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Volume

LIPIcs, Volume 138

44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

MFCS 2019, August 26-30, 2019, Aachen, Germany

Editors: Peter Rossmanith, Pinar Heggernes, and Joost-Pieter Katoen

Document

Complete Volume

DOI: 10.4230/LIPIcs.MFCS.2019

LIPIcs, Volume 138, MFCS'19, Complete Volume

Authors: Peter Rossmanith, Pinar Heggernes, and Joost-Pieter Katoen

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

LIPIcs, Volume 138, MFCS'19, Complete Volume

Cite as

44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Proceedings{rossmanith_et_al:LIPIcs.MFCS.2019,
  title =	{{LIPIcs, Volume 138, MFCS'19, Complete Volume}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019},
  URN =		{urn:nbn:de:0030-drops-112092},
  doi =		{10.4230/LIPIcs.MFCS.2019},
  annote =	{Keywords: Theory of computation}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.MFCS.2019.0

Front Matter, Table of Contents, Preface, Conference Organization

Authors: Peter Rossmanith, Pinar Heggernes, and Joost-Pieter Katoen

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

Front Matter, Table of Contents, Preface, Conference Organization

Cite as

44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{rossmanith_et_al:LIPIcs.MFCS.2019.0,
  author =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.0},
  URN =		{urn:nbn:de:0030-drops-109444},
  doi =		{10.4230/LIPIcs.MFCS.2019.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.MFCS.2019.1

Trustworthy Graph Algorithms (Invited Talk)

Authors: Mohammad Abdulaziz, Kurt Mehlhorn, and Tobias Nipkow

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

The goal of the LEDA project was to build an easy-to-use and extendable library of correct and efficient data structures, graph algorithms and geometric algorithms. We report on the use of formal program verification to achieve an even higher level of trustworthiness. Specifically, we report on an ongoing and largely finished verification of the blossom-shrinking algorithm for maximum cardinality matching.

Cite as

Mohammad Abdulaziz, Kurt Mehlhorn, and Tobias Nipkow. Trustworthy Graph Algorithms (Invited Talk). In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{abdulaziz_et_al:LIPIcs.MFCS.2019.1,
  author =	{Abdulaziz, Mohammad and Mehlhorn, Kurt and Nipkow, Tobias},
  title =	{{Trustworthy Graph Algorithms}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.1},
  URN =		{urn:nbn:de:0030-drops-109456},
  doi =		{10.4230/LIPIcs.MFCS.2019.1},
  annote =	{Keywords: graph algorithms, formal correct proofs, Isabelle, LEDA, certifying algorithms}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.MFCS.2019.2

Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time (Invited Talk)

Authors: Alexandra Silva

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

Guarded Kleene Algebra with Tests (GKAT) is a variation on Kleene Algebra with Tests (KAT) that arises by restricting the union (+) and iteration (*) operations from KAT to predicate-guarded versions. We develop the (co)algebraic theory of GKAT and show how it can be efficiently used to reason about imperative programs. In contrast to KAT, whose equational theory is PSPACE-complete, we show that the equational theory of GKAT is (almost) linear time. We also provide a full Kleene theorem and prove completeness for an analogue of Salomaa’s axiomatization of Kleene Algebra. We will also discuss how this result has practical implications in the verification of programs, with examples from network and probabilistic programming. This is joint work with Nate Foster, Justin Hsu, Tobias Kappe, Dexter Kozen, and Steffen Smolka.

Cite as

Alexandra Silva. Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time (Invited Talk). In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{silva:LIPIcs.MFCS.2019.2,
  author =	{Silva, Alexandra},
  title =	{{Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.2},
  URN =		{urn:nbn:de:0030-drops-109462},
  doi =		{10.4230/LIPIcs.MFCS.2019.2},
  annote =	{Keywords: Kleene algebra, verification, decision procedures}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.MFCS.2019.3

Picking Random Vertices (Invited Talk)

Authors: Daniel Lokshtanov

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

We survey some recent graph algorithms that are based on picking a vertex at random and declaring it to be a part of the solution. This simple idea has been deployed to obtain state-of-the-art parameterized, exact exponential time, and approximation algorithms for a number of problems, such as Feedback Vertex Set and 3-Hitting Set. We will also discuss a recent 2-approximation algorithm for Feedback Vertex Set in Tournaments that is based on picking a vertex at random and declaring it to not be part of the solution.

