34 Search Results for "P�hlsen, Stephan"


Document
Self-Stabilizing Clock Synchronization in Probabilistic Networks

Authors: Bernadette Charron-Bost and Louis Penet de Monterno

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)


Abstract
We consider the fundamental problem of clock synchronization in a synchronous multi-agent system. Each agent holds a clock with an arbitrary initial value, and clocks must eventually indicate the same value, modulo some integer P. A known solution for this problem in dynamic networks is the self-stabilization SAP (for self-adaptive period) algorithm, which uses finite memory and relies solely on the assumption of a finite dynamic diameter in the communication network. This paper extends the results on this algorithm to probabilistic communication networks: We introduce the concept of strong connectivity with high probability and we demonstrate that in any probabilistic communication network satisfying this hypothesis, the SAP algorithm synchronizes clocks with high probability. The proof of such a probabilistic hyperproperty is based on novel tools and relies on weak assumptions about the probabilistic communication network, making it applicable to a wide range of networks, including the classical push model. We provide an upper bound on time and space complexity. Building upon previous works by Feige et al. and Pittel, the paper provides solvability results and evaluates the stabilization time and space complexity of SAP in two specific cases of communication topologies.

Cite as

Bernadette Charron-Bost and Louis Penet de Monterno. Self-Stabilizing Clock Synchronization in Probabilistic Networks. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{charronbost_et_al:LIPIcs.DISC.2023.12,
  author =	{Charron-Bost, Bernadette and Penet de Monterno, Louis},
  title =	{{Self-Stabilizing Clock Synchronization in Probabilistic Networks}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.12},
  URN =		{urn:nbn:de:0030-drops-191389},
  doi =		{10.4230/LIPIcs.DISC.2023.12},
  annote =	{Keywords: Self-stabilization, Clock synchronization, Probabilistic networks}
}
Document
Approximating Highly Inapproximable Problems on Graphs of Bounded Twin-Width

Authors: Pierre Bergé, Édouard Bonnet, Hugues Déprés, and Rémi Watrigant

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
For any ε > 0, we give a polynomial-time n^ε-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an O(1)-sequence. This result is derived from the following time-approximation trade-off: We establish an O(1)^{2^q-1}-approximation algorithm running in time exp(O_q(n^{2^{-q}})), for every integer q ⩾ 0. Guided by the same framework, we obtain similar approximation algorithms for Min Coloring and Max Induced Matching. In general graphs, all these problems are known to be highly inapproximable: for any ε > 0, a polynomial-time n^{1-ε}-approximation for any of them would imply that P=NP [Håstad, FOCS '96; Zuckerman, ToC '07; Chalermsook et al., SODA '13]. We generalize the algorithms for Max Independent Set and Max Induced Matching to the independent (induced) packing of any fixed connected graph H. In contrast, we show that such approximation guarantees on graphs of bounded twin-width given with an O(1)-sequence are very unlikely for Min Independent Dominating Set, and somewhat unlikely for Longest Path and Longest Induced Path. Regarding the existence of better approximation algorithms, there is a (very) light evidence that the obtained approximation factor of n^ε for Max Independent Set may be best possible. This is the first in-depth study of the approximability of problems in graphs of bounded twin-width. Prior to this paper, essentially the only such result was a polynomial-time O(1)-approximation algorithm for Min Dominating Set [Bonnet et al., ICALP '21].

Cite as

Pierre Bergé, Édouard Bonnet, Hugues Déprés, and Rémi Watrigant. Approximating Highly Inapproximable Problems on Graphs of Bounded Twin-Width. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{berge_et_al:LIPIcs.STACS.2023.10,
  author =	{Berg\'{e}, Pierre and Bonnet, \'{E}douard and D\'{e}pr\'{e}s, Hugues and Watrigant, R\'{e}mi},
  title =	{{Approximating Highly Inapproximable Problems on Graphs of Bounded Twin-Width}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.10},
  URN =		{urn:nbn:de:0030-drops-176629},
  doi =		{10.4230/LIPIcs.STACS.2023.10},
  annote =	{Keywords: Approximation algorithms, bounded twin-width}
}
Document
Self-Stabilizing Clock Synchronization in Dynamic Networks

Authors: Bernadette Charron-Bost and Louis Penet de Monterno

Published in: LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)


