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Documents authored by Reinald, Amadeus

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.
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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}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2021.10
Twin-Width and Polynomial Kernels

Authors: Édouard Bonnet, Eun Jung Kim, Amadeus Reinald, Stéphan Thomassé, and Rémi Watrigant

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract
We study the existence of polynomial kernels for parameterized problems without a polynomial kernel on general graphs, when restricted to graphs of bounded twin-width. It was previously observed in [Bonnet et al., ICALP'21] that the problem k-Independent Set allows no polynomial kernel on graph of bounded twin-width by a very simple argument, which extends to several other problems such as k-Independent Dominating Set, k-Path, k-Induced Path, k-Induced Matching. In this work, we examine the k-Dominating Set and variants of k-Vertex Cover for the existence of polynomial kernels. As a main result, we show that k-Dominating Set does not admit a polynomial kernel on graphs of twin-width at most 4 under a standard complexity-theoretic assumption. The reduction is intricate, especially due to the effort to bring the twin-width down to 4, and it can be tweaked to work for Connected k-Dominating Set and Total k-Dominating Set with a slightly worse bound on the twin-width. On the positive side, we obtain a simple quadratic vertex kernel for Connected k-Vertex Cover and Capacitated k-Vertex Cover on graphs of bounded twin-width. These kernels rely on that graphs of bounded twin-width have Vapnik-Chervonenkis (VC) density 1, that is, for any vertex set X, the number of distinct neighborhoods in X is at most c⋅|X|, where c is a constant depending only on the twin-width. Interestingly the kernel applies to any graph class of VC density 1, and does not require a witness sequence. We also present a more intricate O(k^{1.5}) vertex kernel for Connected k-Vertex Cover. Finally we show that deciding if a graph has twin-width at most 1 can be done in polynomial time, and observe that most graph optimization/decision problems can be solved in polynomial time on graphs of twin-width at most 1.
Cite as

Édouard Bonnet, Eun Jung Kim, Amadeus Reinald, Stéphan Thomassé, and Rémi Watrigant. Twin-Width and Polynomial Kernels. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bonnet_et_al:LIPIcs.IPEC.2021.10,
  author =	{Bonnet, \'{E}douard and Kim, Eun Jung and Reinald, Amadeus and Thomass\'{e}, St\'{e}phan and Watrigant, R\'{e}mi},
  title =	{{Twin-Width and Polynomial Kernels}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.10},
  URN =		{urn:nbn:de:0030-drops-153932},
  doi =		{10.4230/LIPIcs.IPEC.2021.10},
  annote =	{Keywords: Twin-width, kernelization, lower bounds, Dominating Set}
}
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