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Documents authored by Pierron, Théo

Document
DOI: 10.4230/LIPIcs.SoCG.2024.22
Reconfiguration of Plane Trees in Convex Geometric Graphs

Authors: Nicolas Bousquet, Lucas de Meyer, Théo Pierron, and Alexandra Wesolek

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
A non-crossing spanning tree of a set of points in the plane is a spanning tree whose edges pairwise do not cross. Avis and Fukuda in 1996 proved that there always exists a flip sequence of length at most 2n-4 between any pair of non-crossing spanning trees (where n denotes the number of points). Hernando et al. proved that the length of a minimal flip sequence can be of length at least (3/2) n. Two recent results of Aichholzer et al. and Bousquet et al. improved the Avis and Fukuda upper bound by proving that there always exists a flip sequence of length respectively at most 2n-log n and 2n-√n when the points are in convex position. We pursue the investigation of the convex case by improving the upper bound by a linear factor for the first time in 30 years. We prove that there always exists a flip sequence between any pair of non-crossing spanning trees T₁,T₂ of length at most c n where c ≈ 1.95. Our result is actually stronger since we prove that, for any two trees T₁,T₂, there exists a flip sequence from T₁ to T₂ of length at most c |T₁ ⧵ T₂|. We also improve the best lower bound in terms of the symmetric difference by proving that there exists a pair of trees T₁,T₂ such that a minimal flip sequence has length (5/3) |T₁ ⧵ T₂|, improving the lower bound of Hernando et al. by considering the symmetric difference instead of the number of vertices. We generalize this lower bound construction to non-crossing flips (where we close the gap between upper and lower bounds) and rotations.
Cite as

Nicolas Bousquet, Lucas de Meyer, Théo Pierron, and Alexandra Wesolek. Reconfiguration of Plane Trees in Convex Geometric Graphs. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bousquet_et_al:LIPIcs.SoCG.2024.22,
  author =	{Bousquet, Nicolas and de Meyer, Lucas and Pierron, Th\'{e}o and Wesolek, Alexandra},
  title =	{{Reconfiguration of Plane Trees in Convex Geometric Graphs}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.22},
  URN =		{urn:nbn:de:0030-drops-199673},
  doi =		{10.4230/LIPIcs.SoCG.2024.22},
  annote =	{Keywords: Reconfiguration, Non-crossing trees, flip distance}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2021.22
Local Certification of Graph Decompositions and Applications to Minor-Free Classes

Authors: Nicolas Bousquet, Laurent Feuilloley, and Théo Pierron

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Abstract
Local certification consists in assigning labels to the nodes of a network to certify that some given property is satisfied, in such a way that the labels can be checked locally. In the last few years, certification of graph classes received a considerable attention. The goal is to certify that a graph G belongs to a given graph class 𝒢. Such certifications with labels of size O(log n) (where n is the size of the network) exist for trees, planar graphs and graphs embedded on surfaces. Feuilloley et al. ask if this can be extended to any class of graphs defined by a finite set of forbidden minors. In this work, we develop new decomposition tools for graph certification, and apply them to show that for every small enough minor H, H-minor-free graphs can indeed be certified with labels of size O(log n). We also show matching lower bounds using a new proof technique.
Cite as

Nicolas Bousquet, Laurent Feuilloley, and Théo Pierron. Local Certification of Graph Decompositions and Applications to Minor-Free Classes. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bousquet_et_al:LIPIcs.OPODIS.2021.22,
  author =	{Bousquet, Nicolas and Feuilloley, Laurent and Pierron, Th\'{e}o},
  title =	{{Local Certification of Graph Decompositions and Applications to Minor-Free Classes}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.22},
  URN =		{urn:nbn:de:0030-drops-157970},
  doi =		{10.4230/LIPIcs.OPODIS.2021.22},
  annote =	{Keywords: Local certification, proof-labeling schemes, locally checkable proofs, graph decompositions, minor-free graphs}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2021.8
(Sub)linear Kernels for Edge Modification Problems Towards Structured Graph Classes

