space defined by monotone graph properties. A monotone graph property P is a property of graphs such that
A monotone symmetric family of graphs is a family defined by such a property. One of the first observations made about random graphs by Erdos and Renyi in their seminal work on random graph theory [12] was the existence of threshold phenomena, the fact that for many interesting properties P , the probability of P appearing in G(n, p) exhibits a sharp increase at a certain critical value of the parameter p. Bollob ́as and Thomason proved the existence of threshold functions for all monotone set properties ([6]), and in [14] it is shown that this behavior is quite general, and that all monotone graph properties exhibit threshold behavior, i.e. the probability of their appearance increases from values very close to 0 to values close to 1 in a very small interval. More precise analysis of the size of the threshold interval is done in [7]. This threshold behavior which occurs in various settings which arise in combinatorics and computer science is an instance of the phenomenon of phase transitions which is the subject of much interest in statistical physics. One of the main questions that arises in studying phase transitions is: how “sharp” is the transition? For example, one of the motivations for this paper arose from the question of the sharpness of the phase transition for the property of satisfiability of a random kCNF Boolean formula. Nati Linial, who introduced me to this problem, suggested that although much concrete analysis was being performed on this problem the best approach would be to find general conditions for sharpness of the phase transition, answering the question posed in [14] as to the relation between the length of the threshold interval and the value of the critical probability. 
27.09.59983 Wojciech Buczek 
Optymalizacja Kombinatoryczna On an early paper of Maryam Mirzakhani 
In this seminar, we will talk about Maryam Mirzakhani, who had an enormous influence on research about Combinatorics. We will study her idea of creating a small (with (only!) 63 vertices), non4choosable planar graph, which is also 3choosable. We will also consider other problems she worked on. 
19.06.59960 Maciej Nemś 
Optymalizacja Kombinatoryczna Avoiding squares over words with lists of size three amongst four symbols 
Word creation from lists of size t is a problem where for alphabet Σ each sign of created word is chosen from a list of t different signs from Σ. Word is "squarefree" when it does not contain any squares. A square is a word of form ww with w being a nonempty word. The author first shows that there are at least 2.45^{n} squarefree words of length n created from lists of 4. This is an improvement from the previous bound which is 2^{n}. After that, the main result of the paper is shown which is an existence of at least 1.25^{n} words of length n from lists of 3. 
16.09.59905 Piotr Kaliciak, Kamil Galewski 
A Simple Algorithm for Graph Reconstruction 
Praca skupia się na efektywnej rekonstrukcji grafu, przy pomocy zapytań o odległości między wierzchołkami. Rozważane grafy są spójne, nieważone oraz mają ograniczony stopień, a celem jest znalezienie wszystkich krawędzi w grafie. Analizowany jest prosty algorytm rekonstrukcji. Autorzy dowodzą, że na ∆regularnym grafie wykonuje on O(n*polylog(n)) zapytań. Ponadto można go zmodyfikować pod inne rodzaje zapytań. Co więcej, algorytm ten łatwo jest zrównoleglić. W przypadku grafów o ograniczonym stopniu, algorytm potrzebuje o(n^{2}) zapytań. 
23.07.57222 Sergey Norin McGill University 
Informatyka Teoretyczna Brambles, stack number and topological overlap 
A (strict) bramble in a graph G is a collection of subgraphs of G such that the union of any number of them is connected. The order of a bramble is the smallest size of a set of vertices that intersects each of the subgraphs in it. Brambles have long been part of the graph minor theory toolkit, in particular, because a bramble of high order is an obstruction to existence of a low width tree decomposition. 
12.02.40795 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna From 123 conjecture to Riemann hypothesis 
We consider some coloring issues related to the famous Erdős Discrepancy Problem. A set of the form A_{s},_{k}={s,2s,…,ks}, with s,k ∈ N, is called a homogeneous arithmetic progression. We prove that for every fixed k there exists a 2coloring of N such that every set A_{s,k} is perfectly balanced (the numbers of red and blue elements in the set A_{s,k} differ by at most one). This prompts reflection on various restricted versions of Erdős' problem, obtained by imposing diverse confinements on parameters s,k. In a slightly different direction, we discuss a majority variant of the problem, in which each set A_{s,k} should have an excess of elements colored differently than the first element in the set. This problem leads, unexpectedly, to some deep questions concerning completely multiplicative functions with values in {+1,−1}. In particular, whether there is such a function with partial sums bounded from above. 
17.03.38057 Alex Scott University of Oxford 
Informatyka Teoretyczna Induced subgraphs of induced subgraphs of large chromatic number 
We prove that for every graph F with at least one edge there is a constant c_{F }and there are graphs H of arbitrarily large chromatic number and the same clique number as F such that every Ffree induced subgraph of H has chromatic number at most c_{F.} (Here a graph is Ffree if it does not contain an induced copy of F.) This generalizes theorems of Briański, Davies and Walczak, and of Carbonero, Hompe, Moore and Spirkl. We further show an analogous statement where clique number is replaced by odd girth. Joint work with Antonio Girao, Freddie Illingworth, Emil Powierski, Michael Savery, Youri Tamitegama and Jane Tan. 
14.01.21653 Marcin Serwin 
Optymalizacja Kombinatoryczna Can a party represent its constituency? 
Upon gaining p% votes in an election in a proportional system, a party appoints p% of its proposed candidates to represent the party. The order of candidates to appoint is chosen beforehand. This may create tensions if the party members are not perfectly aligned politically, if some candidates of particular tendency are lower down the list and thus less likely to be appointed. This presentation examines the problem of existence and characterization of the list that would not create such tension and related problems. 
07.10.21629 Piotr Kaliciak 
Optymalizacja Kombinatoryczna 2Listcoloring planar graphs without monochromatic triangles 
The author is considering a planar graph, where every vertex has a list of 2 colors, and every coloring of this graph has to choose for every vertex one of these two colors. Unlike the standard colorings, the author doesn't mind having a monochromatic edge, but he tries to avoid having a monochromatic triangle. In this paper, he not only proves, that every planar graph can be colored this way, for every list assignment, but also he proves a stronger result for graphs with some vertices precolored. 
04.01.21575 Bartłomiej Błoniarz, Inka Sokołowska 
On Problems Related to Unbounded SubsetSum: A Unified Combinatorial Approach 
Unbounded SubsetSum to problem w którym dane są liczby c,u oraz n liczb całkowitych w_{1},...,w_{n} z przedziału [1,u]. Trzeba odpowiedzieć na pytanie czy istnieją liczby całkowite m_{1},...,m_{n} spełniające c = w_{1}*m_{1} + ... + w_{n}*m_{n}. W wersji alltarget problemu dana jest liczba naturalna t i należy podać odpowiedź dla wszystkich instancji z c z przedziału [0,t]. Praca skupia się na trzech generalizacjach tego problemu: 1. Alltarget Unbounded Knapsack  wariant dobrze znanego problemu plecakowego, dla którego przedstawiony jest algorytm Õ(T(u)+t) gdzie T(n) to czas obliczania (min,+)splotu dla tablic długości n 2. Alltarget CoinChange  wariant problemu wydawania reszty, dla którego przedstawiony jest algorytm Õ(u+t) 3. Residue Table, dla którego przedstawiony jest algorytm Õ(u). 
10.11.18891 Marcin Briański Jagiellonian 
Informatyka Teoretyczna Separating polynomial χboundedness from χboundedness and thereabouts 
If a graph contains no large complete subgraph but nonetheless has high chromatic number what can we say about the structure of such a graph? This question naturally leads to investigation of χbounded classes of graphs — graph classes where a graph needs to contain a large complete subgraph in order to have high chromatic number. This an active subfield of graph theory with many long standing open problems as well as interesting recent developments. In this talk I will present a construction of a hereditary class of graphs which is χbounded but not polynomially χbounded. This construction provides a negative answer to a conjecture of Esperet that every χbounded hereditary class of graphs is polynomially χbounded. The construction is inspired by a recent paper of Carbonero, Hompe, Moore, and Spirkl which provided a counterexample to another conjecture of Esperet. This is joint work with James Davies and Bartosz Walczak (available at arXiv:2201.08814) 
06.05.18782 Aleksander Katan 
Podstawy Informatyki A simple proof of the undecidability of strong normalization by Paweł Urzyczyn 
The purpose of this note is to give a methodologically simple proof of the undecidability of strong normalization in the pure lambda calculus. For this we show how to represent an arbitrary partial recursive function by a term whose application to any Church numeral is either strongly normalizable or has no normal form. Intersection types are used for the strong normalization argument. 
21.09.87362 Katarzyna Król 
Optymalizacja Kombinatoryczna On ListColoring Outerplanar Graphs 
An outerplanar graf is a planar graph whose vertices can all be drawn on the outer face. The author researched the problem of coloring outerplanar graphs from lists. First, it is shown that the outerplanar graph is Lcolorable if satisfies L(v) ≥ min{deg(v),4} and is bipartite. Then additional assumptions are searched for so that a similar inequality could define Lcolorability in general outerplanar graphs. The results given by the author are the best possible for each condition in the bounds and hypotheses. 
14.06.87339 Jędrzej Kula 
Optymalizacja Kombinatoryczna Multiple list colouring of planar graphs 
Since every planar graph G can be colored by 4 colors, there is also an integer m such that G is (4m,m)choosable. The problem here is that such m is changing with G. The author of this paper proves that there cannot be such a universal m that every planar graph is (4m,m)choosable. To be precise he shows that for each positive integer m, there is a planar graph G which is not (4m+⌊(2m1)/9⌋,m)choosable. Also, he poses some conjectures about planar graphs multiple list coloring. 
09.09.87284 Tomasz Buczyński, Łukasz Gniecki 
On Determinism Versus NonDeterminism and Related Problems 
Pokazujemy, że dla wielotaśmowych maszyn Turinga działających w czasie liniowym, niedeterminizm jest mocniejszy od determinizmu, czyli że klasa języków rozpoznawanych przez takie maszyny deterministyczne jest ścisłą podklasą języków rozpoznawanych przez takie maszyny niedeterministyczne. 
18.07.84601 Raphael Steiner ETH Zürich 
Informatyka Teoretyczna New bounds for relatives of Hadwiger's conjecture 
In this talk, I will present some recent results on two variants of Hadwiger's conjecture. First, I will discuss the socalled Odd Hadwiger's conjecture, a strengthening of Hadwiger's conjecture proposed by Gerards and Seymour in 1995. First I will show how, using a simple new trick, one can reduce the problem of coloring graphs with no odd K_{t}minor to coloring graphs with no K_{t}minor up to a constant factor of 2, thereby improving previous upper bounds for this problem. Then, I will outline how a similar idea can be used to significantly improve the known bounds for clustered colorings of odd K_{t}minor free graphs, in which we look for (possibly improper) colorings with monochromatic components of small size. Second, I will discuss the socalled List Hadwiger's conjecture, which states that there exists a constant c such that every graph with no K_{t}minor is ctchoosable (i.e., list colorable). I will show a probabilistic construction of a new lower bound 2to(t) for list coloring K_{t}minor free graphs, this refutes a conjecture by Kawarabayashi and Mohar which stated that one can take c=3/2. I will then show how some wellchosen modifications to our construction can be used to prove lower bounds also for list coloring Hminor free graphs where H is noncomplete. In particular, I will show that K_{s,t}minor free graphs for large comparable s and t can have list chromatic number at least (1o(1))(s+t+min(s,t)), this refutes a 2001 conjecture by Woodall. 
10.01.84492 Filip Synowiec 
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 generalize the previous results for any (reasonable) sequence of integers which enables us, in particular, to solve the above satisfiability question. We also analyze 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) phenomenon. 
16.05.68197 Jędrzej Hodor 
Optymalizacja Kombinatoryczna Clustered Coloring and Hadwiger's conjecture 
Hadwiger conjecture states, that for every K_{s+1} minor free graph it can be colored with s colors. For now, it is wide open. There are plenty of wellknown results improving the bound on the number of colors. However, there exists another approach to make the problem easier. We can relax the notion of proper coloring. A graph class can be ηclustered colored with n colors if in every graph only n colors are used and the size of each monochromatic component is bounded by η. Liu and Wood proved that for a class of graphs excluding K_{s+1} minor can be η(s)clustered colored with s+2 colors, which is almost optimal (s < s+2). I will describe their approach and prove the result in a simplified case. 