Abstract
We consider the fundamental problem of periodic clock synchronization in a synchronous multi-agent system. Each agent holds a clock with an arbitrary initial value, and clocks must eventually be congruent, modulo some positive integer P. Previous algorithms worked in static networks with drastic connectivity properties and assumed that global informations are available at each node. In this paper, we propose a finite-state algorithm for time-varying topologies that does not require any global knowledge on the network. The only assumption is the existence of some integer D such that any two nodes can communicate in each sequence of D consecutive rounds, which extends the notion of strong connectivity in static network to dynamic communication patterns. The smallest such D is called the dynamic diameter of the network. If an upper bound on the diameter is provided, then our algorithm achieves synchronization within 3D rounds, whatever the value of the upper bound. Otherwise, using an adaptive mechanism, synchronization is achieved with little performance overhead. Our algorithm is parameterized by a function g, which can be tuned to favor either time or space complexity. Then, we explore a further relaxation of the connectivity requirement: our algorithm still works if there exists a positive integer R such that the network is rooted over each sequence of R consecutive rounds, and if eventually the set of roots is stable. In particular, it works in any rooted static network.

Cite as

Bernadette Charron-Bost and Louis Penet de Monterno. Self-Stabilizing Clock Synchronization in Dynamic Networks. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{charronbost_et_al:LIPIcs.OPODIS.2022.28,
  author =	{Charron-Bost, Bernadette and Penet de Monterno, Louis},
  title =	{{Self-Stabilizing Clock Synchronization in Dynamic Networks}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.28},
  URN =		{urn:nbn:de:0030-drops-176480},
  doi =		{10.4230/LIPIcs.OPODIS.2022.28},
  annote =	{Keywords: Self-stabilization, Clock synchronization, Dynamic networks}
}
Document
Twin-Width VIII: Delineation and Win-Wins

Authors: Édouard Bonnet, Dibyayan Chakraborty, Eun Jung Kim, Noleen Köhler, Raul Lopes, and Stéphan Thomassé

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)


Abstract
We introduce the notion of delineation. A graph class C is said delineated by twin-width (or simply, delineated) if for every hereditary closure D of a subclass of C, it holds that D has bounded twin-width if and only if D is monadically dependent. An effective strengthening of delineation for a class C implies that tractable FO model checking on C is perfectly understood: On hereditary closures of subclasses D of C, FO model checking on D is fixed-parameter tractable (FPT) exactly when D has bounded twin-width. Ordered graphs [BGOdMSTT, STOC '22] and permutation graphs [BKTW, JACM '22] are effectively delineated, while subcubic graphs are not. On the one hand, we prove that interval graphs, and even, rooted directed path graphs are delineated. On the other hand, we observe or show that segment graphs, directed path graphs (with arbitrarily many roots), and visibility graphs of simple polygons are not delineated. In an effort to draw the delineation frontier between interval graphs (that are delineated) and axis-parallel two-lengthed segment graphs (that are not), we investigate the twin-width of restricted segment intersection classes. It was known that (triangle-free) pure axis-parallel unit segment graphs have unbounded twin-width [BGKTW, SODA '21]. We show that K_{t,t}-free segment graphs, and axis-parallel H_t-free unit segment graphs have bounded twin-width, where H_t is the half-graph or ladder of height t. In contrast, axis-parallel H₄-free two-lengthed segment graphs have unbounded twin-width. We leave as an open question whether unit segment graphs are delineated. More broadly, we explore which structures (large bicliques, half-graphs, or independent sets) are responsible for making the twin-width large on the main classes of intersection and visibility graphs. Our new results, combined with the FPT algorithm for first-order model checking on graphs given with O(1)-sequences [BKTW, JACM '22], give rise to a variety of algorithmic win-win arguments. They all fall in the same framework: If p is an FO definable graph parameter that effectively functionally upperbounds twin-width on a class C, then p(G) ⩾ k can be decided in FPT time f(k) ⋅ |V(G)|^O(1). For instance, we readily derive FPT algorithms for k-Ladder on visibility graphs of 1.5D terrains, and k-Independent Set on visibility graphs of simple polygons. This showcases that the theory of twin-width can serve outside of classes of bounded twin-width.

Cite as

Édouard Bonnet, Dibyayan Chakraborty, Eun Jung Kim, Noleen Köhler, Raul Lopes, and Stéphan Thomassé. Twin-Width VIII: Delineation and Win-Wins. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bonnet_et_al:LIPIcs.IPEC.2022.9,
  author =	{Bonnet, \'{E}douard and Chakraborty, Dibyayan and Kim, Eun Jung and K\"{o}hler, Noleen and Lopes, Raul and Thomass\'{e}, St\'{e}phan},
  title =	{{Twin-Width VIII: Delineation and Win-Wins}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.9},
  URN =		{urn:nbn:de:0030-drops-173650},
  doi =		{10.4230/LIPIcs.IPEC.2022.9},
  annote =	{Keywords: Twin-width, intersection graphs, visibility graphs, monadic dependence and stability, first-order model checking}
}
Document
Predicting Distance and Direction from Text Locality Descriptions for Biological Specimen Collections

Authors: Ruoxuan Liao, Pragyan P. Das, Christopher B. Jones, Niloofar Aflaki, and Kristin Stock

Published in: LIPIcs, Volume 240, 15th International Conference on Spatial Information Theory (COSIT 2022)


Abstract
A considerable proportion of records that describe biological specimens (flora, soil, invertebrates), and especially those that were collected decades ago, are not attached to corresponding geographical coordinates, but rather have their location described only through textual descriptions (e.g. North Canterbury, Selwyn River near bridge on Springston-Leeston Rd). Without geographical coordinates, millions of records stored in museum collections around the world cannot be mapped. We present a method for predicting the distance and direction associated with human language location descriptions which focuses on the interpretation of geospatial prepositions and the way in which they modify the location represented by an associated reference place name (e.g. near the Manawatu River). We study eight distance-oriented prepositions and eight direction-oriented prepositions and use machine learning regression to predict distance or direction, relative to the reference place name, from a collection of training data. The results show that, compared with a simple baseline, our model improved distance predictions by up to 60% and direction predictions by up to 31%.

Cite as

Ruoxuan Liao, Pragyan P. Das, Christopher B. Jones, Niloofar Aflaki, and Kristin Stock. Predicting Distance and Direction from Text Locality Descriptions for Biological Specimen Collections. In 15th International Conference on Spatial Information Theory (COSIT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 240, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{liao_et_al:LIPIcs.COSIT.2022.4,
  author =	{Liao, Ruoxuan and Das, Pragyan P. and Jones, Christopher B. and Aflaki, Niloofar and Stock, Kristin},
  title =	{{Predicting Distance and Direction from Text Locality Descriptions for Biological Specimen Collections}},
  booktitle =	{15th International Conference on Spatial Information Theory (COSIT 2022)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-257-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{240},
  editor =	{Ishikawa, Toru and Fabrikant, Sara Irina and Winter, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2022.4},
  URN =		{urn:nbn:de:0030-drops-168892},
  doi =		{10.4230/LIPIcs.COSIT.2022.4},
  annote =	{Keywords: geospatial prepositions, biological specimen collections, georeferencing, natural language processing, locative expressions, locality descriptions, geoparsing, geocoding, geographic information retrieval, regression, machine learning}
}
Document
Invited Talk
A Brief Tour in Twin-Width (Invited Talk)

Authors: Stéphan Thomassé

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
This is an introduction to the notion of twin-width, with emphasis on how it interacts with first-order model checking and enumerative combinatorics. Even though approximating twin-width remains a challenge in general graphs, it is now well understood for ordered graphs, where bounded twin-width coincides with many other complexity gaps. For instance classes of graphs with linear FO-model checking, small classes, or NIP classes are exactly bounded twin-width classes. Some other applications of twin-width are also presented.

Cite as

Stéphan Thomassé. A Brief Tour in Twin-Width (Invited Talk). In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 6:1-6:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{thomasse:LIPIcs.ICALP.2022.6,
  author =	{Thomass\'{e}, St\'{e}phan},
  title =	{{A Brief Tour in Twin-Width}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{6:1--6:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.6},
  URN =		{urn:nbn:de:0030-drops-163473},
  doi =		{10.4230/LIPIcs.ICALP.2022.6},
  annote =	{Keywords: Twin-width, matrices, ordered graphs, enumerative combinatorics, model theory, algorithms, computational complexity, Ramsey theory}
}
Document
Track A: Algorithms, Complexity and Games
Deciding Twin-Width at Most 4 Is NP-Complete

Authors: Pierre Bergé, Édouard Bonnet, and Hugues Déprés

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
We show that determining if an n-vertex graph has twin-width at most 4 is NP-complete, and requires time 2^Ω(n/log n) unless the Exponential-Time Hypothesis fails. Along the way, we give an elementary proof that n-vertex graphs subdivided at least 2 log n times have twin-width at most 4. We also show how to encode trigraphs H (2-edge colored graphs involved in the definition of twin-width) into graphs G, in the sense that every d-sequence (sequence of vertex contractions witnessing that the twin-width is at most d) of G inevitably creates H as an induced subtrigraph, whereas there exists a partial d-sequence that actually goes from G to H. We believe that these facts and their proofs can be of independent interest.

Cite as

Pierre Bergé, Édouard Bonnet, and Hugues Déprés. Deciding Twin-Width at Most 4 Is NP-Complete. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{berge_et_al:LIPIcs.ICALP.2022.18,
  author =	{Berg\'{e}, Pierre and Bonnet, \'{E}douard and D\'{e}pr\'{e}s, Hugues},
  title =	{{Deciding Twin-Width at Most 4 Is NP-Complete}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.18},
  URN =		{urn:nbn:de:0030-drops-163595},
  doi =		{10.4230/LIPIcs.ICALP.2022.18},
  annote =	{Keywords: Twin-width, lower bounds}
}
Document
Automorphisms of Random Trees

Authors: Christoffer Olsson and Stephan Wagner

Published in: LIPIcs, Volume 225, 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)


Abstract
We study the size of the automorphism group of two different types of random trees: Galton-Watson trees and Pólya trees. In both cases, we prove that it asymptotically follows a log-normal distribution. While the proof for Galton-Watson trees mainly relies on probabilistic arguments and a general result on additive tree functionals, generating functions are used in the case of Pólya trees.

Cite as

Christoffer Olsson and Stephan Wagner. Automorphisms of Random Trees. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{olsson_et_al:LIPIcs.AofA.2022.16,
  author =	{Olsson, Christoffer and Wagner, Stephan},
  title =	{{Automorphisms of Random Trees}},
  booktitle =	{33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-230-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{225},
  editor =	{Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2022.16},
  URN =		{urn:nbn:de:0030-drops-161026},
  doi =		{10.4230/LIPIcs.AofA.2022.16},
  annote =	{Keywords: random tree, Galton-Watson tree, P\'{o}lya tree, automorphism group, central limit theorem}
}
Document
Twin-Width and Polynomial Kernels

Authors: Édouard Bonnet, Eun Jung Kim, Amadeus Reinald, Stéphan Thomassé, and Rémi Watrigant

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)


Abstract
We study the existence of polynomial kernels for parameterized problems without a polynomial kernel on general graphs, when restricted to graphs of bounded twin-width. It was previously observed in [Bonnet et al., ICALP'21] that the problem k-Independent Set allows no polynomial kernel on graph of bounded twin-width by a very simple argument, which extends to several other problems such as k-Independent Dominating Set, k-Path, k-Induced Path, k-Induced Matching. In this work, we examine the k-Dominating Set and variants of k-Vertex Cover for the existence of polynomial kernels. As a main result, we show that k-Dominating Set does not admit a polynomial kernel on graphs of twin-width at most 4 under a standard complexity-theoretic assumption. The reduction is intricate, especially due to the effort to bring the twin-width down to 4, and it can be tweaked to work for Connected k-Dominating Set and Total k-Dominating Set with a slightly worse bound on the twin-width. On the positive side, we obtain a simple quadratic vertex kernel for Connected k-Vertex Cover and Capacitated k-Vertex Cover on graphs of bounded twin-width. These kernels rely on that graphs of bounded twin-width have Vapnik-Chervonenkis (VC) density 1, that is, for any vertex set X, the number of distinct neighborhoods in X is at most c⋅|X|, where c is a constant depending only on the twin-width. Interestingly the kernel applies to any graph class of VC density 1, and does not require a witness sequence. We also present a more intricate O(k^{1.5}) vertex kernel for Connected k-Vertex Cover. Finally we show that deciding if a graph has twin-width at most 1 can be done in polynomial time, and observe that most graph optimization/decision problems can be solved in polynomial time on graphs of twin-width at most 1.

Cite as

Édouard Bonnet, Eun Jung Kim, Amadeus Reinald, Stéphan Thomassé, and Rémi Watrigant. Twin-Width and Polynomial Kernels. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{bonnet_et_al:LIPIcs.IPEC.2021.10,
  author =	{Bonnet, \'{E}douard and Kim, Eun Jung and Reinald, Amadeus and Thomass\'{e}, St\'{e}phan and Watrigant, R\'{e}mi},
  title =	{{Twin-Width and Polynomial Kernels}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.10},
  URN =		{urn:nbn:de:0030-drops-153932},
  doi =		{10.4230/LIPIcs.IPEC.2021.10},
  annote =	{Keywords: Twin-width, kernelization, lower bounds, Dominating Set}
}
Document
An Algorithmic Weakening of the Erdős-Hajnal Conjecture

Authors: Édouard Bonnet, Stéphan Thomassé, Xuan Thang Tran, and Rémi Watrigant

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)


Abstract
We study the approximability of the Maximum Independent Set (MIS) problem in H-free graphs (that is, graphs which do not admit H as an induced subgraph). As one motivation we investigate the following conjecture: for every fixed graph H, there exists a constant δ > 0 such that MIS can be n^{1-δ}-approximated in H-free graphs, where n denotes the number of vertices of the input graph. We first prove that a constructive version of the celebrated Erdős-Hajnal conjecture implies ours. We then prove that the set of graphs H satisfying our conjecture is closed under the so-called graph substitution. This, together with the known polynomial-time algorithms for MIS in H-free graphs (e.g. P₆-free and fork-free graphs), implies that our conjecture holds for many graphs H for which the Erdős-Hajnal conjecture is still open. We then focus on improving the constant δ for some graph classes: we prove that the classical Local Search algorithm provides an OPT^{1-1/t}-approximation in K_{t, t}-free graphs (hence a √{OPT}-approximation in C₄-free graphs), and, while there is a simple √n-approximation in triangle-free graphs, it cannot be improved to n^{1/4-ε} for any ε > 0 unless NP ⊆ BPP. More generally, we show that there is a constant c such that MIS in graphs of girth γ cannot be n^{c/(γ)}-approximated. Up to a constant factor in the exponent, this matches the ratio of a known approximation algorithm by Monien and Speckenmeyer, and by Murphy. To the best of our knowledge, this is the first strong (i.e., Ω(n^δ) for some δ > 0) inapproximability result for Maximum Independent Set in a proper hereditary class.

Cite as

Édouard Bonnet, Stéphan Thomassé, Xuan Thang Tran, and Rémi Watrigant. An Algorithmic Weakening of the Erdős-Hajnal Conjecture. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bonnet_et_al:LIPIcs.ESA.2020.23,
  author =	{Bonnet, \'{E}douard and Thomass\'{e}, St\'{e}phan and Tran, Xuan Thang and Watrigant, R\'{e}mi},
  title =	{{An Algorithmic Weakening of the Erd\H{o}s-Hajnal Conjecture}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.23},
  URN =		{urn:nbn:de:0030-drops-128894},
  doi =		{10.4230/LIPIcs.ESA.2020.23},
  annote =	{Keywords: Approximation, Maximum Independent Set, H-free Graphs, Erd\H{o}s-Hajnal conjecture}
}
Document
Value Iteration Using Universal Graphs and the Complexity of Mean Payoff Games

Authors: Nathanaël Fijalkow, Paweł Gawrychowski, and Pierre Ohlmann

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)


Abstract
We study the computational complexity of solving mean payoff games. This class of games can be seen as an extension of parity games, and they have similar complexity status: in both cases solving them is in NP ∩ coNP and not known to be in P. In a breakthrough result Calude, Jain, Khoussainov, Li, and Stephan constructed in 2017 a quasipolynomial time algorithm for solving parity games, which was quickly followed by a few other algorithms with the same complexity. Our objective is to investigate how these techniques can be extended to mean payoff games. The starting point is the combinatorial notion of universal trees: all quasipolynomial time algorithms for parity games have been shown to exploit universal trees. Universal graphs extend universal trees to arbitrary (positionally determined) objectives. We show that they yield a family of value iteration algorithms for solving mean payoff games which includes the value iteration algorithm due to Brim, Chaloupka, Doyen, Gentilini, and Raskin. The contribution of this paper is to prove tight bounds on the complexity of algorithms for mean payoff games using universal graphs. We consider two parameters: the largest weight N in absolute value and the number k of weights. The dependence in N in the existing value iteration algorithm is linear, we show that this can be improved to N^{1 - 1/n} and obtain a matching lower bound. However, we show that we cannot break the linear dependence in the exponent in the number k of weights implying that universal graphs do not yield a quasipolynomial time algorithm for solving mean payoff games.

