7 Search Results for "Berthe, Gaétan"

Document
DOI: 10.4230/LIPIcs.FUN.2026.7
Nemesis, an Escape Game in Graphs

Authors: Pierre Bergé, Antoine Dailly, and Yan Gerard

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
We define a new escape game in graphs that we call Nemesis. The game is played on a graph having a subset of vertices labeled as exits and the goal of one of the two players, called the fugitive, is to reach one of these exit vertices. The second player, i.e. the fugitive adversary, is called the Nemesis. Her goal is to trap the fugitive in a connected component which does not contain any exit. At each round of the game, the fugitive moves from one vertex to an adjacent vertex. Then the Nemesis deletes one edge anywhere in the graph. The game ends when either the fugitive reached an exit or when he is in a connected component that does not contain any exit. In trees and graphs of maximum degree bounded by 3, Nemesis can be solved in linear time. For arbitrary graphs, we show that Nemesis is PSPACE-complete, and that it is NP-hard on planar multigraphs. We extend our results to the related Cat Herding problem, proving its PSPACE-completeness.
Cite as

Pierre Bergé, Antoine Dailly, and Yan Gerard. Nemesis, an Escape Game in Graphs. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{berge_et_al:LIPIcs.FUN.2026.7,
  author =	{Berg\'{e}, Pierre and Dailly, Antoine and Gerard, Yan},
  title =	{{Nemesis, an Escape Game in Graphs}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.7},
  URN =		{urn:nbn:de:0030-drops-257261},
  doi =		{10.4230/LIPIcs.FUN.2026.7},
  annote =	{Keywords: Graphs, Evasion and Pursuit Games, PSPACE-completeness, Quantified SAT, Canadian Traveler Problem, Cat Herding Problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.50
Lexicographic Transductions of Finite Words

Authors: Emmanuel Filiot, Nathan Lhote, and Pierre-Alain Reynier

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Regular transductions over finite words have linear input-to-output growth. This class of transductions enjoys many characterizations, such as transductions computable by two-way transducers as well as transductions definable in MSO (in the sense of Courcelle). Recently, regular transductions have been extended by Bojańczyk to polyregular transductions, which have polynomial growth, and are characterized by pebble transducers and MSO interpretations. Another class of interest is that of transductions defined by streaming string transducers or marble transducers, which have exponential growth and are incomparable with polyregular transductions. In this paper, we consider MSO set interpretations (MSOSI) over finite words, that were introduced by Colcombet and Loeding. MSOSI are a natural candidate for the class of "regular transductions with exponential growth", and are rather well behaved. However, MSOSI for now lacks two desirable properties that regular and polyregular transductions have. The first property is to have an automata description. This property is closely related to a second property, that of being regularity preserving, meaning preserving regular languages under inverse image. We first show that if MSOSI are (effectively) regularity preserving then any automatic ω-word has a decidable MSO theory, an almost 20 years old conjecture of Bárány. Our main contribution is the introduction of a class of transductions of exponential growth, which we call lexicographic transductions. We provide three different presentations for this class: first, as the closure of simple transductions (recognizable transductions) under a single operator called maplex; second, as a syntactic fragment of MSOSI (but the regular languages are given by automata instead of formulas); and third, we give an automaton based model called nested marble transducers, which generalize both marble transducers and pebble transducers. We show that this class enjoys many nice properties including being regularity preserving.
Cite as

Emmanuel Filiot, Nathan Lhote, and Pierre-Alain Reynier. Lexicographic Transductions of Finite Words. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{filiot_et_al:LIPIcs.MFCS.2025.50,
  author =	{Filiot, Emmanuel and Lhote, Nathan and Reynier, Pierre-Alain},
  title =	{{Lexicographic Transductions of Finite Words}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{50:1--50:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.50},
  URN =		{urn:nbn:de:0030-drops-241572},
  doi =		{10.4230/LIPIcs.MFCS.2025.50},
  annote =	{Keywords: Transducers, Automata, MSO, Logical interpretations, Automatic structures}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.26
Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set

