8 Search Results for "Limouzy, Vincent"

Document
DOI: 10.4230/LIPIcs.GD.2025.10
The Bend Number of Cocomparability Graphs

Authors: Todor Antić, Vit Jelínek, Martin Pergel, Felix Schröder, Peter Stumpf, and Pavel Valtr

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
We introduce a new complexity measure for cocomparability graphs of posets or in other words, intersection graphs of piecewise linear functions, the bend number. We prove that cocomparability graphs of bounded bend number are not too plentiful and give two hierarchies of classes of cocomparability graphs, depending on whether the piecewise linear functions are restricted to slopes of ±1 (diagonal case) or not (general case). These hierarchies give a gradation between permutation graphs and cocomparability graphs.
Cite as

Todor Antić, Vit Jelínek, Martin Pergel, Felix Schröder, Peter Stumpf, and Pavel Valtr. The Bend Number of Cocomparability Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{antic_et_al:LIPIcs.GD.2025.10,
  author =	{Anti\'{c}, Todor and Jel{\'\i}nek, Vit and Pergel, Martin and Schr\"{o}der, Felix and Stumpf, Peter and Valtr, Pavel},
  title =	{{The Bend Number of Cocomparability Graphs}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{10:1--10:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.10},
  URN =		{urn:nbn:de:0030-drops-249963},
  doi =		{10.4230/LIPIcs.GD.2025.10},
  annote =	{Keywords: Intersection Graphs, Bend Number, Piecewise Linear Functions, Graph Class Hierarchy, Cocomparability Graphs, Permutation Graphs, Poset Dimension}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.15
Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs

Authors: Emanuel Castelo, Oscar Defrain, and Guilherme C. M. Gomes

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Enumerating minimal dominating sets with polynomial delay in bipartite graphs is a long-standing open problem. To date, even the subcase of chordal bipartite graphs is open, with the best known algorithm due to Golovach, Heggernes, Kanté, Kratsch, Sæther, and Villanger running in incremental-polynomial time. We improve on this result by providing a polynomial delay and space algorithm enumerating minimal dominating sets in chordal bipartite graphs. Additionally, we show that the total and connected variants admit polynomial and incremental-polynomial delay algorithms, respectively, within the same class. This provides an alternative proof of a result by Golovach et al. for total dominating sets, and answers an open question for the connected variant. Finally, we give evidence that the techniques used in this paper cannot be generalized to bipartite graphs for (total) minimal dominating sets, unless P = NP, and show that enumerating minimal connected dominating sets in bipartite graphs is harder than enumerating minimal transversals in general hypergraphs.
Cite as

Emanuel Castelo, Oscar Defrain, and Guilherme C. M. Gomes. Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{castelo_et_al:LIPIcs.WADS.2025.15,
  author =	{Castelo, Emanuel and Defrain, Oscar and C. M. Gomes, Guilherme},
  title =	{{Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.15},
  URN =		{urn:nbn:de:0030-drops-242467},
  doi =		{10.4230/LIPIcs.WADS.2025.15},
  annote =	{Keywords: algorithmic enumeration, minimal dominating sets, connected dominating sets, total dominating sets, chordal bipartite graphs, sequential method, polynomial delay}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.19
Designing Output Sensitive Algorithms for Subgraph Enumeration

Authors: Alessio Conte, Kazuhiro Kurita, Andrea Marino, Giulia Punzi, Takeaki Uno, and Kunihiro Wasa

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
The enumeration of all subgraphs respecting some structural property is a fundamental task in theoretical computer science, with practical applications in many branches of data mining and network analysis. It is often of interest to only consider solutions (subgraphs) that are maximal under inclusion, and to achieve output-sensitive complexity, i.e., bounding the running time with respect to the number of subgraphs produced. In this paper, we provide a survey of techniques for designing output-sensitive algorithms for subgraph enumeration, including partition-based approaches such as flashlight search, solution-graph traversal methods such as reverse search, and cost amortization strategies such as push-out amortization. We also briefly discuss classes of efficiency, hardness of enumeration, and variants such as approximate enumeration. The paper is meant as an accessible handbook for learning the basics of the field and as a practical reference for selecting state-of-the-art subgraph enumeration strategies fitting to one’s needs.
Cite as

Alessio Conte, Kazuhiro Kurita, Andrea Marino, Giulia Punzi, Takeaki Uno, and Kunihiro Wasa. Designing Output Sensitive Algorithms for Subgraph Enumeration. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 19:1-19:40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{conte_et_al:OASIcs.Grossi.19,
  author =	{Conte, Alessio and Kurita, Kazuhiro and Marino, Andrea and Punzi, Giulia and Uno, Takeaki and Wasa, Kunihiro},
  title =	{{Designing Output Sensitive Algorithms for Subgraph Enumeration}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{19:1--19:40},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.19},
  URN =		{urn:nbn:de:0030-drops-238180},
  doi =		{10.4230/OASIcs.Grossi.19},
  annote =	{Keywords: Graph algorithms, Graph enumeration, Output sensitive enumeration}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.9
Spanner Enumeration for Temporal Graphs