Cite as

Nathanaël Fijalkow, Paweł Gawrychowski, and Pierre Ohlmann. Value Iteration Using Universal Graphs and the Complexity of Mean Payoff Games. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{fijalkow_et_al:LIPIcs.MFCS.2020.34,
  author =	{Fijalkow, Nathana\"{e}l and Gawrychowski, Pawe{\l} and Ohlmann, Pierre},
  title =	{{Value Iteration Using Universal Graphs and the Complexity of Mean Payoff Games}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.34},
  URN =		{urn:nbn:de:0030-drops-127011},
  doi =		{10.4230/LIPIcs.MFCS.2020.34},
  annote =	{Keywords: Mean payoff games, Universal graphs, Value iteration}
}
Document
On the Probability That a Random Digraph Is Acyclic

Authors: Dimbinaina Ralaivaosaona, Vonjy Rasendrahasina, and Stephan Wagner

Published in: LIPIcs, Volume 159, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)


Abstract
Given a positive integer n and a real number p ∈ [0,1], let D(n,p) denote the random digraph defined in the following way: each of the binom(n,2) possible edges on the vertex set {1,2,3,…,n} is included with probability 2p, where all edges are independent of each other. Thereafter, a direction is chosen independently for each edge, with probability 1/2 for each possible direction. In this paper, we study the probability that a random instance of D(n,p) is acyclic, i.e., that it does not contain a directed cycle. We find precise asymptotic formulas for the probability of a random digraph being acyclic in the sparse regime, i.e., when np = O(1). As an example, for each real number μ, we find an exact analytic expression for φ(μ) = lim_{n→ ∞} n^{1/3} ℙ{D(n,1/n (1+μ n^{-1/3})) is acyclic}.

Cite as

Dimbinaina Ralaivaosaona, Vonjy Rasendrahasina, and Stephan Wagner. On the Probability That a Random Digraph Is Acyclic. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{ralaivaosaona_et_al:LIPIcs.AofA.2020.25,
  author =	{Ralaivaosaona, Dimbinaina and Rasendrahasina, Vonjy and Wagner, Stephan},
  title =	{{On the Probability That a Random Digraph Is Acyclic}},
  booktitle =	{31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-147-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{159},
  editor =	{Drmota, Michael and Heuberger, Clemens},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2020.25},
  URN =		{urn:nbn:de:0030-drops-120557},
  doi =		{10.4230/LIPIcs.AofA.2020.25},
  annote =	{Keywords: Random digraphs, acyclic digraphs, asymptotics}
}
Document
The Independent Set Problem Is FPT for Even-Hole-Free Graphs

Authors: Edin Husić, Stéphan Thomassé, and Nicolas Trotignon

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)


Abstract
The class of even-hole-free graphs is very similar to the class of perfect graphs, and was indeed a cornerstone in the tools leading to the proof of the Strong Perfect Graph Theorem. However, the complexity of computing a maximum independent set (MIS) is a long-standing open question in even-hole-free graphs. From the hardness point of view, MIS is W[1]-hard in the class of graphs without induced 4-cycle (when parameterized by the solution size). Halfway of these, we show in this paper that MIS is FPT when parameterized by the solution size in the class of even-hole-free graphs. The main idea is to apply twice the well-known technique of augmenting graphs to extend some initial independent set.