Cite as

Daniel Lokshtanov. Picking Random Vertices (Invited Talk). In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{lokshtanov:LIPIcs.MFCS.2019.3,
  author =	{Lokshtanov, Daniel},
  title =	{{Picking Random Vertices}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.3},
  URN =		{urn:nbn:de:0030-drops-109478},
  doi =		{10.4230/LIPIcs.MFCS.2019.3},
  annote =	{Keywords: Graph Algorithm}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.MFCS.2019.4

Popular Matchings: Good, Bad, and Mixed (Invited Talk)

Authors: Telikepalli Kavitha

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

We consider the landscape of popular matchings in a bipartite graph G where every vertex has strict preferences over its neighbors. This is a very well-studied model in two-sided matching markets. A matching M is popular if it does not lose a head-to-head election against any matching, where each vertex casts a vote for the matching where it gets a better assignment. Roughly speaking, a popular matching is one such that there is no matching where more vertices are happier. The notion of popularity is more relaxed than stability: a classical notion studied for the last several decades. Popular matchings always exist in G since stable matchings always exist in a bipartite graph and every stable matching is popular. Algorithmically speaking, the landscape of popular matching seems to have only a few bright spots. Every stable matching is a min-size popular matching and there are also simple linear time algorithms for computing a max-size popular matching and for the popular edge problem. All these algorithms reduce the popular matching problem to an appropriate question in stable matchings and solve the corresponding stable matching problem. We now know NP-hardness results for many popular matching problems. These include the min-cost/max-weight popular matching problem and the problem of deciding if G admits a popular matching that is neither a min-size nor a max-size popular matching. For non-bipartite graphs, it is NP-hard to even decide if a popular matching exists or not. A mixed matching is a probability distribution or a lottery over matchings. A popular mixed matching is one that never loses a head-to-head election against any mixed matching. As an allocation mechanism, a popular mixed matching has several nice properties. Moreover, finding a max-weight or min-cost popular mixed matching in G is easy (by solving a linear program). Interestingly, there is always an optimal popular mixed matching Pi with a simple structure: Pi = {(M_0,1/2),(M_1,1/2)} where M_0 and M_1 are matchings in G. Popular mixed matchings always exist in non-bipartite graphs as well and can be computed in polynomial time.

Cite as

Telikepalli Kavitha. Popular Matchings: Good, Bad, and Mixed (Invited Talk). In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kavitha:LIPIcs.MFCS.2019.4,
  author =	{Kavitha, Telikepalli},
  title =	{{Popular Matchings: Good, Bad, and Mixed}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{4:1--4:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.4},
  URN =		{urn:nbn:de:0030-drops-109489},
  doi =		{10.4230/LIPIcs.MFCS.2019.4},
  annote =	{Keywords: Matchings under preferences, Algorithms, NP-Hardness}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.MFCS.2019.5

Petri Net Reachability Problem (Invited Talk)

Authors: Jérôme Leroux

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. In this presentation, we overview decidability and complexity results over the last fifty years about the Petri net reachability problem.

Cite as

Jérôme Leroux. Petri Net Reachability Problem (Invited Talk). In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 5:1-5:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{leroux:LIPIcs.MFCS.2019.5,
  author =	{Leroux, J\'{e}r\^{o}me},
  title =	{{Petri Net Reachability Problem}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{5:1--5:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.5},
  URN =		{urn:nbn:de:0030-drops-109493},
  doi =		{10.4230/LIPIcs.MFCS.2019.5},
  annote =	{Keywords: Petri net, Reachability problem, Formal verification, Concurrency}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2019.6

