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Documents authored by Mary, Arnaud

Document
DOI: 10.4230/LIPIcs.ESA.2025.29
The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration

Authors: Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A dominating set of a graph G = (V,E) is a set of vertices D ⊆ V whose closed neighborhood is V, i.e., N[D] = V. We view a dominating set as a collection of tokens placed on the vertices of D. In the token sliding variant of the Dominating Set Reconfiguration problem (TS-DSR), we seek to transform a source dominating set into a target dominating set in G by sliding tokens along edges, and while maintaining a dominating set all along the transformation. TS-DSR is known to be PSPACE-complete even restricted to graphs of pathwidth w, for some non-explicit constant w and to be XL-complete parameterized by the size k of the solution. The first contribution of this article consists in using a novel approach to provide the first explicit constant for which the TS-DSR problem is PSPACE-complete, a question that was left open in the literature. From a parameterized complexity perspective, the token jumping variant of DSR, i.e., where tokens can jump to arbitrary vertices, is known to be FPT when parameterized by the size of the dominating sets on nowhere dense classes of graphs. But, in contrast, no non-trivial result was known about TS-DSR. We prove that DSR is actually much harder in the sliding model since it is XL-complete when restricted to bounded pathwidth graphs and even when parameterized by k plus the feedback vertex set number of the graph. This gives, for the first time, a difference of behavior between the complexity under token sliding and token jumping for some problem on graphs of bounded treewidth. All our results are obtained using a brand new method, based on the hardness of the so-called Tape Reconfiguration problem, a problem we believe to be of independent interest. We complement these hardness results with a positive result showing that DSR (parameterized by k) in the sliding model is FPT on planar graphs, also answering an open problem from the literature.
Cite as

Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron. The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bousquet_et_al:LIPIcs.ESA.2025.29,
  author =	{Bousquet, Nicolas and Deschamps, Quentin and Mary, Arnaud and Mouawad, Amer E. and Pierron, Th\'{e}o},
  title =	{{The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.29},
  URN =		{urn:nbn:de:0030-drops-244974},
  doi =		{10.4230/LIPIcs.ESA.2025.29},
  annote =	{Keywords: combinatorial reconfiguration, parameterized complexity, structural graph parameters, treewidth, dominating set}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.33
Polynomial Delay Algorithm for Minimal Chordal Completions

Authors: Caroline Brosse, Vincent Limouzy, and Arnaud Mary

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

Abstract
Motivated by the problem of enumerating all tree decompositions of a graph, we consider in this article the problem of listing all the minimal chordal completions of a graph. In [Carmeli et al., 2020] (Pods 2017) Carmeli et al. proved that all minimal chordal completions or equivalently all proper tree decompositions of a graph can be listed in incremental polynomial time using exponential space. The total running time of their algorithm is quadratic in the number of solutions and the existence of an algorithm whose complexity depends only linearly on the number of solutions remained open. We close this question by providing a polynomial delay algorithm to solve this problem which, moreover, uses polynomial space. Our algorithm relies on Proximity Search, a framework recently introduced by Conte and Uno [Conte and Uno, 2019] (Stoc 2019) which has been shown powerful to obtain polynomial delay algorithms, but generally requires exponential space. In order to obtain a polynomial space algorithm for our problem, we introduce a new general method called canonical path reconstruction to design polynomial delay and polynomial space algorithms based on proximity search.
Cite as

Caroline Brosse, Vincent Limouzy, and Arnaud Mary. Polynomial Delay Algorithm for Minimal Chordal Completions. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{brosse_et_al:LIPIcs.ICALP.2022.33,
  author =	{Brosse, Caroline and Limouzy, Vincent and Mary, Arnaud},
  title =	{{Polynomial Delay Algorithm for Minimal Chordal Completions}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{33:1--33:16},
  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.2022.33},
  URN =		{urn:nbn:de:0030-drops-163740},
  doi =		{10.4230/LIPIcs.ICALP.2022.33},
  annote =	{Keywords: Graph Algorithm, Algorithmic Enumeration, Minimal chordal completions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.80
A General Framework for Enumerating Equivalence Classes of Solutions

Authors: Yishu Wang, Arnaud Mary, Marie-France Sagot, and Blerina Sinaimeri

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
When a problem has more than one solution, it is often important, depending on the underlying context, to enumerate (i.e., to list) them all. Even when the enumeration can be done in polynomial delay, that is, spending no more than polynomial time to go from one solution to the next, this can be costly as the number of solutions themselves may be huge, including sometimes exponential. Furthermore, depending on the application, many of these solutions can be considered equivalent. The problem of an efficient enumeration of the equivalence classes or of one representative per class (without generating all the solutions), although identified as a need in many areas, has been addressed only for very few specific cases. In this paper, we provide a general framework that solves this problem in polynomial delay for a wide variety of contexts, including optimization ones that can be addressed by dynamic programming algorithms, and for certain types of equivalence relations between solutions.
Cite as