06.02.68174 Grzegorz Gawryał 
Optymalizacja Kombinatoryczna The Catalan matroid 
A path of length 2n, that starts in (0,0) and at each step moves from (x,y) to (x+1,y+1) or (x+1,y1) is a Dyck path, if it ends in (2n,0) and never passes below y=0 line. Such paths are counted by Catalan numbers. In this presentation, we'll show, that the Dyck paths for fixed n form a matroid. We'll show what are bases, independent sets, and other matroidrelated terms in this object, explore some properties of this matroid, and see how it generalizes to shifted matroids. 
06.05.68119 Mateusz Pach, Michał Wronka 
Making Life More Confusing for Firefighters 
Problem Firefighter polega na opracowaniu strategii rozsyłania strażaków do obrony wierzchołków grafu przed rozprzestrzeniającym się przez krawędzie ogniem, tak by jak najmniej wierzchołków spłonęło; problem ten jest NPtrudny dla znakomitej większości klas grafów. By zamodelować scenariusz z cywilami pomagającymi strażakom, wprowadzamy problem Temporal Firefighter będący rozszerzeniem na dynamiczne grafy. Pokazujemy, że problem Temporal Firefighter jest NPtrudny i pozostaje taki dla wszystkich klas grafów (poza jedną) o których wiadomo, że posiadają wielomianowe rozwiązanie problemu Firefighter. Pokazujemy też algorytm FPT dla Temporal Firefighter, parametryzowany wartością vertexintervalmembershipwidth. 
12.03.65436 Mathieu Mari University of Warsaw and IDEASNCBR 
Informatyka Teoretyczna A (2+ε)Approximation Algorithm for Maximum Independent Set of Rectangles 
We study the Maximum Independent Set of Rectangles (MISR) problem, where we are given a set of axisparallel rectangles in the plane and the goal is to select a subset of nonoverlapping rectangles of maximum cardinality. In a recent breakthrough, Mitchell [2021] obtained the first constantfactor approximation algorithm for MISR. His algorithm achieves an approximation ratio of 10 and it is based on a dynamic program that intuitively recursively partitions the input plane into special polygons called cornerclipped rectangles (CCRs), without intersecting certain special horizontal line segments called fences. In this talk, I will present a (2+ϵ)approximation algorithm for MISR which is also based on a recursive partitioning scheme. First, we use a partition into a class of axisparallel polygons with constant complexity each that are more general than CCRs. This allows us to provide an arguably simpler analysis and at the same time already improves the approximation ratio to 4. Then, using a more elaborate charging scheme and a recursive partitioning into general axisparallel polygons with constant complexity, we improve our approximation ratio to 2+ϵ. In particular, we construct a recursive partitioning based on more general fences which can be sequences of up to O(1/ϵ) line segments each. This partitioning routine and our other new ideas may be useful for future work towards a PTAS for MISR. At the end of the talk, I will present a bunch of open questions related to the problem.
This is a joint work with Waldo Gálvez, Arindam Khan, Tobias Mömke, Madhusudhan Reddy and Andreas Wiese 
05.09.65326 Michał Woźny 
Podstawy Informatyki COUNTING WITH IRRATIONAL TILES by SCOTT GARRABRANT and IGOR PAK 
We introduce and study the number of tilings of unit height rectangles with irrational tiles. We prove that the class of sequences of these numbers coincides with the class of diagonals of Nrational generating functions and a class of certain binomial multisums. We then give asymptotic applications and establish connections to hypergeometric functions and Catalan numbers. 
02.10.49008 Krzysztof Ziobro 
Optymalizacja Kombinatoryczna A note on polynomials and ffactors of graphs 
The factor of a graph is its spanning subgraph which adheres to given constraints on the degrees. The authors of the article discuss the ffactor, which for every vertex defines a set of possible degrees. The main result shows a new sufficient condition for the existence of an ffactor in a given graph. Authors obtain it by using Combinatorial Nullstellensatz. 
29.12.48953 Ignacy Buczek, Michał Woźny 
Sorting Balls and Water: Equivalence and Computational Complexity 
Problemy sortowania od długiego czasu są obiektem różnego rodzaju badań. Ostatnio dwie gry na telefon w tematyce sortowania zyskały na popularności. W tych grach, gracz ma do dyspozycji urny wypełnione kolorowymi obiektami (w przypadku jednej są to kule, a w przypadku drugiej woda) oraz kilka pustych urn, a jego celem jest posortowanie obiektów zgodnie z kolorami. W jednym ruchu może on przenieść obiekty z jednej urny do drugiej, jeżeli kolor przenoszonych obiektów zgadza się z kolorem najwyższego obiektu docelowej urny lub urna ta jest pusta. W pracy autorzy badają złożoność obliczeniową tych łamigłówek. Na początku pokazują, że te gry są w równoważne pod kątem rozwiązywalności. Dokładniej mówiąc, rozwiązywalność stanu początkowego gry nie zależy od tego czy obiekty zachowują się jak kule, czy jak woda. Dowodzą również, że dla każdej takinstancji istnieje rozwiązanie wielomianowego rozmiaru, co pokazuje, że problem rozwiązywalności tych łamigłówek jest w NP. Następnie uzasadniają, że ten problem jest NPzupełny. Znajdują również wielomianowe algorytmy dla szczególnych przypadków. Na samym końcu zastanawiają się, jak wiele pustych urn jest potrzebnych, aby instancja była rozwiązywalna niezależnie od początkowego rozmieszczenia obiektów. Pokazują nietrywialne ograniczenia (dolne i górne) zależne od ilości początkowo zapełnionych urn i ich pojemności. 
05.11.46270 Marek Sokołowski University of Warsaw 
Informatyka Teoretyczna Graphs of bounded twinwidth are quasipolynomially χbounded 
We prove that for every t∈ℕ there is a constant γ(t) such that every graph with twinwidth at most t and clique number ω has chromatic number bounded by 2^{γ(t) log^{4t+3} ω}. In other words, we prove that graph classes of bounded twinwidth are quasipolynomially χbounded. This provides a significant step towards resolving the question of Bonnet et al. [ICALP 2021] about whether they are polynomially χbounded. This is a joint work with Michał Pilipczuk 
30.04.46161 Ignacy Buczek 
Podstawy Informatyki Dömösi, Horváth and Ito’s Hypothesis on the Language of Primitive Words 
A word is called primitive if it is not a repetition of another word. The language of all primitive words over a fixed alphabet \Sigma is denoted as Q. We consider the question of whether Q over \Sigma with at least 2 different characters is contextfree or not. We show that Q is not regular and that it is contextsensitive. We exclude Q from language classes that are inbetween the classes of regular languages and contextfree languages, such as unambiguous contextfree languages, linear contextfree languages, and deterministic contextfree languages. We also show that Q satisfies a number of contextfreelike conditions, such as the BarHillel lemma, the Ogden condition, the nonempty version of the strong BaderMoura condition, and strengthened interchange property. In addition, we analyze some less typical (and unsuccessful) attempts of proving noncontextfreeness of Q. 
01.07.27105 Pat Morin Carleton University 
Informatyka Teoretyczna Free Sets in Planar Graphs 
A kvertex set S of vertices in a planar graph G is free if, for any kpoint set X, there exists a noncrossing straightline drawing of G with the vertices of S mapped to the points in X. In this talk we survey the history and applications of free sets and present two recent results [1,2]: 1. Free sets and collinear sets: If G has any drawing in which all vertices of S appear on a line, then S is a free set. 2. Free sets and dual circumference: If G has bounded degree, then the size of the largest collinear set in G is proportional to the length of the longest cycle in the dual of G. [1] Vida Dujmović, Fabrizio Frati, Daniel Gonçalves, Pat Morin, and Günter Rote: Every collinear set in a planar graph is free. Discrete & Computational Geometry, 65:999–1027, 2021. [2] Vida Dujmovic, Pat Morin: Dual Circumference and Collinear Sets. SoCG 2019: 29:129:17. 
24.02.7940 Jarosław Byrka University of Wrocław 
Informatyka Teoretyczna Online Facility Location with Linear Delay 
We study the problem of online facility location with delay. In this problem, a sequence of n clients appear in the metric space, and they need to be eventually connected to some open facility. The clients do not have to be connected immediately, but such a choice comes with a penalty: each client incurs a waiting cost (the difference between its arrival and connection time). At any point in time, an algorithm may decide to open a facility and connect any subset of clients to it. This is a wellstudied problem both of its own, and within the general class of network design problems with delays. Joint work with Marcin Bienkowski, Martin Böhm and Jan Marcinkowski 
23.02.76419 Bartosz Podkanowicz 
Optymalizacja Kombinatoryczna Alon Tarsi number of planar graphs 
We prove that the AlonTarsi number of a planar graph is less or equal to 5. Alon Tarsi number is an important parameter for the graph. It is greater than the choice number and paintability for every graph. We show the modification of the standard argument presented by Carsten Thomassen. We construct a special orientation that doesn't have Euler subgraphs and allows us to reason about the AlonTarsi number. 
16.11.76395 Jędrzej Kula 
Optymalizacja Kombinatoryczna Bipartite Perfect Matching is in quasiNC 
The class NC represents the problems that have efficient parallel algorithms. In this work, the authors present two algorithms. The first algorithm proves that the perfect matching problem for bipartite graphs is in quasiNC^{2}. The second algorithm proves that the same problem is in the RNC class and uses only O(log^{2} n) random bits. Note that a complete derandomization would be achieved when the number of random bits comes down to O(log n). 
22.07.76383 Krzysztof Pióro 
Optymalizacja Kombinatoryczna Graph coloring game 
In the game coloring game two players are given graph and a set of k colors. Players take turns, coloring properly an uncolored vertex. The goal of the first player is to complete the coloring of the graph, while the other one tries to prevent him from achieving it. The game chromatic number of a graph is the minimum number of colors needed for the first player to win. In this presentation I will show bounds for the game chromatic number for some classes of graphs. 
02.10.73649 Sławomir Lasota University of Warsaw 
Informatyka Teoretyczna Improved Ackermannian lower bound for the reachability problem of vector addition systems 
Vector addition systems, equivalent to Petri nets, are an established model of concurrency with widespread applications. The reachability problem, where we ask whether from a given initial configuration there exists a sequence of valid execution steps reaching a given final configuration, is the central algorithmic problem for this model. The complexity of the problem has remained, until recently, one of the hardest open questions in verification of concurrent systems. A first upper bound has been provided only in 2015 by Leroux and Schmitz, then refined by the same authors to Ackermannian upper bound in 2019. The exponential space lower bound, shown by Lipton already in 1976, remained the only known for over 40 years until a breakthrough nonelementary lower bound by Czerwiński et al in 2019. Finally, a matching Ackermannian lower bound announced in 2021 by Czerwiński and Orlikowski, and independently by Leroux, established the complexity of the problem.
I will present an improvement of the former construction, making it conceptually simpler and more direct and, on the way, improving the lower bound for vector addition systems in fixed dimension (or, equivalently, Petri nets with fixed number of places). 
28.03.73540 Jakub Fedak 
Podstawy Informatyki Exact enumeration of satisfiable 2SAT formulae by Sergey Dovgal, Elie de Panafeu and Vlady Ravelomanana 
We obtain exact expressions counting the satisfiable 2SAT formulae and describe the structure of associated implication digraphs. Our approach is based on generating function manipulations. To reject the combinatorial specificities of the implication digraphs, we introduce a new kind of generating function, the Implication generating function, inspired by the Graphic generating function used in digraph enumeration. Using the underlying recurrences, we make accurate numerical predictions of the phase transition curve of the 2SAT problem inside the critical window. We expect these exact formulae to be amenable to rigorous asymptotic analysis using complex analytic tools, leading to a more detailed picture of the 2SAT phase transition in the future.

16.03.57218 Szymon Salabura 
Optymalizacja Kombinatoryczna The Hats game. On max degree and diameter 
In the Hats game, the sages, located at graph vertices, try to guess colors of their own hats, only seeing colors of hats on sages at the adjacent vertices. If using a deterministic strategy, at least one sage can guess the color of his own hat correctly, we say that the sages win. In this presentation, we consider the hat guessing number  the maximum number of possible colors, for which the sages can guarantee the win. We will see examples of graphs contradicting the previously stated hypothesis, that the hat guessing number is smaller than the graph's maximal degree + 1. We also show its independence from the graph's diameter. 