Authors: Gabriel Bathie, Nicolas Bousquet, and Théo Pierron

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

Abstract
In a (parameterized) graph edge modification problem, we are given a graph G, an integer k and a (usually well-structured) class of graphs 𝒢, and ask whether it is possible to transform G into a graph G' ∈ 𝒢 by adding and/or removing at most k edges. Parameterized graph edge modification problems received considerable attention in the last decades. In this paper, we focus on finding small kernels for edge modification problems. One of the most studied problems is the Cluster Editing problem, in which the goal is to partition the vertex set into a disjoint union of cliques. Even if this problem admits a 2k kernel [Cao and Chen, 2012], this kernel does not reduce the size of most instances. Therefore, we explore the question of whether linear kernels are a theoretical limit in edge modification problems, in particular when the target graphs are very structured (such as a partition into cliques for instance). We prove, as far as we know, the first sublinear kernel for an edge modification problem. Namely, we show that Clique + Independent Set Deletion, which is a restriction of Cluster Deletion, admits a kernel of size O(k/log k). We also obtain small kernels for several other edge modification problems. We prove that Split Addition (and the equivalent Split Deletion) admits a linear kernel, improving the existing quadratic kernel of Ghosh et al. [Ghosh et al., 2015]. We complement this result by proving that Trivially Perfect Addition admits a quadratic kernel (improving the cubic kernel of Guo [Guo, 2007]), and finally prove that its triangle-free version (Starforest Deletion) admits a linear kernel, which is optimal under ETH.
Cite as

Gabriel Bathie, Nicolas Bousquet, and Théo Pierron. (Sub)linear Kernels for Edge Modification Problems Towards Structured Graph Classes. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bathie_et_al:LIPIcs.IPEC.2021.8,
  author =	{Bathie, Gabriel and Bousquet, Nicolas and Pierron, Th\'{e}o},
  title =	{{(Sub)linear Kernels for Edge Modification Problems Towards Structured Graph Classes}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{8:1--8:14},
  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.2021.8},
  URN =		{urn:nbn:de:0030-drops-153918},
  doi =		{10.4230/LIPIcs.IPEC.2021.8},
  annote =	{Keywords: kernelization, graph editing, split graphs, (sub)linear kernels}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2021.29
PACE Solver Description: PaSTEC - PAths, Stars and Twins to Edit Towards Clusters

Authors: Valentin Bartier, Gabriel Bathie, Nicolas Bousquet, Marc Heinrich, Théo Pierron, and Ulysse Prieto

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

Abstract
This document describes our exact Cluster Editing solver, PaSTEC, which got the third place in the 2021 PACE Challenge.
Cite as

Valentin Bartier, Gabriel Bathie, Nicolas Bousquet, Marc Heinrich, Théo Pierron, and Ulysse Prieto. PACE Solver Description: PaSTEC - PAths, Stars and Twins to Edit Towards Clusters. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 29:1-29:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bartier_et_al:LIPIcs.IPEC.2021.29,
  author =	{Bartier, Valentin and Bathie, Gabriel and Bousquet, Nicolas and Heinrich, Marc and Pierron, Th\'{e}o and Prieto, Ulysse},
  title =	{{PACE Solver Description: PaSTEC - PAths, Stars and Twins to Edit Towards Clusters}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{29:1--29:4},
  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.2021.29},
  URN =		{urn:nbn:de:0030-drops-154129},
  doi =		{10.4230/LIPIcs.IPEC.2021.29},
  annote =	{Keywords: cluster editing, exact algorithm, star packing, twins}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2021.33
PACE Solver Description: μSolver - Heuristic Track

Authors: Valentin Bartier, Gabriel Bathie, Nicolas Bousquet, Marc Heinrich, Théo Pierron, and Ulysse Prieto

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

Abstract
This document describes our heuristic Cluster Editing solver, μSolver, which got the third place in the 2021 PACE Challenge. We present the local search and kernelization techniques for Cluster Editing that are implemented in the solver.
Cite as

Valentin Bartier, Gabriel Bathie, Nicolas Bousquet, Marc Heinrich, Théo Pierron, and Ulysse Prieto. PACE Solver Description: μSolver - Heuristic Track. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 33:1-33:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bartier_et_al:LIPIcs.IPEC.2021.33,
  author =	{Bartier, Valentin and Bathie, Gabriel and Bousquet, Nicolas and Heinrich, Marc and Pierron, Th\'{e}o and Prieto, Ulysse},
  title =	{{PACE Solver Description: \muSolver - Heuristic Track}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{33:1--33:3},
  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.2021.33},
  URN =		{urn:nbn:de:0030-drops-154161},
  doi =		{10.4230/LIPIcs.IPEC.2021.33},
  annote =	{Keywords: kernelization, graph editing, clustering, local search}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2021.49
Brief Announcement: Local Certification of Graph Decompositions and Applications to Minor-Free Classes

