10 Search Results for "Bergé, Pierre"

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)

Copy BibTex To Clipboard

@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.STACS.2026.42
Computing Twin-Width via Treedepth and Vertex Integrity

Authors: Robert Ganian and Mathis Rocton

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Twin-width is a graph parameter that has become central to explaining the fixed-parameter tractability of first-order model checking across many graph classes. Despite its algorithmic importance, computing twin-width remains poorly understood: even recognizing graphs of twin-width at most four is NP-hard, and no fixed-parameter approximations parameterized by twin-width itself are known. A recent approach towards breaking this barrier focuses on first developing fixed-parameter algorithms for computing or approximating twin-width under parameterizations distinct from twin-width. Our first result establishes that approximating twin-width is fixed-parameter tractable when parameterized by treedepth, thereby breaking the long-standing barrier that all previous tractable parameterizations were based on deletion distance. The proof proceeds via oriented twin-width, yielding the first constructive evidence that this variant may be easier to handle algorithmically. As our second main result, we show that computing twin-width exactly is fixed-parameter tractable with respect to vertex integrity. This constitutes the first non-trivial parameterized algorithm for computing optimal contraction sequences.
Cite as

Robert Ganian and Mathis Rocton. Computing Twin-Width via Treedepth and Vertex Integrity. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{ganian_et_al:LIPIcs.STACS.2026.42,
  author =	{Ganian, Robert and Rocton, Mathis},
  title =	{{Computing Twin-Width via Treedepth and Vertex Integrity}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{42:1--42:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.42},
  URN =		{urn:nbn:de:0030-drops-255318},
  doi =		{10.4230/LIPIcs.STACS.2026.42},
  annote =	{Keywords: twin-width, fixed-parameter algorithms, treedepth, vertex integrity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.3
Linear Matroid Intersection Is in Catalytic Logspace

Authors: Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Linear matroid intersection is an important problem in combinatorial optimization. Given two linear matroids over the same ground set, the linear matroid intersection problem asks you to find a common independent set of maximum size. The deep interest in linear matroid intersection is due to the fact that it generalises many classical problems in theoretical computer science, such as bipartite matching, edge disjoint spanning trees, rainbow spanning tree, and many more. We study this problem in the model of catalytic computation: space-bounded machines are granted access to catalytic space, which is additional working memory that is full with arbitrary data that must be preserved at the end of its computation. Although linear matroid intersection has had a polynomial time algorithm for over 50 years, it remains an important open problem to show that linear matroid intersection belongs to any well studied subclass of {P}. We address this problem for the class catalytic logspace (CL) with a polynomial time bound (CLP). Recently, Agarwala and Mertz (2025) showed that bipartite maximum matching can be computed in the class CLP ⊆ {P}. This was the first subclass of {P} shown to contain bipartite matching, and additionally the first problem outside TC¹ shown to be contained in CL. We significantly improve the result of Agarwala and Mertz by showing that linear matroid intersection can be computed in CLP.
Cite as

Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra. Linear Matroid Intersection Is in Catalytic Logspace. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.3,
  author =	{Agarwala, Aryan and Alekseev, Yaroslav and Vinciguerra, Antoine},
  title =	{{Linear Matroid Intersection Is in Catalytic Logspace}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.3},
  URN =		{urn:nbn:de:0030-drops-252908},
  doi =		{10.4230/LIPIcs.ITCS.2026.3},
  annote =	{Keywords: Catalytic Computing, Computational Complexity, Matroid Theory, Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.1
Polymorphic Cycle Basis in a Sequence of Graphs to Analyze the Structural Evolution of a Molecular Dynamic Trajectory

Authors: Ylène Aboulfath, Dominique Barth, Thierry Mautor, Dimitri Watel, and Marc-Antoine Weisser

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
Molecular dynamics analysis is a fundamental topic in chemistry, in particular the study of the formation and dissolution of hydrogen bonds over time. The dynamics of these bonds create and break cycles which are crucial to the structure of the molecules. The challenge in cycle analysis is twofold: there is an exponential number of cycles, and some cycles are very close. We introduce a graph-based approach using minimum cycle bases to assist in molecular dynamics analysis. Given a set of graphs representing a molecule trajectory, we determine, for each graph, a minimum cycle basis and construct a graph of cycles which represents the cycles of minimum bases and their interactions. Then, we aggregate all information from these graphs of cycles into a polygraph. Each vertex of the polygraph represents a class of cycles appearing in different minimum bases and playing equivalent roles in the trajectory. This paper introduces our approach, establishes the complexity of associated problems, and suggests an implementation. Simulations are conducted on both real and generated data to evaluate the performance of our approach.
Cite as

