2 Search Results for "Charbit, Pierre"

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.117
On the Size of Good-For-Games Rabin Automata and Its Link with the Memory in Muller Games

Authors: Antonio Casares, Thomas Colcombet, and Karoliina Lehtinen

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

Abstract
In this paper, we look at good-for-games Rabin automata that recognise a Muller language (a language that is entirely characterised by the set of letters that appear infinitely often in each word). We establish that minimal such automata are exactly of the same size as the minimal memory required for winning Muller games that have this language as their winning condition. We show how to effectively construct such minimal automata. Finally, we establish that these automata can be exponentially more succinct than equivalent deterministic ones, thus proving as a consequence that chromatic memory for winning a Muller game can be exponentially larger than unconstrained memory.
Cite as

Antonio Casares, Thomas Colcombet, and Karoliina Lehtinen. On the Size of Good-For-Games Rabin Automata and Its Link with the Memory in Muller Games. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 117:1-117:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{casares_et_al:LIPIcs.ICALP.2022.117,
  author =	{Casares, Antonio and Colcombet, Thomas and Lehtinen, Karoliina},
  title =	{{On the Size of Good-For-Games Rabin Automata and Its Link with the Memory in Muller Games}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{117:1--117:20},
  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.2022.117},
  URN =		{urn:nbn:de:0030-drops-164580},
  doi =		{10.4230/LIPIcs.ICALP.2022.117},
  annote =	{Keywords: Infinite duration games, Muller games, Rabin conditions, omega-regular languages, memory in games, good-for-games automata}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2018.17
Parameterized Complexity of Independent Set in H-Free Graphs

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

Published in: LIPIcs, Volume 115, 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

Abstract
In this paper, we investigate the complexity of Maximum Independent Set (MIS) in the class of H-free graphs, that is, graphs excluding a fixed graph as an induced subgraph. Given that the problem remains NP-hard for most graphs H, we study its fixed-parameter tractability and make progress towards a dichotomy between FPT and W[1]-hard cases. We first show that MIS remains W[1]-hard in graphs forbidding simultaneously K_{1, 4}, any finite set of cycles of length at least 4, and any finite set of trees with at least two branching vertices. In particular, this answers an open question of Dabrowski et al. concerning C_4-free graphs. Then we extend the polynomial algorithm of Alekseev when H is a disjoint union of edges to an FPT algorithm when H is a disjoint union of cliques. We also provide a framework for solving several other cases, which is a generalization of the concept of iterative expansion accompanied by the extraction of a particular structure using Ramsey's theorem. Iterative expansion is a maximization version of the so-called iterative compression. We believe that our framework can be of independent interest for solving other similar graph problems. Finally, we present positive and negative results on the existence of polynomial (Turing) kernels for several graphs H.
Cite as

Édouard Bonnet, Nicolas Bousquet, Pierre Charbit, Stéphan Thomassé, and Rémi Watrigant. Parameterized Complexity of Independent Set in H-Free Graphs. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 17:1-17:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{bonnet_et_al:LIPIcs.IPEC.2018.17,
  author =	{Bonnet, \'{E}douard and Bousquet, Nicolas and Charbit, Pierre and Thomass\'{e}, St\'{e}phan and Watrigant, R\'{e}mi},
  title =	{{Parameterized Complexity of Independent Set in H-Free Graphs}},
  booktitle =	{13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
  pages =	{17:1--17:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-084-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{115},
  editor =	{Paul, Christophe and Pilipczuk, Michal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2018.17},
  URN =		{urn:nbn:de:0030-drops-102183},
  doi =		{10.4230/LIPIcs.IPEC.2018.17},
  annote =	{Keywords: Parameterized Algorithms, Independent Set, H-Free Graphs}
}
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