Authors: Nicolas Bousquet, Laurent Feuilloley, and Théo Pierron

Published in: LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

Abstract
Local certification consists in assigning labels to the nodes of a network to certify that some given property is satisfied, in such a way that the labels can be checked locally. In the last few years, certification of graph classes received a considerable attention. The goal is to certify that a graph G belongs to a given graph class 𝒢. Such certifications with labels of size O(log n) (where n is the size of the network) exist for trees, planar graphs and graphs embedded on surfaces. Feuilloley et al. ask if this can be extended to any class of graphs defined by a finite set of forbidden minors. In this paper, we develop new decomposition tools for graph certification, and apply them to show that for every small enough minor H, H-minor-free graphs can indeed be certified with labels of size O(log n). We also show matching lower bounds with a new simple proof technique.
Cite as

Nicolas Bousquet, Laurent Feuilloley, and Théo Pierron. Brief Announcement: Local Certification of Graph Decompositions and Applications to Minor-Free Classes. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 49:1-49:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bousquet_et_al:LIPIcs.DISC.2021.49,
  author =	{Bousquet, Nicolas and Feuilloley, Laurent and Pierron, Th\'{e}o},
  title =	{{Brief Announcement: Local Certification of Graph Decompositions and Applications to Minor-Free Classes}},
  booktitle =	{35th International Symposium on Distributed Computing (DISC 2021)},
  pages =	{49:1--49:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-210-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{209},
  editor =	{Gilbert, Seth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.49},
  URN =		{urn:nbn:de:0030-drops-148515},
  doi =		{10.4230/LIPIcs.DISC.2021.49},
  annote =	{Keywords: Local certification, proof-labeling schemes, locally checkable proofs, graph decompositions, minor-free graphs}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2019.15
Parameterized Complexity of Edge-Coloured and Signed Graph Homomorphism Problems

Authors: Florent Foucaud, Hervé Hocquard, Dimitri Lajou, Valia Mitsou, and Théo Pierron

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

Abstract
We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from an edge-coloured graph G to an edge-coloured graph H is a vertex-mapping from G to H that preserves adjacencies and edge-colours. We consider the property of having a homomorphism to a fixed edge-coloured graph H, which generalises the classic vertex-colourability property. The question we are interested in is the following: given an edge-coloured graph G, can we perform k graph operations so that the resulting graph admits a homomorphism to H? The operations we consider are vertex-deletion, edge-deletion and switching (an operation that permutes the colours of the edges incident to a given vertex). Switching plays an important role in the theory of signed graphs, that are 2-edge-coloured graphs whose colours are the signs + and -. We denote the corresponding problems (parameterized by k) by Vertex Deletion-H-Colouring, Edge Deletion-H-Colouring and Switching-H-Colouring. These problems generalise the extensively studied H-Colouring problem (where one has to decide if an input graph admits a homomorphism to a fixed target H). For 2-edge-coloured H, it is known that H-Colouring already captures the complexity of all fixed-target Constraint Satisfaction Problems. Our main focus is on the case where H is an edge-coloured graph of order at most 2, a case that is already interesting since it includes standard problems such as Vertex Cover, Odd Cycle Transversal and Edge Bipartization. For such a graph H, we give a PTime/NP-complete complexity dichotomy for all three Vertex Deletion-H-Colouring, Edge Deletion-H-Colouring and Switching-H-Colouring problems. Then, we address their parameterized complexity. We show that all Vertex Deletion-H-Colouring and Edge Deletion-H-Colouring problems for such H are FPT. This is in contrast with the fact that already for some H of order 3, unless PTime = NP, none of the three considered problems is in XP, since 3-Colouring is NP-complete. We show that the situation is different for Switching-H-Colouring: there are three 2-edge-coloured graphs H of order 2 for which Switching-H-Colouring is W[1]-hard, and assuming the ETH, admits no algorithm in time f(k)n^{o(k)} for inputs of size n and for any computable function f. For the other cases, Switching-H-Colouring is FPT.
Cite as

Florent Foucaud, Hervé Hocquard, Dimitri Lajou, Valia Mitsou, and Théo Pierron. Parameterized Complexity of Edge-Coloured and Signed Graph Homomorphism Problems. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{foucaud_et_al:LIPIcs.IPEC.2019.15,
  author =	{Foucaud, Florent and Hocquard, Herv\'{e} and Lajou, Dimitri and Mitsou, Valia and Pierron, Th\'{e}o},
  title =	{{Parameterized Complexity of Edge-Coloured and Signed Graph Homomorphism Problems}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.15},
  URN =		{urn:nbn:de:0030-drops-114765},
  doi =		{10.4230/LIPIcs.IPEC.2019.15},
  annote =	{Keywords: Graph homomorphism, Graph modification, Edge-coloured graph, Signed graph}
}
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