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Documents authored by Crombez, Loïc

Document
CG Challenge
DOI: 10.4230/LIPIcs.SoCG.2022.71
Shadoks Approach to Minimum Partition into Plane Subgraphs (CG Challenge)

Authors: Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard, and Aldo Gonzalez-Lorenzo

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
We explain the heuristics used by the Shadoks team to win first place in the CG:SHOP 2022 challenge that considers the minimum partition into plane subgraphs. The goal is to partition a set of segments into as few subsets as possible such that segments in the same subset do not cross each other. The challenge has given 225 instances containing between 2500 and 75000 segments. For every instance, our solution was the best among all 32 participating teams.
Cite as

Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard, and Aldo Gonzalez-Lorenzo. Shadoks Approach to Minimum Partition into Plane Subgraphs (CG Challenge). In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 71:1-71:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{crombez_et_al:LIPIcs.SoCG.2022.71,
  author =	{Crombez, Lo\"{i}c and da Fonseca, Guilherme D. and Gerard, Yan and Gonzalez-Lorenzo, Aldo},
  title =	{{Shadoks Approach to Minimum Partition into Plane Subgraphs}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{71:1--71:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.71},
  URN =		{urn:nbn:de:0030-drops-160794},
  doi =		{10.4230/LIPIcs.SoCG.2022.71},
  annote =	{Keywords: Plane graphs, graph coloring, intersection graph, conflict optimizer, line segments, computational geometry}
}
Document
CG Challenge
DOI: 10.4230/LIPIcs.SoCG.2021.63
Shadoks Approach to Low-Makespan Coordinated Motion Planning (CG Challenge)

Authors: Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard, Aldo Gonzalez-Lorenzo, Pascal Lafourcade, and Luc Libralesso

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
This paper describes the heuristics used by the Shadoks team for the CG:SHOP 2021 challenge on motion planning. Using the heuristics outlined in this paper, our team won first place with the best solution to 202 out of 203 instances and optimal solutions to at least 105 of them.
Cite as

Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard, Aldo Gonzalez-Lorenzo, Pascal Lafourcade, and Luc Libralesso. Shadoks Approach to Low-Makespan Coordinated Motion Planning (CG Challenge). In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 63:1-63:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{crombez_et_al:LIPIcs.SoCG.2021.63,
  author =	{Crombez, Lo\"{i}c and da Fonseca, Guilherme D. and Gerard, Yan and Gonzalez-Lorenzo, Aldo and Lafourcade, Pascal and Libralesso, Luc},
  title =	{{Shadoks Approach to Low-Makespan Coordinated Motion Planning}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{63:1--63:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.63},
  URN =		{urn:nbn:de:0030-drops-138622},
  doi =		{10.4230/LIPIcs.SoCG.2021.63},
  annote =	{Keywords: heuristics, motion planning, digital geometry, shortest path}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.11
Efficient Algorithms for Battleship

Authors: Loïc Crombez, Guilherme D. da Fonseca, and Yan Gerard

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
We consider an algorithmic problem inspired by the Battleship game. In the variant of the problem that we investigate, there is a unique ship of shape S ⊂ ℤ² which has been translated in the lattice ℤ². We assume that a player has already hit the ship with a first shot and the goal is to sink the ship using as few shots as possible, that is, by minimizing the number of missed shots. While the player knows the shape S, which position of S has been hit is not known. Given a shape S of n lattice points, the minimum number of misses that can be achieved in the worst case by any algorithm is called the Battleship complexity of the shape S and denoted c(S). We prove three bounds on c(S), each considering a different class of shapes. First, we have c(S) ≤ n-1 for arbitrary shapes and the bound is tight for parallelogram-free shapes. Second, we provide an algorithm that shows that c(S) = O(log n) if S is an HV-convex polyomino. Third, we provide an algorithm that shows that c(S) = O(log log n) if S is a digital convex set. This last result is obtained through a novel discrete version of the Blaschke-Lebesgue inequality relating the area and the width of any convex body.
Cite as

Loïc Crombez, Guilherme D. da Fonseca, and Yan Gerard. Efficient Algorithms for Battleship. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{crombez_et_al:LIPIcs.FUN.2021.11,
  author =	{Crombez, Lo\"{i}c and da Fonseca, Guilherme D. and Gerard, Yan},
  title =	{{Efficient Algorithms for Battleship}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.11},
  URN =		{urn:nbn:de:0030-drops-127728},
  doi =		{10.4230/LIPIcs.FUN.2021.11},
  annote =	{Keywords: Polyomino, digital geometry, decision tree, lattice, HV-convexity, convexity}
}
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