An Improved Online Algorithm for the Traveling Repairperson Problem on a Line

Authors: Marcin Bienkowski and Hsiang-Hsuan Liu

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

In the online variant of the traveling repairperson problem (TRP), requests arrive in time at points of a metric space X and must be eventually visited by a server. The server starts at a designated point of X and travels at most at unit speed. Each request has a given weight and once the server visits its position, the request is considered serviced; we call such time completion time of the request. The goal is to minimize the weighted sum of completion times of all requests. In this paper, we give a 5.429-competitive deterministic algorithm for line metrics improving over 5.829-competitive solution by Krumke et al. (TCS 2003). Our result is obtained by modifying the schedule by serving requests that are close to the origin first. To compute the competitive ratio of our approach, we use a charging scheme, and later evaluate its properties using a factor-revealing linear program which upper-bounds the competitive ratio.

Cite as

Marcin Bienkowski and Hsiang-Hsuan Liu. An Improved Online Algorithm for the Traveling Repairperson Problem on a Line. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bienkowski_et_al:LIPIcs.MFCS.2019.6,
  author =	{Bienkowski, Marcin and Liu, Hsiang-Hsuan},
  title =	{{An Improved Online Algorithm for the Traveling Repairperson Problem on a Line}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{6:1--6:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.6},
  URN =		{urn:nbn:de:0030-drops-109503},
  doi =		{10.4230/LIPIcs.MFCS.2019.6},
  annote =	{Keywords: traveling repairperson problem, competitive analysis, minimizing completion time, factor-revealing LP}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2019.7

Query-Competitive Sorting with Uncertainty

Authors: Magnús M. Halldórsson and Murilo Santos de Lima

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of n data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the actual value, and we may allow an error threshold in the sorting. The goal is to find a nearly-sorted permutation by performing a minimum-cost set of queries. We show that an offline optimum query set can be found in polynomial time, and that both oblivious and adaptive problems have simple query-competitive algorithms. The query-competitiveness for the oblivious problem is n for uniform query costs, and unbounded for arbitrary costs; for the adaptive problem, the ratio is 2. We then present a unified adaptive strategy for uniform query costs that yields: (i) a 3/2-query-competitive randomized algorithm; (ii) a 5/3-query-competitive deterministic algorithm if the dependency graph has no 2-components after some preprocessing, which has query-competitive ratio 3/2 + O(1/k) if the components obtained have size at least k; (iii) an exact algorithm if the intervals constitute a laminar family. The first two results have matching lower bounds, and we have a lower bound of 7/5 for large components. We also show that the advice complexity of the adaptive problem is floor[n/2] if no error threshold is allowed, and ceil[n/3 * lg 3] for the general case.

Cite as

Magnús M. Halldórsson and Murilo Santos de Lima. Query-Competitive Sorting with Uncertainty. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{halldorsson_et_al:LIPIcs.MFCS.2019.7,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and de Lima, Murilo Santos},
  title =	{{Query-Competitive Sorting with Uncertainty}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.7},
  URN =		{urn:nbn:de:0030-drops-109519},
  doi =		{10.4230/LIPIcs.MFCS.2019.7},
  annote =	{Keywords: online algorithms, sorting, randomized algorithms, advice complexity, threshold tolerance graphs}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2019.8

Better Bounds for Online Line Chasing

Authors: Marcin Bienkowski, Jarosław Byrka, Marek Chrobak, Christian Coester, Łukasz Jeż, and Elias Koutsoupias

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

We study online competitive algorithms for the line chasing problem in Euclidean spaces R^d, where the input consists of an initial point P_0 and a sequence of lines X_1, X_2, ..., X_m, revealed one at a time. At each step t, when the line X_t is revealed, the algorithm must determine a point P_t in X_t. An online algorithm is called c-competitive if for any input sequence the path P_0, P_1 , ..., P_m it computes has length at most c times the optimum path. The line chasing problem is a variant of a more general convex body chasing problem, where the sets X_t are arbitrary convex sets. To date, the best competitive ratio for the line chasing problem was 28.1, even in the plane. We improve this bound by providing a simple 3-competitive algorithm for any dimension d. We complement this bound by a matching lower bound for algorithms that are memoryless in the sense of our algorithm, and a lower bound of 1.5358 for arbitrary algorithms. The latter bound also improves upon the previous lower bound of sqrt{2}~=1.412 for convex body chasing in 2 dimensions.