Authors: Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
A spanner of a temporal graph is a subset of edges that preserves connectivity over time between vertices. A minimal spanner is one in which no additional edges can be removed without breaking this connectivity. Our focus is on enumerating minimal spanners for a given temporal graph. We explore several variations of this problem based on the type of connectivity that must be maintained, ranging from one-to-all connectivity to one-to-all-to-one, many-to-all, and finally all-to-all connectivity. We establish that these problems become progressively harder: (i) We present a polynomial-delay enumeration algorithm for one-to-all connectivity; (ii) We prove Dual-hardness for both one-to-all-to-one and many-to-all connectivity, even in the restricted case of two-to-all; (iii) Finally, for all-to-all connectivity, we show that enumeration cannot be performed in output-polynomial time unless P = NP.
Cite as

Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno. Spanner Enumeration for Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kurita_et_al:LIPIcs.SAND.2025.9,
  author =	{Kurita, Kazuhiro and Marino, Andrea and Schoeters, Jason and Uno, Takeaki},
  title =	{{Spanner Enumeration for Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.9},
  URN =		{urn:nbn:de:0030-drops-230621},
  doi =		{10.4230/LIPIcs.SAND.2025.9},
  annote =	{Keywords: temporal graphs, temporal spanners, one-to-all connectivity, all-to-all connectivity enumeration, NP-completeness, Dual-hardness, binary partition tree, flashlight search, polynomial delay}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.8
Enumeration of Minimal Hitting Sets Parameterized by Treewidth

Authors: Batya Kenig and Dan Shlomo Mizrahi

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
Enumerating the minimal hitting sets of a hypergraph is a problem which arises in many data management applications that include constraint mining, discovering unique column combinations, and enumerating database repairs. Previously, Eiter et al. [Thomas Eiter et al., 2003] showed that the minimal hitting sets of an n-vertex hypergraph, with treewidth w, can be enumerated with delay O^*(n^w) (ignoring polynomial factors), with space requirements that scale with the output size. We improve this to fixed-parameter-linear delay, following an FPT preprocessing phase. The memory consumption of our algorithm is exponential with respect to the treewidth of the hypergraph.
Cite as

Batya Kenig and Dan Shlomo Mizrahi. Enumeration of Minimal Hitting Sets Parameterized by Treewidth. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kenig_et_al:LIPIcs.ICDT.2025.8,
  author =	{Kenig, Batya and Mizrahi, Dan Shlomo},
  title =	{{Enumeration of Minimal Hitting Sets Parameterized by Treewidth}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.8},
  URN =		{urn:nbn:de:0030-drops-229498},
  doi =		{10.4230/LIPIcs.ICDT.2025.8},
  annote =	{Keywords: Enumeration, Hitting sets}
}
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)

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@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.ISAAC.2022.12
Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond

Authors: Dibyayan Chakraborty, Antoine Dailly, Sandip Das, Florent Foucaud, Harmender Gahlawat, and Subir Kumar Ghosh

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
A path is isometric if it is a shortest path between its endpoints. In this article, we consider the graph covering problem Isometric Path Cover, where we want to cover all the vertices of the graph using a minimum-size set of isometric paths. Although this problem has been considered from a structural point of view (in particular, regarding applications to pursuit-evasion games), it is little studied from the algorithmic perspective. We consider Isometric Path Cover on chordal graphs, and show that the problem is NP-hard for this class. On the positive side, for chordal graphs, we design a 4-approximation algorithm and an FPT algorithm for the parameter solution size. The approximation algorithm is based on a reduction to the classic path covering problem on a suitable directed acyclic graph obtained from a breadth first search traversal of the graph. The approximation ratio of our algorithm is 3 for interval graphs and 2 for proper interval graphs. Moreover, we extend the analysis of our approximation algorithm to k-chordal graphs (graphs whose induced cycles have length at most k) by showing that it has an approximation ratio of k+7 for such graphs, and to graphs of treelength at most 𝓁, where the approximation ratio is at most 6𝓁+2.
Cite as

Dibyayan Chakraborty, Antoine Dailly, Sandip Das, Florent Foucaud, Harmender Gahlawat, and Subir Kumar Ghosh. Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chakraborty_et_al:LIPIcs.ISAAC.2022.12,
  author =	{Chakraborty, Dibyayan and Dailly, Antoine and Das, Sandip and Foucaud, Florent and Gahlawat, Harmender and Ghosh, Subir Kumar},
  title =	{{Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.12},
  URN =		{urn:nbn:de:0030-drops-172974},
  doi =		{10.4230/LIPIcs.ISAAC.2022.12},
  annote =	{Keywords: Shortest paths, Isometric path cover, Chordal graph, Interval graph, AT-free graph, Approximation algorithm, FPT algorithm, Treewidth, Chordality, Treelength}
}
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}
}
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