Ylène Aboulfath, Dominique Barth, Thierry Mautor, Dimitri Watel, and Marc-Antoine Weisser. Polymorphic Cycle Basis in a Sequence of Graphs to Analyze the Structural Evolution of a Molecular Dynamic Trajectory. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{aboulfath_et_al:LIPIcs.SEA.2025.1,
  author =	{Aboulfath, Yl\`{e}ne and Barth, Dominique and Mautor, Thierry and Watel, Dimitri and Weisser, Marc-Antoine},
  title =	{{Polymorphic Cycle Basis in a Sequence of Graphs to Analyze the Structural Evolution of a Molecular Dynamic Trajectory}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{1:1--1:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.1},
  URN =		{urn:nbn:de:0030-drops-232399},
  doi =		{10.4230/LIPIcs.SEA.2025.1},
  annote =	{Keywords: Graph theory, Cycle basis, Molecular analysis}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.16
Yeo’s Theorem for Locally Colored Graphs: the Path to Sequentialization in Linear Logic

Authors: Rémi Di Guardia, Olivier Laurent, Lorenzo Tortora de Falco, and Lionel Vaux Auclair

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
We revisit sequentialization proofs associated with the Danos-Regnier correctness criterion in the theory of proof nets of linear logic. Our approach relies on a generalization of Yeo’s theorem for graphs, based on colorings of half-edges. This happens to be the appropriate level of abstraction to extract sequentiality information from a proof net without modifying its graph structure. We thus obtain different ways of recovering a sequent calculus derivation from a proof net inductively, by relying on a splitting ⅋-vertex, on a splitting ⊗-vertex, on a splitting terminal vertex, etc. The proof of our Yeo-style theorem relies on a key lemma that we call cusp minimization. Given a coloring of half-edges, a cusp in a path is a vertex whose adjacent half-edges in the path have the same color. And, given a cycle with at least one cusp and subject to suitable hypotheses, cusp minimization constructs a cycle with strictly less cusps. In the absence of cusp-free cycles, cusp minimization is then enough to ensure the existence of a splitting vertex, i.e. a vertex that is a cusp of any cycle it belongs to. Our theorem subsumes several graph-theoretical results, including some known to be equivalent to Yeo’s theorem. The novelty is that they can be derived in a straightforward way, just by defining a dedicated coloring, again without any modification of the underlying graph structure (vertices and edges) - similar results from the literature required more involved encodings.
Cite as

Rémi Di Guardia, Olivier Laurent, Lorenzo Tortora de Falco, and Lionel Vaux Auclair. Yeo’s Theorem for Locally Colored Graphs: the Path to Sequentialization in Linear Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{diguardia_et_al:LIPIcs.FSCD.2025.16,
  author =	{Di Guardia, R\'{e}mi and Laurent, Olivier and Tortora de Falco, Lorenzo and Vaux Auclair, Lionel},
  title =	{{Yeo’s Theorem for Locally Colored Graphs: the Path to Sequentialization in Linear Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.16},
  URN =		{urn:nbn:de:0030-drops-236317},
  doi =		{10.4230/LIPIcs.FSCD.2025.16},
  annote =	{Keywords: Linear Logic, Proof Net, Sequentialization, Graph Theory, Yeo’s Theorem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.6
Twin-Width One

Authors: Jungho Ahn, Hugo Jacob, Noleen Köhler, Christophe Paul, Amadeus Reinald, and Sebastian Wiederrecht

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We investigate the structure of graphs of twin-width at most 1, and obtain the following results: - Graphs of twin-width at most 1 are permutation graphs. In particular they have an intersection model and a linear structure. - There is always a 1-contraction sequence closely following a given permutation diagram. - Based on a recursive decomposition theorem, we obtain a simple algorithm running in linear time that produces a 1-contraction sequence of a graph, or guarantees that it has twin-width more than 1. - We characterise distance-hereditary graphs based on their twin-width and deduce a linear time algorithm to compute optimal sequences on this class of graphs.
Cite as

Jungho Ahn, Hugo Jacob, Noleen Köhler, Christophe Paul, Amadeus Reinald, and Sebastian Wiederrecht. Twin-Width One. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{ahn_et_al:LIPIcs.STACS.2025.6,
  author =	{Ahn, Jungho and Jacob, Hugo and K\"{o}hler, Noleen and Paul, Christophe and Reinald, Amadeus and Wiederrecht, Sebastian},
  title =	{{Twin-Width One}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.6},
  URN =		{urn:nbn:de:0030-drops-228319},
  doi =		{10.4230/LIPIcs.STACS.2025.6},
  annote =	{Keywords: Twin-width, Hereditary graph classes, Intersection model}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.19
The Canadian Traveller Problem on Outerplanar Graphs

Authors: Laurent Beaudou, Pierre Bergé, Vsevolod Chernyshev, Antoine Dailly, Yan Gerard, Aurélie Lagoutte, Vincent Limouzy, and Lucas Pastor

