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Documents authored by Rocton, Mathis

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DOI: 10.4230/LIPIcs.IPEC.2024.3
Twin-Width Meets Feedback Edges and Vertex Integrity

Authors: Jakub Balabán, Robert Ganian, and Mathis Rocton

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

Abstract
The approximate computation of twin-width has attracted significant attention already since the moment the parameter was introduced. A recently proposed approach (STACS 2024) towards obtaining a better understanding of this question is to consider the approximability of twin-width via fixed-parameter algorithms whose running time depends not on twin-width itself, but rather on parameters which impose stronger restrictions on the input graph. The first step that article made in this direction is to establish the fixed-parameter approximability of twin-width (with an additive error of 1) when the runtime parameter is the feedback edge number. Here, we make several new steps in this research direction and obtain: - An asymptotically tight bound between twin-width and the feedback edge number; - A significantly improved fixed-parameter approximation algorithm for twin-width under the same runtime parameter (i.e., the feedback edge number) which circumvents many of the technicalities of the original result and simultaneously avoids its formerly non-elementary runtime dependency; - An entirely new fixed-parameter approximation algorithm for twin-width when the runtime parameter is the vertex integrity of the graph.
Cite as

Jakub Balabán, Robert Ganian, and Mathis Rocton. Twin-Width Meets Feedback Edges and Vertex Integrity. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{balaban_et_al:LIPIcs.IPEC.2024.3,
  author =	{Balab\'{a}n, Jakub and Ganian, Robert and Rocton, Mathis},
  title =	{{Twin-Width Meets Feedback Edges and Vertex Integrity}},
  booktitle =	{19th International Symposium on Parameterized and Exact Computation (IPEC 2024)},
  pages =	{3:1--3:22},
  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.2024.3},
  URN =		{urn:nbn:de:0030-drops-222293},
  doi =		{10.4230/LIPIcs.IPEC.2024.3},
  annote =	{Keywords: twin-width, fixed-parameter algorithms, feedback edge number, vertex integrity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.7
Computing Twin-Width Parameterized by the Feedback Edge Number

Authors: Jakub Balabán, Robert Ganian, and Mathis Rocton

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
The problem of whether and how one can compute the twin-width of a graph - along with an accompanying contraction sequence - lies at the forefront of the area of algorithmic model theory. While significant effort has been aimed at obtaining a fixed-parameter approximation for the problem when parameterized by twin-width, here we approach the question from a different perspective and consider whether one can obtain (near-)optimal contraction sequences under a larger parameterization, notably the feedback edge number k. As our main contributions, under this parameterization we obtain (1) a linear bikernel for the problem of either computing a 2-contraction sequence or determining that none exists and (2) an approximate fixed-parameter algorithm which computes an 𝓁-contraction sequence (for an arbitrary specified 𝓁) or determines that the twin-width of the input graph is at least 𝓁. These algorithmic results rely on newly obtained insights into the structure of optimal contraction sequences, and as a byproduct of these we also slightly tighten the bound on the twin-width of graphs with small feedback edge number.
Cite as

Jakub Balabán, Robert Ganian, and Mathis Rocton. Computing Twin-Width Parameterized by the Feedback Edge Number. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{balaban_et_al:LIPIcs.STACS.2024.7,
  author =	{Balab\'{a}n, Jakub and Ganian, Robert and Rocton, Mathis},
  title =	{{Computing Twin-Width Parameterized by the Feedback Edge Number}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{7:1--7:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.7},
  URN =		{urn:nbn:de:0030-drops-197170},
  doi =		{10.4230/LIPIcs.STACS.2024.7},
  annote =	{Keywords: twin-width, parameterized complexity, kernelization, feedback edge number}
}
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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