Cite as

Marcin Bienkowski, Jarosław Byrka, Marek Chrobak, Christian Coester, Łukasz Jeż, and Elias Koutsoupias. Better Bounds for Online Line Chasing. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bienkowski_et_al:LIPIcs.MFCS.2019.8,
  author =	{Bienkowski, Marcin and Byrka, Jaros{\l}aw and Chrobak, Marek and Coester, Christian and Je\.{z}, {\L}ukasz and Koutsoupias, Elias},
  title =	{{Better Bounds for Online Line Chasing}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.8},
  URN =		{urn:nbn:de:0030-drops-109521},
  doi =		{10.4230/LIPIcs.MFCS.2019.8},
  annote =	{Keywords: convex body chasing, line chasing, competitive analysis}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2019.9

Nash Equilibria in Games over Graphs Equipped with a Communication Mechanism

Authors: Patricia Bouyer and Nathan Thomasset

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

We study pure Nash equilibria in infinite-duration games on graphs, with partial visibility of actions but communication (based on a graph) among the players. We show that a simple communication mechanism consisting in reporting the deviator when seeing it and propagating this information is sufficient for characterizing Nash equilibria. We propose an epistemic game construction, which conveniently records important information about the knowledge of the players. With this abstraction, we are able to characterize Nash equilibria which follow the simple communication pattern via winning strategies. We finally discuss the size of the construction, which would allow efficient algorithmic solutions to compute Nash equilibria in the original game.

Cite as

Patricia Bouyer and Nathan Thomasset. Nash Equilibria in Games over Graphs Equipped with a Communication Mechanism. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bouyer_et_al:LIPIcs.MFCS.2019.9,
  author =	{Bouyer, Patricia and Thomasset, Nathan},
  title =	{{Nash Equilibria in Games over Graphs Equipped with a Communication Mechanism}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.9},
  URN =		{urn:nbn:de:0030-drops-109532},
  doi =		{10.4230/LIPIcs.MFCS.2019.9},
  annote =	{Keywords: Multiplayer games, Nash equilibria, partial information}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2019.10

Parity Games: Zielonka’s Algorithm in Quasi-Polynomial Time

Authors: Paweł Parys

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

Calude, Jain, Khoussainov, Li, and Stephan (2017) proposed a quasi-polynomial-time algorithm solving parity games. After this breakthrough result, a few other quasi-polynomial-time algorithms were introduced; none of them is easy to understand. Moreover, it turns out that in practice they operate very slowly. On the other side there is Zielonka’s recursive algorithm, which is very simple, exponential in the worst case, and the fastest in practice. We combine these two approaches: we propose a small modification of Zielonka’s algorithm, which ensures that the running time is at most quasi-polynomial. In effect, we obtain a simple algorithm that solves parity games in quasi-polynomial time. We also hope that our algorithm, after further optimizations, can lead to an algorithm that shares the good performance of Zielonka’s algorithm on typical inputs, while reducing the worst-case complexity on difficult inputs.

Cite as

Paweł Parys. Parity Games: Zielonka’s Algorithm in Quasi-Polynomial Time. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{parys:LIPIcs.MFCS.2019.10,
  author =	{Parys, Pawe{\l}},
  title =	{{Parity Games: Zielonka’s Algorithm in Quasi-Polynomial Time}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.10},
  URN =		{urn:nbn:de:0030-drops-109543},
  doi =		{10.4230/LIPIcs.MFCS.2019.10},
  annote =	{Keywords: Parity games, Zielonka’s algorithm, quasi-polynomial time}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2019.11