Authors: Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph G and a parameter k, one has to decide if there is a set S of at most k vertices such that G-S is acyclic. Assuming the Exponential Time Hypothesis, it is known that FVS cannot be solved in time 2^{o(k)}n^{𝒪(1)} in general graphs. To overcome this, many recent results considered FVS restricted to particular intersection graph classes and provided such 2^{o(k)}n^{𝒪(1)} algorithms. In this paper we provide generic conditions on a graph class for the existence of an algorithm solving FVS in subexponential FPT time, i.e. time 2^k^ε poly(n), for some ε < 1, where n denotes the number of vertices of the instance and k the parameter. On the one hand this result unifies algorithms that have been proposed over the years for several graph classes such as planar graphs, map graphs, unit-disk graphs, pseudo-disk graphs, and string graphs of bounded edge-degree. On the other hand it extends the tractability horizon of FVS to new classes that are not amenable to previously used techniques, in particular intersection graphs of "thin" objects like segment graphs or more generally s-string graphs.
Cite as

Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond. Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berthe_et_al:LIPIcs.ICALP.2025.26,
  author =	{Berthe, Ga\'{e}tan and Bougeret, Marin and Gon\c{c}alves, Daniel and Raymond, Jean-Florent},
  title =	{{Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.26},
  URN =		{urn:nbn:de:0030-drops-234036},
  doi =		{10.4230/LIPIcs.ICALP.2025.26},
  annote =	{Keywords: Subexponential FPT algorithms, geometric intersection graphs}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2024.13
Kick the Cliques

Authors: Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond

Published in: LIPIcs, Volume 321, 19th International Symposium on Parameterized and Exact Computation (IPEC 2024)

Abstract
In the K_r-Hitting problem, given a graph G and an integer k one has to decide if there exists a set of at most k vertices whose removal destroys all r-cliques of G. In this paper we give an algorithm for K_r-Hitting that runs in subexponential FPT time on graph classes satisfying two simple conditions related to cliques and treewidth. As an application we show that our algorithm solves K_r-Hitting in time - 2^{O_r(k^{(r+1)/(r+2)}log k)} ⋅ n^{O_r(1)} in pseudo-disk graphs and map-graphs; - 2^{O_{t,r}(k^{2/3}log k)} ⋅ n^{O_r(1)} in K_{t,t}-subgraph-free string graphs; and - 2^{O_{H,r}(k^{2/3}log k)} ⋅ n^{O_r(1)} in H-minor-free graphs.
Cite as

Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond. Kick the Cliques. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{berthe_et_al:LIPIcs.IPEC.2024.13,
  author =	{Berthe, Ga\'{e}tan and Bougeret, Marin and Gon\c{c}alves, Daniel and Raymond, Jean-Florent},
  title =	{{Kick the Cliques}},
  booktitle =	{19th International Symposium on Parameterized and Exact Computation (IPEC 2024)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-353-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{321},
  editor =	{Bonnet, \'{E}douard and Rz\k{a}\.{z}ewski, Pawe{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2024.13},
  URN =		{urn:nbn:de:0030-drops-222397},
  doi =		{10.4230/LIPIcs.IPEC.2024.13},
  annote =	{Keywords: Subexponential FPT algorithms, implicit hitting set problems, geometric intersection graphs}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2024.11
Subexponential Algorithms in Geometric Graphs via the Subquadratic Grid Minor Property: The Role of Local Radius

Authors: Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
We investigate the existence in geometric graph classes of subexponential parameterized algorithms for cycle-hitting problems like Triangle Hitting (TH), Feedback Vertex Set (FVS) or Odd Cycle Transversal (OCT). These problems respectively ask for the existence in a graph G of a set X of at most k vertices such that G-X is triangle-free, acyclic, or bipartite. It is know that subexponential FPT algorithms of the form 2^o(k)n^𝒪(1) exist in planar and even H-minor free graphs from bidimensionality theory [Demaine et al. 2005], and there is a recent line of work lifting these results to geometric graph classes consisting of intersection of similarly sized "fat" objects ([Fomin et al. 2012], [Grigoriev et al. 2014], or disk graphs [Lokshtanov et al. 2022], [An et al. 2023]). In this paper we first identify sufficient conditions, for any graph class 𝒞 included in string graphs, to admit subexponential FPT algorithms for any problem in 𝒫, a family of bidimensional problems where one has to find a set of size at most k hitting a fixed family of graphs, containing in particular FVS. Informally, these conditions boil down to the fact that for any G ∈ 𝒞, the local radius of G (a new parameter introduced in [Lokshtanov et al. 2023]) is polynomial in the clique number of G and in the maximum matching in the neighborhood of a vertex. To demonstrate the applicability of this generic result, we bound the local radius for two special classes: intersection graphs of axis-parallel squares and of contact graphs of segments in the plane. This implies that any problem Π ∈ 𝒫 (in particular, FVS) can be solved in: - 2^𝒪(k^{3/4}log k) n^𝒪(1)-time in contact segment graphs, - 2^𝒪(k^{9/10}log k) n^𝒪(1) in intersection graphs of axis-parallel squares On the positive side, we also provide positive results for TH by solving it in: - 2^𝒪(k^{3/4}log k) n^𝒪(1)-time in contact segment graphs, - 2^𝒪(√dt²(log t)k^{2/3}log k) n^𝒪(1)-time in K_{t,t}-free d-DIR graphs (intersection of segments with d slopes) On the negative side, assuming the ETH we rule out the existence of algorithms solving: - TH and OCT in time 2^o(n) in 2-DIR graphs and more generally in time 2^o(√{Δn}) in 2-DIR graphs with maximum degree Δ, and - TH, FVS, and OCT in time 2^o(√n) in K_{2,2}-free contact-2-DIR graphs of maximum degree 6. Observe that together, these results show that the absence of large K_{t,t} is a necessary and sufficient condition for the existence of subexponential FPT algorithms for TH in 2-DIR.
Cite as

Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond. Subexponential Algorithms in Geometric Graphs via the Subquadratic Grid Minor Property: The Role of Local Radius. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{berthe_et_al:LIPIcs.SWAT.2024.11,
  author =	{Berthe, Ga\'{e}tan and Bougeret, Marin and Gon\c{c}alves, Daniel and Raymond, Jean-Florent},
  title =	{{Subexponential Algorithms in Geometric Graphs via the Subquadratic Grid Minor Property: The Role of Local Radius}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.11},
  URN =		{urn:nbn:de:0030-drops-200519},
  doi =		{10.4230/LIPIcs.SWAT.2024.11},
  annote =	{Keywords: geometric intersection graphs, subexponential FPT algorithms, cycle-hitting problems, bidimensionality}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2023.38
PACE Solver Description: Touiouidth

Authors: Gaétan Berthe, Yoann Coudert-Osmont, Alexander Dobler, Laure Morelle, Amadeus Reinald, and Mathis Rocton

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
We describe Touiouidth, a twin-width solver for the exact-track of the 2023 PACE Challenge: Twin Width. Our solver is based on a simple branch and bound algorithm with search space reductions and is implemented in C++.
Cite as

Gaétan Berthe, Yoann Coudert-Osmont, Alexander Dobler, Laure Morelle, Amadeus Reinald, and Mathis Rocton. PACE Solver Description: Touiouidth. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 38:1-38:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{berthe_et_al:LIPIcs.IPEC.2023.38,
  author =	{Berthe, Ga\'{e}tan and Coudert-Osmont, Yoann and Dobler, Alexander and Morelle, Laure and Reinald, Amadeus and Rocton, Mathis},
  title =	{{PACE Solver Description: Touiouidth}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{38:1--38:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.38},
  URN =		{urn:nbn:de:0030-drops-194576},
  doi =		{10.4230/LIPIcs.IPEC.2023.38},
  annote =	{Keywords: Twinwidth, Pace Challenge}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2022.31
PACE Solver Description: DreyFVS

Authors: Gabriel Bathie, Gaétan Berthe, Yoann Coudert-Osmont, David Desobry, Amadeus Reinald, and Mathis Rocton

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

Abstract
We describe DreyFVS, a heuristic for Directed Feedback Vertex Set submitted to the 2022 edition of Parameterized Algorithms and Computational Experiments Challenge. The Directed Feedback Vertex Set problem asks to remove a minimal number of vertices from a digraph such that the resulting digraph is acyclic. Our algorithm first performs a guess on a reduced instance by leveraging the Sinkhorn-Knopp algorithm, to then improve this solution by pipelining two local search methods.
Cite as

Gabriel Bathie, Gaétan Berthe, Yoann Coudert-Osmont, David Desobry, Amadeus Reinald, and Mathis Rocton. PACE Solver Description: DreyFVS. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 31:1-31:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bathie_et_al:LIPIcs.IPEC.2022.31,
  author =	{Bathie, Gabriel and Berthe, Ga\'{e}tan and Coudert-Osmont, Yoann and Desobry, David and Reinald, Amadeus and Rocton, Mathis},
  title =	{{PACE Solver Description: DreyFVS}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{31:1--31:4},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.31},
  URN =		{urn:nbn:de:0030-drops-173870},
  doi =		{10.4230/LIPIcs.IPEC.2022.31},
  annote =	{Keywords: Directed Feedback Vertex Set, Heuristic, Sinkhorn algorithm, Local search}
}
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