Yishu Wang, Arnaud Mary, Marie-France Sagot, and Blerina Sinaimeri. A General Framework for Enumerating Equivalence Classes of Solutions. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 80:1-80:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{wang_et_al:LIPIcs.ESA.2021.80,
  author =	{Wang, Yishu and Mary, Arnaud and Sagot, Marie-France and Sinaimeri, Blerina},
  title =	{{A General Framework for Enumerating Equivalence Classes of Solutions}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{80:1--80:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.80},
  URN =		{urn:nbn:de:0030-drops-146614},
  doi =		{10.4230/LIPIcs.ESA.2021.80},
  annote =	{Keywords: Enumeration algorithms, Equivalence relation, Dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.WABI.2021.3
Making Sense of a Cophylogeny Output: Efficient Listing of Representative Reconciliations

Authors: Yishu Wang, Arnaud Mary, Marie-France Sagot, and Blerina Sinaimeri

Published in: LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)

Abstract
Cophylogeny reconciliation is a powerful method for analyzing host-parasite (or host-symbiont) co-evolution. It models co-evolution as an optimization problem where the set of all optimal solutions may represent different biological scenarios which thus need to be analyzed separately. Despite the significant research done in the area, few approaches have addressed the problem of helping the biologist deal with the often huge space of optimal solutions. In this paper, we propose a new approach to tackle this problem. We introduce three different criteria under which two solutions may be considered biologically equivalent, and then we propose polynomial-delay algorithms that enumerate only one representative per equivalence class (without listing all the solutions). Our results are of both theoretical and practical importance. Indeed, as shown by the experiments, we are able to significantly reduce the space of optimal solutions while still maintaining important biological information about the whole space.
Cite as

Yishu Wang, Arnaud Mary, Marie-France Sagot, and Blerina Sinaimeri. Making Sense of a Cophylogeny Output: Efficient Listing of Representative Reconciliations. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{wang_et_al:LIPIcs.WABI.2021.3,
  author =	{Wang, Yishu and Mary, Arnaud and Sagot, Marie-France and Sinaimeri, Blerina},
  title =	{{Making Sense of a Cophylogeny Output: Efficient Listing of Representative Reconciliations}},
  booktitle =	{21st International Workshop on Algorithms in Bioinformatics (WABI 2021)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-200-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{201},
  editor =	{Carbone, Alessandra and El-Kebir, Mohammed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021.3},
  URN =		{urn:nbn:de:0030-drops-143564},
  doi =		{10.4230/LIPIcs.WABI.2021.3},
  annote =	{Keywords: Cophylogeny, Enumeration, Equivalence relation, Dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.80
The Perfect Matching Reconfiguration Problem

Authors: Marthe Bonamy, Nicolas Bousquet, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Arnaud Mary, Moritz Mühlenthaler, and Kunihiro Wasa

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

Abstract
We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of length four. We are interested in the complexity of this decision problem from the viewpoint of graph classes. We first prove that the problem is PSPACE-complete even for split graphs and for bipartite graphs of bounded bandwidth with maximum degree five. We then investigate polynomial-time solvable cases. Specifically, we prove that the problem is solvable in polynomial time for strongly orderable graphs (that include interval graphs and strongly chordal graphs), for outerplanar graphs, and for cographs (also known as P_4-free graphs). Furthermore, for each yes-instance from these graph classes, we show that a linear number of flip operations is sufficient and we can exhibit a corresponding sequence of flip operations in polynomial time.
Cite as

Marthe Bonamy, Nicolas Bousquet, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Arnaud Mary, Moritz Mühlenthaler, and Kunihiro Wasa. The Perfect Matching Reconfiguration Problem. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 80:1-80:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bonamy_et_al:LIPIcs.MFCS.2019.80,
  author =	{Bonamy, Marthe and Bousquet, Nicolas and Heinrich, Marc and Ito, Takehiro and Kobayashi, Yusuke and Mary, Arnaud and M\"{u}hlenthaler, Moritz and Wasa, Kunihiro},
  title =	{{The Perfect Matching Reconfiguration Problem}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{80:1--80:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.80},
  URN =		{urn:nbn:de:0030-drops-110248},
  doi =		{10.4230/LIPIcs.MFCS.2019.80},
  annote =	{Keywords: Combinatorial Reconfiguration, Graph Algorithms, Perfect Matching}
}
Document
DOI: 10.4230/LIPIcs.STACS.2016.52
Efficient Enumeration of Solutions Produced by Closure Operations

Authors: Arnaud Mary and Yann Strozecki

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Abstract
In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations. More precisely, we prove that we can generate the closure by polymorphisms of a boolean relation with a polynomial delay. Therefore we can compute with polynomial delay the closure of a family of sets by any set of "set operations" (e.g. by union, intersection, difference, symmetric difference ...). To do so, we prove that for any set of operations F, one can decide in polynomial time whether an element belongs to the closure by F of a family of sets. When the relation is over a domain larger than two elements, we prove that our generic enumeration method fails, since the associated decision problem is NP-hard.
Cite as

Arnaud Mary and Yann Strozecki. Efficient Enumeration of Solutions Produced by Closure Operations. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 52:1-52:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{mary_et_al:LIPIcs.STACS.2016.52,
  author =	{Mary, Arnaud and Strozecki, Yann},
  title =	{{Efficient Enumeration of Solutions Produced by Closure Operations}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{52:1--52:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.52},
  URN =		{urn:nbn:de:0030-drops-57538},
  doi =		{10.4230/LIPIcs.STACS.2016.52},
  annote =	{Keywords: enumeration, set saturation, polynomial delay, Post’s lattice}
}
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