27.05.54484 James Davies University of Waterloo 
Informatyka Teoretyczna Ringel's circle problem 
A constellation is a finite collection of circles in the plane in which no three circles are tangent at the same point. In 1959, Ringel asked how many colours are required to colour the circles of a constellation so that tangent circles receive different colours. We present a solution to Ringel's circle problem by constructing constellations that require arbitrarily many colours. Joint work with Chaya Keller, Linda Kleist, Shakhar Smorodinsky, and Bartosz Walczak 
21.11.54374 Daniel Barczyk 
Podstawy Informatyki Narrow Proofs May Be Maximally Long by Albert Atserias and Massimo Lauria 
We prove that there are 3CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size $n^{\Omega (w)}$. This shows that the simple counting argument that any formula refutable in width w must have a proof in size $n^{O (w)}$ is essentially tight. Moreover, our lower bound generalizes to polynomial calculus resolution (PCR) and SheraliAdams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. The lower bound does not extend all the way to Lasserre, however, since we show that there the formulas we study have proofs of constant rank and size polynomial in both n and w.

05.03.38065 Jacek Salata 
Optymalizacja Kombinatoryczna Choosability of K5minorfree graphs 
Thomassen showed in 1994 that all planar graphs are 5choosable and Škrekovski showed in 1998 that all K_{5}minorfree graphs also are 5choosable. In this presentation we will take a look at two different proofs of the latter theorem: the Škrekovski's one from the original paper, and the one proposed by Wenjie Hea, Wenjing Miao and Yufa Shenb in 2007. 
08.11.38052 Demian Banakh 
Optymalizacja Kombinatoryczna A relative of Hadwigers conjecture 
The wellknown open Hadwiger's conjecture asserts that every simple graph G which is not tcolorable has K_{t+1} minor. In this presentation, we will take a look at the proof of a relaxed version of this conjecture (in terms of socalled "defective colorings"  i.e. allowing a "small" number of monochromatic edges), as well as see how it can be useful for solving some other graph problems. 
21.01.35319 Grzegorz Gutowski 
Informatyka Teoretyczna On a problem of Steinhaus 
In this talk, inspired by a "17points" problem of Steinhaus (Problems 6 and 7 from his book "Sto zadań"), we discuss infinite sequences of real numbers in [0,1). 
16.07.35209 Filip Synowiec 
Podstawy Informatyki On ZeroOne and Convergence Laws for Graphs Embeddable on a Fixed Surface by Albert Atserias, Stephan Kreutzer and Marc Noy 
We show that for no surface except for the plane does monadic secondorder logic (MSO) have a zeroonelaw – and not even a convergence law – on the class of (connected) graphs embeddable on the surface. In addition we show that every rational in [0,1] is the limiting probability of some MSO formula. This strongly refutes a conjecture by Heinig et al. (2014) who proved a convergence law for planar graphs, and a zeroone law for connected planar graphs, and also identified the socalled gaps of [0,1]: the subintervals that are not limiting probabilities of any MSO formula. The proof relies on a combination of methods from structural graph theory, especially large facewidth embeddings of graphs on surfaces, analytic combinatorics, and finite model theory, and several parts of the proof may be of independent interest. In particular, we identify precisely the properties that make the zeroone law work on planar graphs but fail for every other surface.

24.10.46278 Wojciech Buczek 
Optymalizacja Kombinatoryczna Parking functions: From combinatorics to probability 
Let's say m drivers have their favourite parking spot in the linear car park with n spots. Now, in some order, drivers will try to park their car at their favourite spot, and if they fail (because other car is standing there), they will try to park at the next avaible spot. If all drivers could park their car, we call this choices a parking function. In this seminar, we will look at this function proporties, create bijection from them to spanning forests and talk about some conjectures related to parking functions. 
29.06.46266 Rafał Kilar 
Optymalizacja Kombinatoryczna A first moment proof of the JohanssonMolloy Theorem 
The paper provides a simple proof of a stronger version of JohanssonMolloy theorem, providing a bound on the list chromatic number of a graph based on maximum degree and neighbouhood density. The new proof only makes use of the first moment method. The counting argument used in the proof is inspired by work by Rosenfeld in the contex of nonrepetitive graph coloring. The result is than extended to graphs with neighbourhoods with bounded density, which strengthens previous results. Lastly, the method is adapted to show asymptotically tight lowe bound on the number of colourings of sparse graphs . 
10.09.43532 Lars Rohwedder EPFL 
Informatyka Teoretyczna A (2+ϵ)approximation algorithm for preemptive weighted flow time on a single machine 
In a recent breakthrough in scheduling, Batra, Garg, and Kumar gave the first constant approximation algorithm for minimizing the sum of weighted flow times. Wiese and I [STOC'21] managed to improve this large unspecified constant to (2+ϵ). I will give a very graphic presentation of the algorithmic techniques behind this. 
19.06.27113 Marcin Serwin 
Optymalizacja Kombinatoryczna Bears with Hats and Independence Polynomials 
A hat guessing game consists of a graph and bears assigned to vertices with a certain hat color. Each bear knows the colors of the bears belonging to the neighborhood of their vertex but does not know their own color. The bears win if at least one of them can guess the color of their hat. This presentation will introduce the aforementioned game, its variants and present findings of Václav Blažej, Pavel Dvořák and Michal Opler regarding fractional hat chromatic number of graphs with independence polynomials. 
22.02.27101 Krzysztof Potępa 
Optymalizacja Kombinatoryczna Weak degeneracy of graphs 
The paper introduces a new graph parameter called "weak degeneracy", a variant of the degeneracy parameter. The authors show various applications of weak degeneracy. For example, it turns out that this new parameter is strongly correlated with graph coloring. Authors derive alternative proofs for several classic upper bounds in graph coloring theory, including 5listcoloring of planar graphs. My presentation will summarize the findings of the paper. 
06.05.24367 István Tomon ETH Zürich 
Informatyka Teoretyczna Ramsey properties of semilinear graphs 
A graph G is semilinear of complexity t if the vertices of G are points in some real space, and the edges of G are determined by the signpatterns of t linear functions. Many natural geometric graph families are semilinear of bounded complexity, e.g. intersection graphs of boxes, shift graphs, interval overlap graphs. There is a long line of research studying the exceptional Ramsey and coloring properties of such geometric graphs; I will show that many of these results can be traced back to their semilinear nature. 
29.10.24257 Katarzyna Król 
Podstawy Informatyki 01 Laws for Maps by Edward A. Bender, Kevin J. Compton,and L. Bruce Richmond 
A class of fnite structures has a 01 law with respect to a logic if every property expressible in the logic has a probability approaching a limit of 0 or 1 as the structure size grows. To formulate 01 laws for maps (i.e., embeddings of graphs in a surface), it is necessary to represent maps as logical structures. Three such representations are given,

12.02.7948 Krzysztof Michalik 
Optymalizacja Kombinatoryczna Improved lower bound for the list chromatic number of graphs with no Kt minor 
This paper begins with recounting known limits regarding Hadwiger's conjecture and related problems including list Hadwiger's conjecture, stating that there does exist constant c, such that K_{t} minor free graph G has list coloring number not exceeding ct. After the introduction, we are presented with proof that such constant has to be at least equal to 2, contrary to previous results, where c was bounded by 4/3 and conjectured to be equal to 3/2. 
18.10.7935 Krzysztof Ziobro 
Optymalizacja Kombinatoryczna Polynomials over structured grids 
Paper discusses properties of multivariate polynomials over finite grids, focaausing on he grids that are in some way "structured". To capture the degree to which a grid is structured, author introduces a notion of nullity, which can give us a numerical measure of structure. It is noted that for more structured grids we can obtain stronger versions of general theorems. This leads to the main results of the paper: the Structured Combinatorial Nullstellensatz and the Complete Coefficient Theorem. 
29.12.5201 Barnaby Martin Durham University 
Informatyka Teoretyczna QCSP monsters and the future of the Chen Conjecture 
We elaborate the complexity of the Quantified Constraint Satisfaction Problem, QCSP(A), where A is a finite idempotent algebra. Such a problem is either in NP or is coNPhard, and the borderline is given precisely according to whether A enjoys the polynomiallygenerated powers (PGP) property. This completes the complexity classification problem for QCSPs modulo that coNPhard cases might have complexity rising up to Pspacecomplete. Our result requires infinite languages, but in this realm represents the proof of a slightly weaker form of a conjecture for QCSP complexity made by Hubie Chen in 2012. The result relies heavily on the algebraic dichotomy between PGP and exponentiallygenerated powers (EGP), proved by Dmitriy Zhuk in 2015, married carefully to previous work of Chen. Finally, we discuss some recent work with Zhuk in which the aforementioned Chen Conjecture is actually shown to be false. Indeed, the complexity landscape for QCSP(B), where B is a finite constraint language, is much richer than was previously thought. 
23.06.5092 Ignacy Buczek 
Podstawy Informatyki Definability on a Random 3CNF Formula by Albert Atserias 
We consider the question of certifying unsatisfiability of random 3CNF formulas. At which densities can we hope for a simple sufficient condition for unsatisfiability that holds almost surely? We study this question from the point of view of definability theory. The main result is that firstorder logic cannot express any sufficient condition that holds almost surely on random 3CNF formulas with $n^{2\alpha}$ clauses, for any irrational positive number \alpha. In contrast, it can when the number of clauses is $n^{2+\alpha}$, for any positive \alpha. As an intermediate step, our proof exploits the planted distribution for 3CNF formulas in a new technical way. Moreover, the proof requires us to extend the methods of Shelah and Spencer for proving the zeroone law for sparse random graphs to arbitrary relational languages.

23.11.70919 Artur Salawa 
Optymalizacja Kombinatoryczna The Open Problems Project 
Paper records open problems in computational geometry and related fields. For every problem, the authors provide a statement, origin, current status, partial results and related problems. My presentation focuses on a few chosen problems explained in a friendly manner. 
29.07.70907 Grzegorz Wawrzesta 
Optymalizacja Kombinatoryczna Density conditions for panchromatic colourings of hypergraphs 
A hypergraph is defined as a pair H = (V, E), where V is a set of vertices and E is a set of subsets of V  these subsets of vertices are called (hyper)edges. Graphs can be then seen as a concretization where all edges are sets of size 2. This can be shortly ascribed to the hypergraph as being 2uniform. Tuniformity is a useful assumption for deriving its properties but sometimes one would wish for more general results. This approach is one of a few that are considered by the authors of the following paper which focuses on boundaries we can put on some characteristic properties of hypergraphs relating to their colorability and listcolorability. During the meeting, the basic concepts of hypergraphs and their colorability will be introduced and then the results of the paper will be interpreted alongside the presentation of the theorems and lemmas (and also an exemplar proof of one of them or two) which are used in the paper to attain the results. 
02.12.70856 Miłosz Januszewski, Szymon Salabura 
A FineGrained Perspective on Approximating Subset Sum and Partition 
W problemie Subset Sum, mając dany zbiór dodatnich liczb X oraz cel t, pytamy czy istnieje dowolny podzbiór sumujący się do dokładnie t. Należy on do klasy problemów NPzupełnych, zatem naturalne jest badanie jego algorytmów aproksymacyjnych  takich, które szukają podzbioru sumującego się do co najmniej 1ε wyniku optymalnego. Aktualnie najlepszy znany algorytm robi to w czasie O(min{n/ε,n+1/ε^{2} log(1/ε)}). W szczególności nie jest znany żaden algorytm rozwiązujący ten problem w O((n+1/ε)^{c}) dla dowolnego c<2. Autorzy w pracy pokazują równoważność tego problemu do MinPlusConvolution przeprowadzając redukcje w obie strony. Dzięki temu uzyskują algorytm aproksymacyjny dla Subset Sum o poprawionym czasie działania oraz udowadniają, że Subset Sum ma algorytm aproksymacyjny w czasie O((n+1/ε)^{c}) dla c<2 wtedy i tylko wtedy, gdy MinPlusConvolution może być rozwiązany w O(n^{c'}) dla c'<2. Druga część równoważności jest jednak sprzeczna z hipotezą trudności tego problemu. Dodatkowo, dla specjalnego wariantu Subset Sum zwanego Partition, autorzy stosują powyższą redukcję otrzymując algorytm aproksymacyjny działający w czasie O(n+1/ε^{3/2}). Jest to pierwszy deterministyczny algorytm z podkwadratową złożonością. 
09.10.68173 Jan Derbisz 
Informatyka Teoretyczna Circulararc graphs and the Helly property 
Circulararc graphs, defined as the intersection graphs of arcs of a fixed circle, are probably one of the simplest classes of intersection graphs, which does not satisfy the Helly property in general (i.e. there are circulararc graphs in which some cliques can be represented by arcs whose common intersection is empty). In particular, some cliques of a circulararc G graph may satisfy the Helly property in some but not all circulararc representations of G. In the Helly Clique Problem, for a given circulararc graph G and some of its cliques C_{1},...,C_{k} (not necessarily maximal in G) one needs to decide whether there exists a circulararc representation of G in which all the cliques C_{1},...,C_{k }satisfy the Helly property. We know that the Helly Clique Problem is NPcomplete and, under the ETH, it can not be solved in time 2^{o(k)}poly(n), where n is the number of vertices of G (Ağaoğlu et al.). In the talk we will consider the Helly Clique Problem in the context of parameterized complexity, where the natural parameter is the number of cliques given in the input. We will show that the Helly Clique Problem: Moreover, we will discuss the relation of the Helly Clique Problem with the recognition problems of socalled Hgraphs; in particular, in the context of those graphs H for which the recognition problem remains open. This is joint work with T. Krawczyk. The talk also includes joint work with D. Ağaoğlu, O. Cagrici, T. Hartmann, P. Hliněný, J. Kratochvíl, T. Krawczyk, and P. Zeman. 
03.04.68064 Michał Woźny 
Podstawy Informatyki Dance of the Starlings by Henk Barendregt, Jorg Endrullis, Jan Willem 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 lambdacalculus 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.

18.07.51754 Maciej Nemś 
Optymalizacja Kombinatoryczna Fair Correlation Clustering 
In this paper authors propose approximation for Correlation Clustering problem with additional constaint of fairness. In a fair version of correlation clustering vertices have also colors and in the end in each cluster there should be "some" number of vertices of each color. What "some" means is dependent on variant of this constraint. Authors first reduce a problem of fair clustering correlation to a problem they call Fairlet Decomposition and then show approximation algorithm for this problem. In the end they describe some experiments they have done to prove Fair Correlation Clustering a viable version of Correlation Clustering. 
23.03.51742 Karolina Gontarek 
Optymalizacja Kombinatoryczna Growth properties of powerfree languages 
Paper surveys common part of two formal language issues. Issue of repetition free words and languages and issue of growth functions for words and languages. Paper gives an overview of current knowledge and search about an intersection of those two areas. It classifies powerfree languages with regard to their growth rate. It also describes methods of esimating complexity of powerfree languages paying attention to amount of computer resources needed by special method. Finally, it presents future directions of research in this area. 
28.07.51691 Aleksander Katan, Roch Wójtowicz 
Filling crosswords is very hard 
Autorzy analizują problem wypełniania krzyżówek, który już był rozważany na przykład przez Garey’a i Johnsona w ich książce „Computers and Intractability: A Guide to the Theory of NPCompleteness”. W problemie tym dostajemy m słów i n poziomych lub pionowych slotów (rubryk) oraz jesteśmy proszeni o wypełnienie ich tak, by przecięcia slotów się zgadzały. Autorzy próbują wskazać źródło trudności tej łamigłówki przyglądając się strukturze grafu przecięć slotów. Skupiają się na przypadku, gdy struktura tego grafu przypomina drzewo. Niestety, jeżeli przyjmiemy, że słowa nie mogą być używane wielokrotnie, okazuje się, że problem pozostaje NPtrudny nawet pod bardzo surowymi restrykcjami, jak na przykład, że graf przecięć jest sumą grafów typu star i alfabet ma rozmiar 
04.06.49008 Nicolas Bousquet CNRS, Lyon 
Informatyka Teoretyczna Local certification of/on sparse graph classes 
Local certification consists in assigning labels to the nodes of a graph in order to certify that some given property is satisfied, in such a way that the labels can be checked locally. In this talk, our goal is to certify that a graph G belongs to a given graph class. Such certifications exist for many sparse graph classes such as trees, planar graphs and graphs embedded on surfaces with labels of logarithmic size. It is open if such a certificate exist for any Hminor free graph class. We present some generic tools which allow us to certify the Hminorfree graphs (with logarithmic labels) for each small enough H. More generally, we consider classes defined by any MSO formula (i.e. the MSOmodel checking problem), and show a local version of the wellknown Courcelle theorem: in bounded treedepth graphs, logarithmic certificates can be obtained for any MSO formula. We will also discuss many open problems related to local certification of/on sparse graph classes. Joint works with Laurent Feuilloley and Théo Pierron 
27.11.48898 Łukasz Selwa 
Podstawy Informatyki An Inverse of the Evaluation Functional for Typed λcalculus by U. Berger and Η. Schwichtenberg 
In any model of typed lambdacalculus containing some basic arithmetic, a functional p >e (procedure —> expression) will be defined which inverts the evaluation functional for typed lambdaterms. Combined with the evaluation functional, p>e yields an efficient normalization algorithm. The method is extended to lambdacalculi with constants and is used to normalize (the lambdarepresentations of) natural deduction proofs of (higher order) arithmetic. A consequence of theoretical interest is a strong completeness theorem for \beta \etareduction, generalizing results of Friedman and Statman. If two lambdaterms have the same value in some model containing representations of the primitive recursive functions (of level 1) then they are provably equal in the \beta \etacalculus. 
27.11.48898 Łukasz Selwa 
An Inverse of the Evaluation Functional for Typed λcalculus by U. Berger and Η. Schwichtenberg 
In any model of typed lambdacalculus containing some basic arithmetic, a functional p >e (procedure —> expression) will be defined which inverts the evaluation functional for typed lambdaterms. Combined with the evaluation functional, p>e yields an efficient normalization algorithm. The method is extended to lambdacalculi with constants and is used to normalize (the lambdarepresentations of) natural deduction proofs of (higher order) arithmetic. A consequence of theoretical interest is a strong completeness theorem for \beta \etareduction, generalizing results of Friedman and Statman. If two lambdaterms have the same value in some model containing representations of the primitive recursive functions (of level 1) then they are provably equal in the \beta \etacalculus. 
28.01.29843 Zdeněk Dvořák Charles University 
Informatyka Teoretyczna On asymptotic dimension of planar and geometric graphs 
A graph class C has asymptotic dimension at most d if for every r, the rth distance power of any graph from C can be colored by d+1 colors so that every monchromatic connected subgraph has bounded weak diameter. In a recent breakthrough result, Bonamy, Bousquet, Esperet, Groenland, Liu, Pirot, and Scott proved that all proper minorclosed classes have asymptotic dimension at most two. We investigate some questions motivated by this result for planar graphs and geometric intersection graphs. Joint work with Sergey Norin 
06.11.13423 Roch Wójtowicz 
Optymalizacja Kombinatoryczna Problems and results on 3chromatic hypergraphs and some related questions 
Authors in this work aim to establish various bounds and constraints on hypergraphs which are kchromatic. Hypergraph is a graph where an edge don’t have to link exactly two vertices. Hypergraph is called simple, when none two of his edges has more then one common point, and is called clique when each two of his edges has at least one common point. Hyper graph is runiform when each of its edges contains exactly r points. Chromatic number is a smallest number k such that you can color points of the graph using k colors in the way that no edge is monochromatic. Main part of the work involves around the impact that being clique or simple has on 3chromatic hypergraph structure. The main reason why those two things are connected is following trivial observation: If a hypergraph has chromatic number > 3 then it has two edges with exactly one common point.

12.07.13411 Grzegorz Gawryał 
Optymalizacja Kombinatoryczna Defective and clustered choosability of sparse graphs 
This paper explores almost proper graph colorings and list colorings  we allow the coloring to be improper, but we impose restrictions on the maximum number of neighbours of any vertex with the same color as the vertex itself (defect) or the maximum allowed size of a monochromatic connected graph component (clustering). The paper provides new bounds on coloring and list coloring number for sparse graphs, i.e. having bounded maximum average degree, taken over all subgraphs, or limited maximum degree. More precisely, the two main results of this paper are the new bounds on defective choosability and clustered choosability of graphs with bounded maximum average degree, being the best known results for graphs with unbounded maximum degree, but bounded maximum average degree, like kstack and kqueue graphs. 
15.11.13360 Mateusz Pach, Michał Wronka 
Determining 4edgeconnected components in linear time 
Prezentujemy pierwszy deterministyczny algorytm obliczający 4spójne krawędziowo składowe w czasie liniowym. Najpierw pokazujemy algorytm znajdujący wszystkie 3cięcia krawędziowe w danym grafie 3spójnym krawędziowo i korzystając z jego wyniku budujemy 4spójne składowe oryginalnego grafu. 
22.09.10677 Torsten Mütze University of Warwick & Charles University 
Informatyka Teoretyczna Efficient generation of elimination trees and Hamilton paths on graph associahedra 
An elimination tree for a connected graph G is a rooted tree on the vertices of G obtained by choosing a root x and recursing on the connected components of G−x to produce the subtrees of x. Elimination trees appear in many guises in computer science and discrete mathematics, and they are closely related to centered colorings and treedepth. They also encode many interesting combinatorial objects, such as bitstrings, permutations and binary trees. We apply the recent HartungHoangMützeWilliams combinatorial generation framework to elimination trees, and prove that all elimination trees for a chordal graph G can be generated by tree rotations using a simple greedy algorithm (see www.combos.org/elim). This yields a short proof for the existence of Hamilton paths on graph associahedra of chordal graphs. Graph associahedra are a general class of highdimensional polytopes introduced by Carr, Devadoss, and Postnikov, whose vertices correspond to elimination trees and whose edges correspond to tree rotations. As special cases of our results, we recover several classical Gray codes for bitstrings, permutations and binary trees, and we obtain a new Gray code for partial permutations. Our algorithm for generating all elimination trees for a chordal graph G can be implemented in time O(m+n) per generated elimination tree, where m and n are the number of edges and vertices of G, respectively. If G is a tree, we improve this to a loopless algorithm running in time O(1) per generated elimination tree. We also prove that our algorithm produces a Hamilton cycle on the graph associahedron of G, rather than just Hamilton path, if the graph G is chordal and 2connected. Moreover, our algorithm characterizes chordality, i.e., it computes a Hamilton path on the graph associahedron of G if and only if G is chordal.
This is joint work with Jean Cardinal (ULB) and Arturo Merino (TU Berlin) 
17.03.10568 Juliusz Wajgelt 
Podstawy Informatyki On Repetitive Right Application of BTerms by Mirai Ikebuchi and Keisuke Nakano 
Bterms are built from the B combinator alone defined by B \f.\g.\x.f (g x), which is well known as a function composition operator. This paper investigates an interesting property of Bterms, that is, whether repetitive right applications of a Bterm cycles or not. We discuss conditions for Bterms to have and not to have the property through a sound and complete equational axiomatization. Specifically, we give examples of Bterms which have the property and show that there are infinitely many Bterms which do not have the property. Also, we introduce a canonical representation of Bterms that is useful to detect cycles, or equivalently, to prove the property, with an efficient algorithm. 
23.07.79070 Piotr Kaliciak, Kamil Galewski 
Turing Completeness and Sid Meier’s Civilization 
W pracy zostało wykazane, że trzy gry strategiczne z serii Sid Meier's Civilization: Sid Meier’s Civilization: Beyond Earth, Sid Meier’s Civilization V, i Sid Meier’s Civilization VI, są zupełne w sensie Turinga. Dla każdej gry została pokazana, oparta na jej mechanikach, konstrukcja uniwersalnej maszyny Turinga. Istnienie takich maszyn oznacza, że pod pewnymi założeniami gry te są nierozstrzygalne. Praca pokazuje działanie przykładowej maszyny  Zajętego Bobra złożonego z trzech stanów, zaimplementowanej w jednej z gier. 