Bidding Mechanisms in Graph Games

Authors: Guy Avni, Thomas A. Henzinger, and Đorđe Žikelić

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

In two-player games on graphs, the players move a token through a graph to produce a finite or infinite path, which determines the qualitative winner or quantitative payoff of the game. We study bidding games in which the players bid for the right to move the token. Several bidding rules were studied previously. In Richman bidding, in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Poorman bidding is similar except that the winner of the bidding pays the "bank" rather than the other player. Taxman bidding spans the spectrum between Richman and poorman bidding. They are parameterized by a constant tau in [0,1]: portion tau of the winning bid is paid to the other player, and portion 1-tau to the bank. While finite-duration (reachability) taxman games have been studied before, we present, for the first time, results on infinite-duration taxman games. It was previously shown that both Richman and poorman infinite-duration games with qualitative objectives reduce to reachability games, and we show a similar result here. Our most interesting results concern quantitative taxman games, namely mean-payoff games, where poorman and Richman bidding differ significantly. A central quantity in these games is the ratio between the two players' initial budgets. While in poorman mean-payoff games, the optimal payoff of a player depends on the initial ratio, in Richman bidding, the payoff depends only on the structure of the game. In both games the optimal payoffs can be found using (different) probabilistic connections with random-turn games in which in each turn, instead of bidding, a coin is tossed to determine which player moves. While the value with Richman bidding equals the value of a random-turn game with an un-biased coin, with poorman bidding, the bias in the coin is the initial ratio of the budgets. We give a complete classification of mean-payoff taxman games that is based on a probabilistic connection: the value of a taxman bidding game with parameter tau and initial ratio r, equals the value of a random-turn game that uses a coin with bias F(tau, r) = (r+tau * (1-r))/(1+tau). Thus, we show that Richman bidding is the exception; namely, for every tau <1, the value of the game depends on the initial ratio. Our proof technique simplifies and unifies the previous proof techniques for both Richman and poorman bidding.

Cite as

Guy Avni, Thomas A. Henzinger, and Đorđe Žikelić. Bidding Mechanisms in Graph Games. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{avni_et_al:LIPIcs.MFCS.2019.11,
  author =	{Avni, Guy and Henzinger, Thomas A. and \v{Z}ikeli\'{c}, {\D}or{\d}e},
  title =	{{Bidding Mechanisms in Graph Games}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{11:1--11:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.11},
  URN =		{urn:nbn:de:0030-drops-109553},
  doi =		{10.4230/LIPIcs.MFCS.2019.11},
  annote =	{Keywords: Bidding games, Richman bidding, poorman bidding, taxman bidding, mean-payoff games, random-turn games}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2019.12

Cluster Deletion on Interval Graphs and Split Related Graphs

Authors: Athanasios L. Konstantinidis and Charis Papadopoulos

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

In the Cluster Deletion problem the goal is to remove the minimum number of edges of a given graph, such that every connected component of the resulting graph constitutes a clique. It is known that the decision version of Cluster Deletion is NP-complete on (P_5-free) chordal graphs, whereas Cluster Deletion is solved in polynomial time on split graphs. However, the existence of a polynomial-time algorithm of Cluster Deletion on interval graphs, a proper subclass of chordal graphs, remained a well-known open problem. Our main contribution is that we settle this problem in the affirmative, by providing a polynomial-time algorithm for Cluster Deletion on interval graphs. Moreover, despite the simple formulation of the algorithm on split graphs, we show that Cluster Deletion remains NP-complete on a natural and slight generalization of split graphs that constitutes a proper subclass of P_5-free chordal graphs. Although the later result arises from the already-known reduction for P_5-free chordal graphs, we give an alternative proof showing an interesting connection between edge-weighted and vertex-weighted variations of the problem. To complement our results, we provide faster and simpler polynomial-time algorithms for Cluster Deletion on subclasses of such a generalization of split graphs.

Cite as

Athanasios L. Konstantinidis and Charis Papadopoulos. Cluster Deletion on Interval Graphs and Split Related Graphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{konstantinidis_et_al:LIPIcs.MFCS.2019.12,
  author =	{Konstantinidis, Athanasios L. and Papadopoulos, Charis},
  title =	{{Cluster Deletion on Interval Graphs and Split Related Graphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.12},
  URN =		{urn:nbn:de:0030-drops-109568},
  doi =		{10.4230/LIPIcs.MFCS.2019.12},
  annote =	{Keywords: Cluster deletion, interval graphs, split graphs}
}

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