Cite as

Edin Husić, Stéphan Thomassé, and Nicolas Trotignon. The Independent Set Problem Is FPT for Even-Hole-Free Graphs. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{husic_et_al:LIPIcs.IPEC.2019.21,
  author =	{Husi\'{c}, Edin and Thomass\'{e}, St\'{e}phan and Trotignon, Nicolas},
  title =	{{The Independent Set Problem Is FPT for Even-Hole-Free Graphs}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{21:1--21:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.21},
  URN =		{urn:nbn:de:0030-drops-114826},
  doi =		{10.4230/LIPIcs.IPEC.2019.21},
  annote =	{Keywords: independent set, FPT algorithm, even-hole-free graph, augmenting graph}
}
Document
When Maximum Stable Set Can Be Solved in FPT Time

Authors: Édouard Bonnet, Nicolas Bousquet, Stéphan Thomassé, and Rémi Watrigant

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)


Abstract
Maximum Independent Set (MIS for short) is in general graphs the paradigmatic W[1]-hard problem. In stark contrast, polynomial-time algorithms are known when the inputs are restricted to structured graph classes such as, for instance, perfect graphs (which includes bipartite graphs, chordal graphs, co-graphs, etc.) or claw-free graphs. In this paper, we introduce some variants of co-graphs with parameterized noise, that is, graphs that can be made into disjoint unions or complete sums by the removal of a certain number of vertices and the addition/deletion of a certain number of edges per incident vertex, both controlled by the parameter. We give a series of FPT Turing-reductions on these classes and use them to make some progress on the parameterized complexity of MIS in H-free graphs. We show that for every fixed t >=slant 1, MIS is FPT in P(1,t,t,t)-free graphs, where P(1,t,t,t) is the graph obtained by substituting all the vertices of a four-vertex path but one end of the path by cliques of size t. We also provide randomized FPT algorithms in dart-free graphs and in cricket-free graphs. This settles the FPT/W[1]-hard dichotomy for five-vertex graphs H.

Cite as

Édouard Bonnet, Nicolas Bousquet, Stéphan Thomassé, and Rémi Watrigant. When Maximum Stable Set Can Be Solved in FPT Time. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 49:1-49:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{bonnet_et_al:LIPIcs.ISAAC.2019.49,
  author =	{Bonnet, \'{E}douard and Bousquet, Nicolas and Thomass\'{e}, St\'{e}phan and Watrigant, R\'{e}mi},
  title =	{{When Maximum Stable Set Can Be Solved in FPT Time}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{49:1--49:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.49},
  URN =		{urn:nbn:de:0030-drops-115458},
  doi =		{10.4230/LIPIcs.ISAAC.2019.49},
  annote =	{Keywords: Parameterized Algorithms, Independent Set, H-Free Graphs}
}
Document
Packing Directed Circuits Quarter-Integrally

Authors: Tomáš Masařík, Irene Muzi, Marcin Pilipczuk, Paweł Rzążewski, and Manuel Sorge

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)


Abstract
The celebrated Erdős-Pósa theorem states that every undirected graph that does not admit a family of k vertex-disjoint cycles contains a feedback vertex set (a set of vertices hitting all cycles in the graph) of size O(k log k). After being known for long as Younger’s conjecture, a similar statement for directed graphs has been proven in 1996 by Reed, Robertson, Seymour, and Thomas. However, in their proof, the dependency of the size of the feedback vertex set on the size of vertex-disjoint cycle packing is not elementary. We show that if we compare the size of a minimum feedback vertex set in a directed graph with quarter-integral cycle packing number, we obtain a polynomial bound. More precisely, we show that if in a directed graph G there is no family of k cycles such that every vertex of G is in at most four of the cycles, then there exists a feedback vertex set in G of size O(k^4). On the way there we prove a more general result about quarter-integral packing of subgraphs of high directed treewidth: for every pair of positive integers a and b, if a directed graph G has directed treewidth Omega(a^6 b^8 log^2(ab)), then one can find in G a family of a subgraphs, each of directed treewidth at least b, such that every vertex of G is in at most four subgraphs.

Cite as

Tomáš Masařík, Irene Muzi, Marcin Pilipczuk, Paweł Rzążewski, and Manuel Sorge. Packing Directed Circuits Quarter-Integrally. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 72:1-72:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{masarik_et_al:LIPIcs.ESA.2019.72,
  author =	{Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Muzi, Irene and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l} and Sorge, Manuel},
  title =	{{Packing Directed Circuits Quarter-Integrally}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{72:1--72:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.72},
  URN =		{urn:nbn:de:0030-drops-111938},
  doi =		{10.4230/LIPIcs.ESA.2019.72},
  annote =	{Keywords: Directed graphs, graph algorithms, linkage, Erd\H{o}s–P\'{o}sa property}
}
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