22.11.76277 Jan Kościsz 
Podstawy Informatyki FIXED POINT COMBINATORS AS FIXED POINTS OF HIGHERORDER FIXED POINT GENERATORS by ANDREW POLONSKY 
Corrado Bohm once observed that if Y is any fixed point combinator (fpc), then Y (\yx:x(yx)) is again fpc. He thus discovered the first \fpc generating scheme" a generic way to build new fpcs from old. Continuing this idea, define an fpc generator to be any sequence of terms G_1, ..., G_n such that Y is fpc then Y G_1...G_n is fpc: In this contribution, we take first steps in studying the structure of (weak) fpc generators. We isolate several robust classes of such generators, by examining their elementary properties like injectivity and (weak) constancy. We provide sufficient conditions for existence of fixed points of a given generator (G_1, ..., G_n): an fpc Y such that Y = Y G_1 ... G_n. We conjecture that weak constancy is a necessary condition for existence of such (higherorder) fixed points. This statement generalizes Statman's conjecture on nonexistence of "double fpcs": fixed points of the generator (G) = (\yx:x(yx)) discovered by Bohm. Finally, we define and make a few observations about the monoid of (weak) fpc generators. This enables us to formulate new conjectures about their structure. 
02.07.73508 David Wood Monash University 
Informatyka Teoretyczna Universality in minorclosed graph classes* 
Stanislaw Ulam asked whether there exists a universal countable planar graph (that is, a countable planar graph that contains every countable planar graph as a subgraph). János Pach (1981) answered this question in the negative. We strengthen this result by showing that every countable graph that contains all countable planar graphs must contain an infinite complete graph as a minor. On the other hand, we construct a countable graph that contains all countable planar graphs and has several key properties such as linear colouring numbers, linear expansion, and every finite nvertex subgraph has O(n^{1/2}) treewidth (which implies the LiptonTarjan separator theorem). More generally, for every fixed positive integer t we construct a countable graph that contains every countable K_{t}minorfree graph and has the above key properties. Joint work with Tony Huynh, Bojan Mohar, Robert Šámal and Carsten Thomassen * exceptionally: Tuesday at 11:00 
18.03.59905 Daniel Bobrzyk, Mateusz Golonka 
Wake Up and Join Me! An EnergyEfficient Algorithm for Maximal Matching in Radio Networks 
22.01.57222 Bartłomiej Kielak 
Informatyka Teoretyczna Inducibility of small oriented graphs 
For a fixed graph H, let i(H, n) be the maximum induced density of H in any graph on n vertices. The limit i(H, n), as n goes to infinity, always exists and is called inducibility of H. Fox, Huang, and Lee proved that for almost all graphs H (think of large 'typical' graphs), inducibility of H can be obtained as the limit of induced density of H in its iterated blowups. Apart from that, inducibility is well understood only for narrow classes of graphs; in particular, it is still not determined for H being a path on 4 vertices. Definition of inducibility can be easily adapted to different settings of combinatorial structures. In this talk, I will focus on the setting of oriented graphs and discuss the inducibility of oriented graphs on at most 4 vertices.
Joint work with Łukasz Bożyk and Andrzej Grzesik 
06.07.40790 Jędrzej Hodor 
Optymalizacja Kombinatoryczna Reconfiguring Independent Sets on Interval Graphs 
In the reconfiguration problem, we are given a set of objects and rules of how one object can be reconfigured into another one. The main questions to be asked are if it is possible to reconfigure two given objects into each other (Reachability Problem) or how long is the shortest possible reconfiguration sequence. We focus on reconfiguring independent sets in a given graph. Two independent sets are reconfigurationadjacent if their symmetric difference consists exactly of two vertices connected by an edge. It is known that for some graph classes the Reachability Problem can be solved in polynomial time. I briefly survey the topic and show that the problem is computationally hard for incomparability graphs. Moreover, I discuss the reconfiguration paths length problem in general and in more detail in the class of interval graphs. 
16.09.38056 Daniel Kráľ Masaryk University in Brno 
Informatyka Teoretyczna Uniform Turán density of hypergraphs 
In the early 1980s, Erdős and Sós, initiated the study of the classical Turán problem with a uniformity condition: the uniform Turán density of a hypergraph H is the infimum over all d for which any sufficiently large hypergraph with the property that all its linearsize subhyperghraphs have density at least d contains H. In particular, they raise the questions of determining the uniform Turán densities of K_{4}^{3}, the complete 4vertex 3uniform hypergraph, and K_{4}^{3}, the hypergraph K_{4}^{3} with an edge removed. The latter question was solved only recently in [Israel J. Math. 211 (2016), 349–366] and [J. Eur. Math. Soc. 97 (2018), 77–97], while the former still remains open for almost 40 years. Prior to our work, the hypergraph K_{4}^{3} was the only 3uniform hypergraph with nonzero uniform Turán density determined exactly. During the talk, we will present the following two results:
The talk is based on results obtained jointly with (subsets of) Matija Bucić, Jacob W. Cooper, Frederik Garbe, Ander Lamaison, Samuel Mohr and David Munhá Correia. 
08.04.21629 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna Open problem session 
Several open problems related to 123 Conjecture are presented. 
12.05.18891 Virginia Vassilevska Williams MIT 
Informatyka Teoretyczna A refined laser method and (slightly) faster matrix multiplication 
Matrix multiplication is one of the most basic linear algebraic operations outside elementary arithmetic. The study of matrix multiplication algorithms is very well motivated from practice, as the applications are plentiful. Matrix multiplication is also of great mathematical interest. Since Strassen's discovery in 1969 that nbyn matrices can be multiplied asymptotically much faster than the bruteforce O(n^{3}) time algorithm, many fascinating techniques have been developed, incorporating ideas from computer science, combinatorics, and algebraic geometry. The fastest algorithms over the last three decades have used Strassen's "laser method" and its optimization by Coppersmith and Winograd. The method has remained unchanged; the algorithms have differed in what the method was applied to. In recent work, joint with Josh Alman, we improve the method so that applying it to the same objects that the old method was applied to immediately yields faster algorithms. Using this new method, we obtain the theoretically fastest algorithm for matrix multiplication to date, with running time O(n^{2.37286}). This talk will give an overview of the main techniques and will also outline our recent improvement of the laser method. 
12.04.49031 Szymon Salabura 
Optymalizacja Kombinatoryczna The Fixing Block Method in Combinatorics on Words 
A word is repetitive if it contains two consecutive identical blocks. A sequence is nonrepetitive up to mod r if each of its mod k (1⩽k⩽r) subsequences is nonrepetitive. Let L be a language of nonrepetitive (up to mod r) words. In this seminar, we are going to take a look at fixing blocks  a special kind of suffixes preventing words of L to have an extension in L. Using the fixing blocks method we are going to show some interesting properties of such languages. We also outline a method of attack for more complex problems.
(the seminar will only be online) 
03.01.49008 Wojciech Węgrzynek 
Optymalizacja Kombinatoryczna Nonrepetetive words: ages and essences 
The age of an infinite word will be the set of all its finite subwords, it's essence will be the set of all finite subwords occurring infinitely many times. The language L_{{121,323}} is the language of all squarefree infinite words, such that they don’t have 121 or 323 as subwords. It turns out if we consider the equivalence relations on L_{{121,323}} in respect to the ages and the essences we will get an uncountable cardinality of equivalence classes and 1 equivalence class respectively.
(the seminar will only be online) 
05.02.46270 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.

05.12.29865 Bartosz Wodziński 
Optymalizacja Kombinatoryczna Zarankiewicz's Problem and some related results 
In 1951, Kazimierz Zarankiewicz posed a problem asking for the largest possible number of edges in a bipartite graph that has a given number of vertices (n) and has no complete bipartite subgraphs of a given size. Although solved for some specific cases, it still remains open in general. It led to some interesting results in extremal graph theory, such as Kővári–Sós–Turán theorem which gives an upper bound for this problem. During the seminar, I will discuss several problems related to forbidding subgraphs, from easy up to unsolved ones. I will also show their connection with some geometric problems such as creating a maximum number of unit distances between n points on a plane.
(the seminar will only be online) 
28.08.29842 Michał Zwonek 
Optymalizacja Kombinatoryczna Polyomino Tilings 
A polyomino is a subset of R^{2} formed by a strongly connected union of axisaligned unit squares centered at locations on the square lattice Z^{2}. Let T = {T_{1},T_{2},...} be an infinite set of finite simply connected closed sets of R^{2}. Provided the elements of T have pairwise disjoint interiors and cover the Euclidean plane, then T is a tiling and the elements of T are called tiles. Provided every T_{i }∈ T is congruent to a common shape T, then T is monohedral, T is the prototile of T, and the elements of T are called copies of T. In this case, T is said to have a tiling. We will go through some of the open problems related to polyomino tilings. (the seminar will only be online) 
01.10.27104 Paweł Rzążewski Warsaw University of Technology 
Informatyka Teoretyczna Treewidth of graphs with forbidden induced subgraphs 
The notion of treewidth and tree decompositions plays a central role in the study of graphs with forbidden minors. Besides structural characterizations, the property of having boundedtreewidth, or a tree decomposision with certain "nice" properties, can be used algorithmically. However, until very recently, there were very few results that allowed to analyze the treewidth of graphs that exclude certain induced subgraphs. Indeed, a large clique has large treewidth, but is Hfree for any graph H which is not a clique. It turns out that some intresting relations between the two worlds can be found if we additionally put some restrictions on vertex degrees  either just by bounding the maximum degree, or, in some cases, by bounding the degeneracy. During the talk we will discuss some results of this flavor. In particular, we will show that
Based on the joint work with Gartland, Lokshtanov, Pilipczuk, Pilipczuk, and with Abrishami, Chudnovsky, and Dibek. 
30.01.24171 Bartosz Walczak 
Informatyka Teoretyczna Coloring polygon visibility graphs and their generalizations 
The visibility graph of a polygon P is formed by the pairs of vertices u and v of P such that the segment uv is disjoint from the exterior of P. We show that the class of polygon visibility graphs is χbounded, thus answering a question by Kára, Pór, and Wood from 2005. Specifically, we prove the bound χ≤3⋅4^{ω−1}. We obtain the same bound for generalizations of polygon visibility graphs in which the polygon is replaced by a curve and straightline segments are replaced by segments in a pseudoline arrangement. The proof is carried through in the setting of ordered graphs. In particular, we show χboundedness of several classes of ordered graphs with excluded ordered substructures. Joint work with James Davies, Tomasz Krawczyk, and Rose McCarty. This is a part of Round the World Relay in Combinatorics organized by Oxford University. Here is the full schedule: http://people.maths.ox.ac.uk/scott/relay.htm And the zoom link for the whole event: 
27.05.7939 Marthe Bonamy Université de Bordeaux 
Informatyka Teoretyczna Graph recolouring 
Given a solution to a problem, we can try and apply a series of elementary operations to it, making sure to remain in the solution space at every step. What kind of solutions can we reach this way? How fast? This is motivated by a variety of applications, from statistical physics to reallife scenarios, including enumeration and sampling. In this talk, we will discuss various positive and negative results, in the special case of graph colouring. 
06.04.76410 Jan Mełech 
Optymalizacja Kombinatoryczna Rödl Nibble 
For positive integers r<k<n let m(n,k,r) be the maximal size of a family F of kelement subsets of [n] such that no r vertices lie in more than one A in F. The ErdösHanani conjecture states that as n grows to infinity m(n,k,r) tends to (n choose r)/(k choose r). Firstly, we will see a sketch of the proof of this conjecture proposed by Vojtech Rödll. Then we will talk about how this is connected with packing in hypergraph and discuss the idea of an algorithm called Rödl nibble that achieves asymptotically optimal packing kuniform hypergraphs. (the seminar will only be online) 
28.12.76386 Krzysztof Pióro 
Optymalizacja Kombinatoryczna Decomposing planar graphs into graphs with degree restrictions 
Given a graph G, its (d,h)decomposition is a partition of a set of edges of this graph into a ddegenerate graph and a graph with maximum degree at most h. We will study (d,h)decomposability of planar graphs and consider the problem of finding minimum h_{d} such that every planar graph is (d,h_{d})decomposable. Since every planar graph is 5degenerate, we will consider only the case of d less than 5. (the seminar will only be online) 
Poprzednie referaty
26.05.2021 Piotr Kawałek 
Informatyka Teoretyczna Constant depth circuits 
We will overview the stateoftheart results and techniques used in proofs of the lower bounds for constant depth circuits. We focus mostly on classes AC[0], ACC[0] and CC[0]. The most important challenges and some open problems are to be discussed. 
29.11.57244 Maciej Nemś 
Optymalizacja Kombinatoryczna Ant Colony Optimization 
Ant Colony Optimization algorithms are part of swarm intelligence approach to solving problems. They are inspired by behavior of ants. After finding a desired destination ants leave pheromones on the way back to the colony. This way all ants can detect the scent and decide to go in the direction suggested by pheromone trail. ACO is based on this concept and involves multiagent computation. Communication between agents is done by changing the stimuli for all agents, to make a certain action. This is similar to ants leaving pheromones. Presentation will include basic concept of Ant Colony Optimization and an example of solving a well known problem using it. I will also present a formalization of ACO into a metaheuristic for combinatorial optimization problems. Presentation will end with talk about current state of ACO, its limitation and possible future.
(the seminar will only be online) 
22.08.57221 Wojciech Buczek 
Optymalizacja Kombinatoryczna Woodall’s conjecture 
Woodall’s conjecture tells us, that any directed cut with at least k edges has at least k disjoint dijoins. Set of edges D is a dijoin if and only if the digraph (V, E ∪ D^{1}) is strongly connected. We will say about the linear programming formulation of this problem, equivalent and related problems to it, and some partial results by Shrijver, Lee and Wakabayashi, and Meszaros. We will also show counterexamples to a generalized version of the conjecture.
(the seminar will only be online) 
25.09.54483 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 
16.04.38056 Vladyslav Rachek, Ruslan Yevdokymov 
Optymalizacja Kombinatoryczna An Introduction to the Discharging Method via Graph Coloring 
The discharging method is a technique that can be used to show that some global properties of a graph imply the existence of local structures. Then, we can sometimes show, that such structures imply that the graph has another global property. The discharging method is thus a "connector" between global properties of a graph (via local properties, e.g. having subgraphs or minors). In the first part of the presentation, we talk about the structure and coloring of sparse and plane graphs. Typical statements will sound like "If there is some global degree bound, then the chromatic number is somehow bounded"
(the seminar will only be online) 
21.05.35318 Grzegorz Gutowski 
Informatyka Teoretyczna Filling blanks in matrices to avoid singularity: progress report 
Given an nbyn generator matrix with entries being subsets of a fixed field we generate the set of all matrices with entries coming from the corresponding entries in the generator matrix. Such a set of matrices is strongly singular if each member is a singular matrix. In this talk I will survey natural generalizations and connections to other problems. In particular, I will describe algorithm by Geelen for maximum rank matrix completion problem. 
20.03.18914 Marcin Serwin 
Optymalizacja Kombinatoryczna AanderaaKarpRosenberg conjecture 
The conjecture deals with queries on graph. More concretely given property of a graph (such as connectedness or nonemptiness) we may ask whether it is possible to recognize a graph with this property without querying all of its edges. It turns out that for many properties it is indeed not possible to do so in a deterministic manner for all graphs. The Aanderaa–Karp–Rosenberg conjecture states that any nontrivial monotone graph property cannot be determined by a deterministic algorithm with less than n(n1)/2 queries. Such graph properties are called evasive, thus this conjecture is sometimes called evasiveness conjecture. (the seminar will only be online) 
10.12.18890 Krzysztof Potępa 
Optymalizacja Kombinatoryczna Orienting Fully Dynamic Graphs with WorstCase Time Bounds 
In the edge orientation problem, one is asked to orient edges of a given graph such that the outdegrees of vertices are bounded by some function. In the fully dynamic variant, we want to process arbitrary edge insertions and deletions in an online fashion. We will show an algorithm for graphs with bounded arboricity that achieves logarithmic outdegree bound and supports updates in O(log n) worstcase time.
(the seminar will only be online) 
13.01.16153 Louis Esperet Université Grenoble Alpes 
Informatyka Teoretyczna Universal graphs and labelling schemes 
Given a graph class C, a graph G is universal for C if it "contains" all the graphs from C. As there are several notions of containment, there are several notions of universal graphs. In this talk I'll mention two versions:
Note that an isometric copy is an induced copy, so the second notion is stronger. These notions are closely related to the notion of labelling schemes in graphs. The goal is to assign labels to the vertices of each graph G from C such that upon reading the labels of any two vertices u and v, we know some properties of u and v in G (whether they are adjacent, or their distance, or whether u is reachable from v if G is a digraph). It turns out that minimizing the size of the labels is equivalent to constructing small universal graphs, at least in the case of induceduniversal graphs. For isometricuniversal graphs some additional work needs to be done. I'll survey some recent progress in this area. In particular I'll show how to construct induceduniversal graphs of almost optimal size for any hereditary class, using the regularity lemma. In particular this implies almost optimal reachabilty labelling schemes in digraphs and comparability labelling schemes in posets, and the construction of an almost optimal universal poset for the class of all nelement posets (of size 2^{n/4+o(n)}). I will also show how to construct isometricuniversal graphs of size 3^{n+o(n)} for the class of all nvertex graphs, answering a question of Peter Winkler. Based on joint work with Marthe Bonamy, Cyril Gavoille, Carla Groenland, and Alex Scott. 
21.09.81862 Mateusz Kaczmarek 
Optymalizacja Kombinatoryczna On triangles in Krminor free graphs 
There is a close connection between minors of the graph and a lower bound on such number k that each edge (or vertex) belongs to at least k triangles. One of the most interesting classes of minors is the class of complete graphs K_{r}. In the paper 'On triangles in K_{r}minor free graphs', Boris Albar and Daniel Gonçalves take a closer look at this class of graphs. Based on their work I will present some interesting results regarding this connection and show how it correlates with Hadwiger's conjecture.
(the seminar will only be online) 
25.10.79124 Daniel Kráľ Masaryk University in Brno 
Informatyka Teoretyczna Quasirandom combinatorial structures 
A combinatorial structure is said to be quasirandom if it resembles a random structure in a certain robust sense. The notion of quasirandom graphs, developed in the work of Rödl, Thomason, Chung, Graham and Wilson in 1980s, is particularly robust as several different properties of truly random graphs, e.g., subgraph density, edge distribution and spectral properties, are satisfied by a large graph if and only if one of them is. We will discuss quasirandom properties of other combinatorial structures, tournaments, permutations and Latin squares in particular, and present several recent results obtained using analytic tools of the theory of combinatorial limits. The talk is based on results obtained with different groups of collaborators, including Timothy F. N. Chan, Jacob W. Cooper, Robert Hancock, Adam Kabela, Ander Lamaison, Taísa Martins, Roberto Parente, Samuel Mohr, Jonathan A. Noel, Yanitsa Pehova, Oleg Pikhurko, Maryam Sharifzadeh, Fiona Skerman and Jan Volec. 
16.05.62697 Bartłomiej Jachowicz 
Optymalizacja Kombinatoryczna Acyclic coloring of graphs with fixed maximum degree 
An acyclic vertex coloring of a graph is a proper vertex coloring such that there are no bichromatic cycles. The acyclic chromatic number of G, denoted as a(G), is the minimum number of colors required for acyclic vertex coloring of graph G. Known problem in this area is to find an upper bound for an acyclic chromatic number for graphs with a fixed maximum degree. One of the first papers on this topic is Hocquard's article "Graphs with maximum degree 6 are acyclically 11colorable". The proofing technique from his work has been used in many later papers that show similar bounds for graphs with fixed maximum grades.
(the seminar will only be online) 
20.06.59959 Paweł Gawrychowski University of Wrocław 
Informatyka Teoretyczna Fully Dynamic Longest Increasing Subsequence 
We revisit the problem of maintaining the longest increasing subsequence (LIS) of an array under (i) inserting an element, and (ii) deleting an element of an array. In a recent breakthrough, Mitzenmacher and Seddighin [STOC 2020] designed an algorithm that maintains an O((1/ϵ)^{O(1/ϵ)})approximation of LIS under both operations with worstcase update time ~O(n^{ϵ}), for any constant ϵ>0. We exponentially improve on their result by designing an algorithm that maintains a (1+ϵ)approximation of LIS under both operations with worstcase update time ~O(ϵ^{−5}). Instead of working with the grid packing technique introduced by Mitzenmacher and Seddighin, we take a different approach building on a new tool that might be of independent interest: LIS sparsification. While this essentially settles the complexity of the approximate version of the problem, the exact version seems more elusive. The only known sublinear solution was given very recently by Kociumaka and Seddighin [STOC 2021] and takes ~O(n^{2/3}) time per update. We show polynomial conditional lower bounds for two natural extensions of this problem: weighted LIS and LIS in any subarray. Joint work with Wojciech Janczewski

10.01.43532 Piotr Mikołajczyk 
Optymalizacja Kombinatoryczna Thomassen's choosability argument revisited 
The Hadwiger Conjecture states that if a graph G does not contain a clique on t vertices as a minor, then G is (t1)colorable. For low values of t (<7) it was already shown that this claim is actually true. Currently, the bestknown upper bound on the chromatic number of K_{t}minorfree graphs is O(ct*sqrt(log(t))) and the proof follows from a degeneracy argument. Unfortunately, this approach cannot be exploited further. However, by revisiting Thomassen's reasoning from '94 we can try to prepare the ground for a new way of attacking the Hadwiger Conjecture based on graph choosability. For that, we will take a look at a new proof of a theorem that every K_{5}minorfree graph is 5choosable.
(the seminar will only be online) 
12.02.40794 Michał Seweryn 
Informatyka Teoretyczna Dimension of posets with kouterplanar cover graphs 
In 2015, Felsner, Trotter, and Wiechert showed that posets with outerplanar cover graphs have bounded dimension. We generalise this result to posets with kouterplanar cover graphs. Namely, we show that posets with kouterplanar cover graph have dimension O(k^{3}). As a consequence, we show that every poset with a planar cover graph and height h has dimension O(h^{3}). This improves the previously best known bound of O(h^{6}) by Kozik, Micek and Trotter. Joint work with Maximilian Gorsky 
04.09.24366 Jędrzej Kula 
Optymalizacja Kombinatoryczna Combinatorial Nullstellensatz 
Proposed by Noga Alon in 1999 an algebraic technique inspired by Hilbert’s Nullstellensatz. Despite being an observation about roots of a polynomial in n variables, it finds a usage in numerous fields  from Combinatorial Number Theory to Graph Theory. The theory itself is simple, but can be used in ingenious ways  appearing even as almost a necessary step to solve a problem during the 2007 IMO competition. During this time slot I will present a theorem and prove it with as I believe a simpler proof constructed by Mateusz Michałek, that is using a basic induction idea over a polynomial degree. Finally we will again follow the original N. Alon paper to see applications of a theorem in the graph coloring problems and some more.
(the seminar will only be online) 
07.10.21628 Mikołaj Bojańczyk University of Warsaw 
Informatyka Teoretyczna Recognisable languages over monads 
Algebraic language theory originated in the study of regular languages via semigroups, instead of automata. The advantage of the semigroup approach is a richer structural theory, e.g. Green’s theory or the Factorisation Forest Theorem. (In contrast, the structural analysis of automata seldom goes beyond such elementary notions as “cycle” or “connected component”.) In this talk, I will discuss a more abstract view on semigroups, as EilenbergMoore algebras over the monad of finite words (aka the list monad in programming languages). Using this abstract view, by changing the monad, one can get the appropriate notion of “semigroup” for objects beyond finite words, e.g. trees or graphs. Sometimes, even theorems can be proved using this abstract view.
This talk is based on the draft monograph

14.06.87338 Andrzej Dorobisz 
Informatyka Teoretyczna Local Computation Algorithms for Coloring of Uniform Hypergraphs 
We present a progress on local computation algorithms for two coloring of kuniform hypergraphs. We focus on instances that (for a parameter α) satisfy strengthened assumption of Local Lemma of the form 2^{1αk}(Δ+1)e<1, where Δ is the bound on the maximum edge degree of the hypergraph. We discuss how previous works on the subject can be used to obtain an algorithm that works in polylogarithmic time per query for α up to about 0.139. Then, we present a procedure that, within similar bounds on running time, solves wider range of instances by allowing α to be at most about 0.227. Joint work with Jakub Kozik 
04.01.70911 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna Local Dimension of Planar Poset 
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. (the seminar will only be online) 
06.02.68173 Marcin Pilipczuk University of Warsaw 
Informatyka Teoretyczna Recent progress in understanding Hfree graphs for H being a path or a subdivided claw 
Graph classes excluding a path or a subdivided claw as an induced subgraph are so far mysterious: on one hand, beside some corner cases, they do not seem to have any good structural description, but on the other hand, a number of combinatorial problems  including Maximum Independent Set (MIS)  lack an NPhardness proof in these graph classes, indicating a possible hidden structure that can be used algorithmically. Furthermore, graphs excluding a fixed path as an induced subgraph were one of the earliest examples of a chibounded graph class, with an elegant proof technique dubbed the Gyarfas' path argument. In the recent years the progress accelerated, leading to, among other results, (a) a quasipolynomialtime algorithm for MIS in graphs excluding a fixed path as an induced subgraph, (b) a QPTAS for MIS in graphs excluding a subdivided claw as an induced subgraph, (c) the proof of the ErdosHajnal property in graph classes excluding a fixed forest and its complement. In the talk, I will survey these results, showing the role of the Gyarfas' path argument in most (all?) of them, and outline research directions for the future. 
29.08.51745 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna The 1/3  2/3 conjecture 
A given pair of two incomparable elements x, y in poset P is called balanced if, of all line extensions P, the element x lies above y by at most 2/3 and on at least 1/3 of all extensions of the poset P. The 1/3  2/3 conjecture says that any poset that is not linear has a balanced pair. The talk presents basic definitions and an overview of the most important results in this field. (the seminar will only be online) 
03.10.49007 Stefan Felsner Technische Universität Berlin 
Informatyka Teoretyczna Combinatorics of Pseudocircle Arrangements 
In this talk we survey results for pseudocircle arrangements. Along the way we present several open problems. Among others we plan to touch the following topics: * The taxonomy of classes of pseudocircle arrangements. The talk includes work of Grünbaum, Snoeyink, Pinchasi, Scheucher, myself, and others. 
23.04.32580 Jędrzej Hodor 
Optymalizacja Kombinatoryczna Polynomial Treedepth Bounds in Linear Colorings 
Centered graph coloring is graph coloring, such that for every connected subgraph, this subgraph contains a vertex with a unique color (we call such a vertex center). Linear coloring is coloring, such that every path has a center. We denote by cen(G) and lin(G) respectively, a minimal number of colors needed. It is obvious that lin(G) ≤ cen(G). What about the other direction? Authors of the paper show that cen ≤ f(lin), where f is a polynomial of the degree 190. Moreover, the authors conjecture that cen ≤ 2 lin for every graph. What is interesting, we don't know how to prove such abound even for trees. Luckily, for some classes of graphs, we can do better than 190poly. During the seminar, I will present results for simple classes of graphs and I will try to sketch the general proof. In particular, I will present a cubic bound for interval graphs. The proof in the paper is incorrect, but I and dr Micek managed to fix it. Finally, I will present our new result for graphs with bounded path width.
(the seminar will only be online) 
28.05.29842 Bartosz Walczak 
Informatyka Teoretyczna Approximating Pathwidth for Graphs of Small Treewidth 
We describe a polynomialtime algorithm which, given a graph G with treewidth t, approximates the pathwidth of G to within a ratio of O(t √ log t). This is the first algorithm to achieve an f(t)approximation for some function f. Our approach builds on the following key insight: every graph with large pathwidth has large treewidth or contains a subdivision of a large complete binary tree. Specifically, we show that every graph with pathwidth at least th+2 has treewidth at least t or contains a subdivision of a complete binary tree of height h+1. The bound th+2 is best possible up to a multiplicative constant. This result was motivated by, and implies (with c=2), the following conjecture of Kawarabayashi and Rossman (SODA'18): there exists a universal constant c such that every graph with pathwidth Ω(k^{c}) has treewidth at least k or contains a subdivision of a complete binary tree of height k. Our main technical algorithm takes a graph G and some (not necessarily optimal) tree decomposition of G of width t' in the input, and it computes in polynomial time an integer h, a certificate that G has pathwidth at least h, and a path decomposition of G of width at most (t'+1)h+1. The certificate is closely related to (and implies) the existence of a subdivision of a complete binary tree of height h. The approximation algorithm for pathwidth is then obtained by combining this algorithm with the approximation algorithm of Feige, Hajiaghayi, and Lee (STOC'05) for treewidth.
Joint work with Carla Groenland, Gwenaël Joret, and Wojciech Nadara. 
07.12.70910 Kamil Kropiewnicki 
Optymalizacja Kombinatoryczna Contextual Reserve Price Optimization in Auctions via MixedInteger Programming 
We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. First, we show that it is not possible to solve this problem in polynomial time unless the Exponential Time Hypothesis fails. Second, we present a strong mixedinteger programming (MIP) formulation for this problem, which is capable of exactly modeling the nonconvex and discontinuous expected reward function. More broadly, we believe this work offers an indication of the strength of optimization methodologies like MIP to exactly model intrinsic discontinuities in machine learning problems. This presentation might be of interest for, among the others, the participants of the Algorithmic Game Theory course as it presents the modern approach for maximizing revenue in secondprice auctions.
(the seminar will only be online) 
04.11.79147 Rafał Burczyński 
Optymalizacja Kombinatoryczna BollobásEldridgeCatlin Conjecture on graph packing 
Let G_{1}, G_{2} be nvertex graphs. We say that they pack if they are edgedisjoint subgraphs of a complete graph on n vertices. The BollobásEldridgeCatlin conjecture states that if (Δ(G_{1}) + 1) (Δ(G_{2}) + 1) < n + 1, then G_{1} and G_{2} pack. During the seminar, we will take a look at current results related to this problem, i.e. classes of graphs for which it has been proven as well as similar conjectures stemming from it. (the seminar will only be online) 
27.07.79124 Weronika Lorenczyk 
Optymalizacja Kombinatoryczna The Cap Set Conjecture 
The cap set problem asks how large can a subset of Z_{/3Z}^{n} be and contain no lines or, more generally, how can large a subset of Z_{/pZ}^{n} be and contain no arithmetic progression. The problem was open until 2016 when its basic version was solved. During the lecture, we'll see the motivation for thinking about this. It appears there are some interesting applications of this result in combinatorics, geometry, and even board games. (the seminar will only be online) 
29.06.59982 Bartosz Wodziński 
Optymalizacja Kombinatoryczna Graph Removal Lemma 
Let H be a graph on h vertices. The Graph Removal Lemma states that for any ε > 0, there exists a constant δ(ε, H) > 0 such that for any nvertex graph G with fewer than δn^{h} subgraphs isomorphic to H, it is possible to eliminate all copies of H by removing at most εn^{2} edges from G. It has several important consequences in number theory, discrete geometry, graph theory, and computer science. During the seminar, I will discuss this lemma and its extensions. I will also tell about some of its applications, such as graph property testing and Szeremedi's Theorem proof.
(the seminar will only be online) 
22.03.59959 Artur Kasymov 
Optymalizacja Kombinatoryczna Machine learning in Combinatorial Optimization 
Machine learning has already leaked almost all areas. What about Combinatorial Optimization? At this seminar, I will present basic ML concepts and methods in CO: Where you can add ML black box in your algorithm? Can heuristics be compared to ML? What are the recent achievements? (the seminar will only be online) 
19.10.57111 Weronika Loreńczyk 
Podstawy Informatyki The Fractal Dimension of SAT Formulas by Carlos Ansotegui, Maria 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 after an intensive experimental process. It is believed that these techniques exploit the underlying structure of industrial instances. However, there is not a precise definition of the notion of structure. Recently, there have been some attempts to analyze this structure in terms of complex networks, with the longterm aim of explaining the success of SAT solving techniques, and possibly improving them. We study the fractal dimension of SAT instances with the aim of complementing the model that describes the structure of industrial instances. We show that many industrial families of formulas are selfsimilar, with a small fractal dimension. We also show how this dimension is affected by the addition of learnt clauses during the execution of SAT solvers. 
21.02.40817 Bruno Pitrus 
Optymalizacja Kombinatoryczna Seven trees in one: objects of categories as complex numbers 
Consider the following absurd argument concerning planar, binary, rooted, unlabelled trees. Every such tree is either the trivial tree or consists of a pair of trees joined together at the root, so the set T of trees is isomorphic to 1+T². Pretend that T is a complex number and solve the quadratic T = 1+T² to find that T is a primitive sixth root of unity and so T⁶ = 1. Deduce that T⁶ is a oneelement set; realize immediately that this is wrong. Notice that T⁷ = T is, however, not obviously wrong, and conclude that it is therefore right. In other words, conclude that there is a bijection T⁷ ≅ T built up out of copies of the original bijection T ≅ 1+T²: a tree is the same as seven trees.
(the seminar will only be online) 
14.11.40793 Krzysztof Pióro 
Optymalizacja Kombinatoryczna Gallai’s conjecture 
A path decomposition of a graph G is a collection of edgedisjoint paths of G that covers the edge set of G. Gallai (1968) conjectured that every connected graph on n vertices admits a path decomposition of cardinality at most ⌈n/2⌉. Gallai’s Conjecture has been verified for many classes of graphs. In this seminar, we will cover some of these graph classes. (the seminar will only be online) 
03.05.37946 Maciej Nemś 
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. 
09.07.21628 Szymon Żak 
Optymalizacja Kombinatoryczna Aleph: Efficient Atomic Broadcast in Asynchronous Networks with Byzantine Nodes 
In this seminar, I will cover general ideas that stand behind Aleph protocol. Aleph is a leaderless, fully asynchronous, Byzantine fault tolerant consensus protocol for ordering messages exchanged among processes. It is based on a distributed construction of a partially ordered set and the algorithm for reaching a consensus on its extension to a total order.
(the seminar will only be online) 
12.10.49030 Jan Mełech 
Optymalizacja Kombinatoryczna Hamiltonian paths/cycles in vertextransitive/symmetric graphs 
Graph is vertextransitive if every vertex has the same local environment, so that no vertex can be distinguished from any other based on the vertices and edges surrounding it. In 1969, Lovasz conjectured that every finite connected vertextransitive graph has Hamiltonian path. Moreover, up to now there are currently only five known connected vertextransitive graphs not containing Hamiltonian cycle. In this seminar we will focus also on some other weaker variants of Lovasz conjecture related to other interesting class of graphs that encode the abstract structures of a groups  Cayley graphs. (the seminar will only be online) 
05.07.49007 Mateusz Kaczmarek 
Optymalizacja Kombinatoryczna From linear lambda terms to rooted trivalent maps 
Recent work on the combinatorics of the linear lambda term shows that it has various connections to the theory of graph surfaces (maps). Based on paper [1] I will present a bijection between linear lambda terms (presented as diagrams) and rooted trivalent maps. Also, I will cover the recent conjecture proposed in 2019 that a special class of planar lambda terms can be counted the same way that rooted bicubic maps.
(the seminar will only be online) 
31.01.46160 Weronika Loreńczyk  canceled 
Podstawy Informatyki The Fractal Dimension of SAT Formulas by Carlos Ansotegui, Maria 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 after an intensive experimental process. It is believed that these techniques exploit the underlying structure of industrial instances. However, there is not a precise definition of the notion of structure. Recently, there have been some attempts to analyze this structure in terms of complex networks, with the longterm aim of explaining the success of SAT solving techniques, and possibly improving them. We study the fractal dimension of SAT instances with the aim of complementing the model that describes the structure of industrial instances. We show that many industrial families of formulas are selfsimilar, with a small fractal dimension. We also show how this dimension is affected by the addition of learnt clauses during the execution of SAT solvers. 
06.06.29865 Wojciech Buczek 
Optymalizacja Kombinatoryczna Inscribed square problem 
Let C be a Jordan curve. We say that polygon P is inscribed in C if all vertices of P belong to C. In the inscribed square problem we ask if every Jordan curve admits an inscribed square. It's also known as "Toeplitz’s conjecture" or the "Square peg problem". In this seminar, we will show some equivalent problems to this conjecture and focus on special cases of the Jordan curves. (the seminar will only be online) 
27.02.29842 Bartłomiej Jachowicz 
Optymalizacja Kombinatoryczna Parameterized by treewidth algorithms for Hamiltonian Cycle 
The Hamiltonian Cycle problem is one of the oldest and most common NPcomplete problems. It consists of checking whether in a given graph there is a cycle visiting each vertex exactly once. I will present a parameterized algorithm based on graph tree decomposition. Assuming that a nice tree decomposition of the width k is known at the input Hamiltonian cycle problem can be solved in a time 2^{(O(k))}n^{(O(1))}. (the seminar will only be online) 
15.08.26994 Katarzyna Król 
Podstawy Informatyki A Lower Bound of the Number of Rewrite Rules Obtained by Homological Methods by Mirai Ikebuchi 
It is wellknown that some equational theories such as groups or boolean algebras can be defined by fewer equational axioms than the original axioms. However, it is not easy to determine if a given set of axioms is the smallest or not. Malbos and Mimram investigated a general method to find a lower bound of the cardinality of the set of equational axioms (or rewrite rules) that is equivalent to a given equational theory (or term rewriting systems), using homological algebra. Their method is an analog of Squier’s homology theory on string rewriting systems. In this paper, we develop the homology theory for term rewriting systems more and provide a better lower bound under a stronger notion of equivalence than their equivalence. The author also implemented a program to compute the lower bounds. 
30.01.10700 Michał Zwonek 
Optymalizacja Kombinatoryczna Approximate Distance Oracles 
Given a finite metric space (V,d), an approximate distance oracle is a data structure which, when queried on two points u,v∈V, returns an approximation to the actual distance between u and v which is within some bounded stretch factor of the true distance. The first work in this area was done by Mikkel Thorup and Uri Zwick, they devised an oracle with construction time being O(kmn^{(1/k)}) and with the space complexity of O(kn^{(1+1/k)}). The achieved stretch, that is the measure of how accurate the answer by the approximate oracle will be, is bounded by (2k1). The query time is O(k), this has been subsequently improved to O(log n) by WulffNilsen and to O(1) by Shiri Chechik. (the seminar will only be online) 
22.10.10676 Wojciech Grabis 
Optymalizacja Kombinatoryczna Doublecritical graph conjecture 
A connected graph G is called doublecritical if the chromatic number of G decreases by two if any two adjacent vertices of G are removed. In 1966, Erdős and Lovász conjectured that the only doublecritical nchromatic graph is the complete graph on n vertices. During the seminar, I will present what has been verified about the conjecture. (the seminar will only be online) 
10.04.7829 Wojciech Węgrzynek 
Podstawy Informatyki The repetition threshold for binary rich words by James Currie, Lucas Mol and Narad Rampersad 
A word of length n is rich if it contains n nonempty palindromic factors. An infinite word is rich if all of its finite factors are rich. Baranwal and Shallit produced an infinite binary rich word with critical exponent $2 + \Sqrt{2}/2$ ( = 2.707) and conjectured that this was the least possible critical exponent for infinite binary rich words (i.e., that the repetition threshold for binary rich words is $2 + \Sqrt{2}/2$ ). In this article, we give a structure theorem for infinite binary rich words that avoid 14/5powers (i.e., repetitions with exponent at least 2.8). As a consequence, we deduce that the repetition threshold for binary rich words is $2 + \Sqrt{2}/2$ , as conjectured by Baranwal and Shallit. This resolves an open problem of Vesti for the binary alphabet; the problem remains open for larger alphabets.

10.11.73671 Krzysztof Potępa 
Optymalizacja Kombinatoryczna Erdős–Hajnal conjecture 
A wellknown theorem of Erdős states that there exists a graph on n vertices, with no clique or independent set of a size larger than O(log n). The Erdős–Hajnal conjecture says it is very different if we consider families of graphs defined by forbidden induced subgraphs. Specifically, it is conjectured that for every graph H, there exists a constant δ(H) such that every Hfree graph G has either a clique or independent set of size V(G)^{δ(H)}. We will discuss some classes of graphs for which the conjecture has been proven, as well as weaker theorems that hold for all graphs. (the seminar will only be online) 
02.08.73648 Marcin Serwin 
Optymalizacja Kombinatoryczna (m,n)cycle cover conjectures 
An (m,n)cycle cover is a covering of a graph consisting of m cycles such that every edge is covered exactly n times. For positive integers m, n it is natural to ask what family of graphs have (m,n)cycle covers. The answers are known for some values, but for many others, they are conjectured or totally open. (the seminar will only be online) 
19.01.70801 Wojtek Grabis 
Podstawy Informatyki (Optimal) Duplication is not Elementary Recursive by Andrea Asperti, Paolo Coppola and Simone Martini 
In 1998 Asperti and Mairson proved that the cost of reducing a lambdaterm using an optimal lambdareducer (a la L´evy) cannot be bound by any elementary function in the number of sharedbeta steps. We prove in this paper that an analogous result holds for Lamping’s abstract algorithm. That is, there is no elementary function in the number of shared beta steps bounding the number of duplication steps of the optimal reducer. This theorem vindicates the oracle of Lamping’s algorithm as the culprit for the negative result of Asperti and Mairson. The result is obtained using as a technical tool Elementary Affine Logic. 
14.09.51635 Michał Zwonek 
Podstawy Informatyki A Confluent Rewriting System Having No Computable, OneStep, Normalizing Strategy by JAKOB GRUE SIMONSEN 
A full and finitely generated ChurchRosser term rewriting system is presented that has no computable onestep, normalizing strategy; the system is both left and rightlinear. The result provides a negative answer to a question posed by Kennaway in 1989: Number 10 on the List of Open Problems in Rewriting. 
21.11.35317 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna Harmonious Coloring of Hypergraphs 
A harmonious coloring of a kuniform hypergraph H is a vertex coloring such that no two vertices in the same edge share the same color, and each kelement subset of colors appears on at most one edge. The harmonious number h(H) is the least number of colors needed for such a coloring. We prove that kuniform hypergraphs of bounded maximum degree Δ satisfy h(H) = O(k√k!m), where m is the number of edges in H which is best possible up to a multiplicative constant. Moreover, for every fixed Δ, this constant tends to 1 with k → ∞. We use a novel method, called entropy compression, that emerged from the algorithmic version of the Lovász Local Lemma due to Moser and Tardos. This is joint work with Sebastian Czerwinski, Jarosław Grytczuk, and Paweł Rzazewski. (the seminar will only be online) 
17.02.35263 Dzianis Pivavarau, Dominik Wielgórski 
Explicit twodeletion codes with redundancy matching the existential bound 
16.07.16152 Piotr Mikołajczyk 
Optymalizacja Kombinatoryczna Polynomial algorithms for CFGs via semiring embeddings 
A few years ago M. Might et al. published somehow unusual approach to parsing contextfree grammars by using derivative operator. Later it was proven, that its worst case complexity is polynomial, putting it on a par with other classical approaches. We introduce an elegant generalization to this method by a generic algorithm parametrized with a semiring. Depending on the chosen algebra we can obtain polynomial algorithms for problems like parsing, recognizing or counting parse trees for CFGs. (the seminar will only be online) 
12.10.16097 Bartłomiej Jachowicz, Mateusz Kaczmarek 
Counting 4Patterns in Permutations Is Equivalent to Counting 4Cycles in Graphs 
02.01.13305 Przemysław Simajchel 
Podstawy Informatyki COMPLEXITY PROBLEMS IN ENUMERATIVE COMBINATORICS by IGOR PAK 
The paper gives a broad survey of recent results in Enumerative Combinatorics and their complexity aspects. 
09.09.79014 CANCELED 
Podstawy Informatyki COMPLEXITY PROBLEMS IN ENUMERATIVE COMBINATORICS by IGOR PAK 
The paper gives a broad survey of recent results in Enumerative Combinatorics and their complexity aspects. 
15.11.62696 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna Conjecture 1/3  2/3 
A given pair of two incomparable elements x, y in poset P is called balanced if, of all line extensions P, the element x lies above y by at most 2/3 and on at least 1/3 of all extensions of the poset P. The 1/3  2/3 conjecture says that any poset that is not linear has a balanced pair. The talk presents basic definitions and an overview of the most important results in this field. (the seminar will only be online) 
12.02.62642 Marcin Serwin, Wojciech Buczek 
A DoubleExponential Lower Bound for the Distinct Vectors Problem 
14.06.59849 Piotr Mikołajczak 
Podstawy Informatyki Asymptotic Approximation by Regular Languages by Ryoma Sin’ya 
This paper investigates a new property of formal languages called REGmeasurability where REG is the class of regular languages. Intuitively, a language L is REGmeasurable if there exists an infinite sequence of regular languages that “converges” to L. A language without REGmeasurability has a complex shape in some sense so that it can not be (asymptotically) approximated by regular languages. We show that several contextfree languages are REGmeasurable (including languages with transcendental generating function and transcendental density, in particular), while a certain simple deterministic contextfree language and the set of primitive words are REGimmeasurable in a strong sense. 
12.07.43531 Vladyslav Rachek 
Optymalizacja Kombinatoryczna Small weak epsilonnets 
Let P be a set of n points in R^{2}, ε > 0. A set of points Q is called a weak εnet for P with respect to a family S of objects (e.g. axisparallel rectangles or convex sets) if every set from S containing more than εn points of P contains a point from Q. Let R be the family of all axisparallel rectangles in R^{2} and ε^{R}_{k} be the smallest real number such that for any P there exists a weak ε^{R}_{k}net of size k. The work by Aronov et al. suggests that the inequality ε^{R}_{k} ≤ 2/(k+3) may hold. In this talk we present the complete proofs of this inequality for k=1,...,5 and prove that this bound is tight for k=1,2,3. Besides, it is not clear how to construct optimal nets. Langerman conjectured that kpoint 2/(k+3)nets can be chosen from some speciffc set of points which are the intersections of grid lines, where the grid is of size k×k. We give counterexamples to this conjecture for nets of size 3 through 6.
(the seminar will only be online) 
07.10.43476 Krzysztof Pióro, Krzysztof Potępa 
Modular Subset Sum 
W problemie Modular Subset Sum dane są liczba naturalna m, nelementowy multizbiór S liczb całkowitych z zakresu od 0 do m1 oraz liczba t, dla której chcemy rozstrzygnąć, czy istnieje podzbiór S, który się do niej sumuje modulo m.
Przedstawimy własne algorytmy rozwiązujące powyższy problem. Wszystkie z nich będą sprowadzały problem Modular Subset Sum do problemu tekstowego. Na początku przedstawimy prosty algorytm działający w czasie O(n + m*log^{2}(m)) wykorzystujący haszowanie i drzewa przedziałowe. Następnie pokażemy jak poprawić jego złożoność do O(n + m*log(m)). Na końcu zaprezentujemy w pełni deterministyczny wariant algorytmu działający w czasie O(n + m*log(m)*α(m)).

07.02.40684 Jędrzej Hodor 
Podstawy Informatyki Bijective link between Chapoton’s new intervals and bipartite planar maps by Wenjie Fang 
In 2006, Chapoton defined a class of Tamari intervals called “new intervals” in his enumeration of Tamari intervals, and he found that these new intervals are equienumerated with bipartite planar maps. We present here a direct bijection between these two classes of objects using a new object called “degree tree”. Our bijection also gives an intuitive proof of an unpublished equidistribution result of some statistics on new intervals given by Chapoton and Fusy. 
06.03.24366 Bartłomiej Bosek 
Optymalizacja Kombinatoryczna From the 123 Conjecture to the Riemann Hypothesis 
A series of open (and solved) problems will be presented at the seminar, starting with the 123 Conjecture and ending with the Riemann Hypothesis. (the seminar will only be online) 
21.07.24252 Patryk Mikos 
Informatyka Teoretyczna Geometric and weight constraints in Online Interval Coloring 
PhD defense  room 0004 
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 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. 
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. 
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. 
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. 