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We study the k-Canadian Traveller Problem, where a weighted graph G = (V,E,ω) with a source s ∈ V and a target t ∈ V are given. This problem also has a hidden input E_* ⊊ E of cardinality at most k representing blocked edges. The objective is to travel from s to t with the minimum distance. At the beginning of the walk, the blockages E_* are unknown: the traveller discovers that an edge is blocked when visiting one of its endpoints. Online algorithms, also called strategies, have been proposed for this problem and assessed with the competitive ratio, i.e., the ratio between the distance actually traversed by the traveller divided by the distance he would have traversed knowing the blockages in advance. Even though the optimal competitive ratio is 2k+1 even on unit-weighted planar graphs of treewidth 2, we design a polynomial-time strategy achieving competitive ratio 9 on unit-weighted outerplanar graphs. This value 9 also stands as a lower bound for this family of graphs as we prove that, for any ε > 0, no strategy can achieve a competitive ratio 9-ε. Finally, we show that it is not possible to achieve a constant competitive ratio (independent of G and k) on weighted outerplanar graphs.
Cite as

Laurent Beaudou, Pierre Bergé, Vsevolod Chernyshev, Antoine Dailly, Yan Gerard, Aurélie Lagoutte, Vincent Limouzy, and Lucas Pastor. The Canadian Traveller Problem on Outerplanar Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{beaudou_et_al:LIPIcs.MFCS.2024.19,
  author =	{Beaudou, Laurent and Berg\'{e}, Pierre and Chernyshev, Vsevolod and Dailly, Antoine and Gerard, Yan and Lagoutte, Aur\'{e}lie and Limouzy, Vincent and Pastor, Lucas},
  title =	{{The Canadian Traveller Problem on Outerplanar Graphs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.19},
  URN =		{urn:nbn:de:0030-drops-205750},
  doi =		{10.4230/LIPIcs.MFCS.2024.19},
  annote =	{Keywords: Canadian Traveller Problem, Online algorithms, Competitive analysis, Outerplanar graphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.10
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)

Copy BibTex To Clipboard

@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.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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.18
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)

Copy BibTex To Clipboard

@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.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
DOI: 10.4230/LIPIcs.STACS.2022.9
Subquadratic-Time Algorithm for the Diameter and All Eccentricities on Median Graphs

Authors: Pierre Bergé, Guillaume Ducoffe, and Michel Habib

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
On sparse graphs, Roditty and Williams [2013] proved that no O(n^{2-ε})-time algorithm achieves an approximation factor smaller than 3/2 for the diameter problem unless SETH fails. We answer here an open question formulated in the literature: can we use the structural properties of median graphs to break this global quadratic barrier? We propose the first combinatorial algorithm computing exactly all eccentricities of a median graph in truly subquadratic time. Median graphs constitute the family of graphs which is the most studied in metric graph theory because their structure represents many other discrete and geometric concepts, such as CAT(0) cube complexes. Our result generalizes a recent one, stating that there is a linear-time algorithm for computing all eccentricities in median graphs with bounded dimension d, i.e. the dimension of the largest induced hypercube (note that 1-dimensional median graphs are exactly the forests). This prerequisite on d is not necessarily anymore to determine all eccentricities in subquadratic time. The execution time of our algorithm is O(n^{1.6456}log^{O(1)} n).
Cite as

Pierre Bergé, Guillaume Ducoffe, and Michel Habib. Subquadratic-Time Algorithm for the Diameter and All Eccentricities on Median Graphs. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{berge_et_al:LIPIcs.STACS.2022.9,
  author =	{Berg\'{e}, Pierre and Ducoffe, Guillaume and Habib, Michel},
  title =	{{Subquadratic-Time Algorithm for the Diameter and All Eccentricities on Median Graphs}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.9},
  URN =		{urn:nbn:de:0030-drops-158192},
  doi =		{10.4230/LIPIcs.STACS.2022.9},
  annote =	{Keywords: Diameter, Eccentricities, Metric graph theory, Median graphs, Hypercubes}
}
  • Refine by Type
  • 10 Document/PDF
  • 5 Document/HTML

  • Refine by Publication Year
  • 3 2026
  • 3 2025
  • 1 2024
  • 1 2023
  • 2 2022

  • Refine by Author
  • 5 Bergé, Pierre
  • 2 Bonnet, Édouard
  • 2 Dailly, Antoine
  • 2 Déprés, Hugues
  • 2 Gerard, Yan
  • Show More...

  • Refine by Series/Journal
  • 10 LIPIcs

  • Refine by Classification
  • 4 Theory of computation → Graph algorithms analysis
  • 3 Mathematics of computing → Graph algorithms
  • 2 Theory of computation → Parameterized complexity and exact algorithms
  • 1 Applied computing → Chemistry
  • 1 Mathematics of computing → Combinatorial algorithms
  • Show More...

  • Refine by Keyword
  • 2 Twin-width
  • 1 Algorithms
  • 1 Approximation algorithms
  • 1 Canadian Traveler Problem
  • 1 Canadian Traveller Problem
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact