100 Search Results for "Goaoc, Xavier"

Volume

LIPIcs, Volume 224

38th International Symposium on Computational Geometry (SoCG 2022)

SoCG 2022, June 7-10, 2022, Berlin, Germany

Editors: Xavier Goaoc and Michael Kerber

Document
DOI: 10.4230/LIPIcs.GD.2024.9
Partitioning Complete Geometric Graphs on Dense Point Sets into Plane Subgraphs

Authors: Adrian Dumitrescu and János Pach

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

Abstract
A complete geometric graph consists of a set P of n points in the plane, in general position, and all segments (edges) connecting them. It is a well known question of Bose, Hurtado, Rivera-Campo, and Wood, whether there exists a positive constant c < 1, such that every complete geometric graph on n points can be partitioned into at most cn plane graphs (that is, noncrossing subgraphs). We answer this question in the affirmative in the special case where the underlying point set P is dense, which means that the ratio between the maximum and the minimum distances in P is of the order of Θ(√n).
Cite as

Adrian Dumitrescu and János Pach. Partitioning Complete Geometric Graphs on Dense Point Sets into Plane Subgraphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 9:1-9:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dumitrescu_et_al:LIPIcs.GD.2024.9,
  author =	{Dumitrescu, Adrian and Pach, J\'{a}nos},
  title =	{{Partitioning Complete Geometric Graphs on Dense Point Sets into Plane Subgraphs}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{9:1--9:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.9},
  URN =		{urn:nbn:de:0030-drops-212939},
  doi =		{10.4230/LIPIcs.GD.2024.9},
  annote =	{Keywords: Convexity, complete geometric Graph, crossing Family, plane Subgraph}
}
Document
DOI: 10.4230/LIPIcs.GD.2024.13
The Price of Upwardness

Authors: Patrizio Angelini, Therese Biedl, Markus Chimani, Sabine Cornelsen, Giordano Da Lozzo, Seok-Hee Hong, Giuseppe Liotta, Maurizio Patrignani, Sergey Pupyrev, Ignaz Rutter, and Alexander Wolff

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

Abstract
Not every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward k-planar drawings of DAGs in which the edges are monotonically increasing in a common direction and every edge is crossed at most k times for some integer k ≥ 1. We show that the number of crossings per edge in a monotone drawing is in general unbounded for the class of bipartite outerplanar, cubic, or bounded pathwidth DAGs. However, it is at most two for outerpaths and it is at most quadratic in the bandwidth in general. From the computational point of view, we prove that upward-k-planarity testing is NP-complete already for k = 1 and even for restricted instances for which upward planarity testing is polynomial. On the positive side, we can decide in linear time whether a single-source DAG admits an upward 1-planar drawing in which all vertices are incident to the outer face.
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Patrizio Angelini, Therese Biedl, Markus Chimani, Sabine Cornelsen, Giordano Da Lozzo, Seok-Hee Hong, Giuseppe Liotta, Maurizio Patrignani, Sergey Pupyrev, Ignaz Rutter, and Alexander Wolff. The Price of Upwardness. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{angelini_et_al:LIPIcs.GD.2024.13,
  author =	{Angelini, Patrizio and Biedl, Therese and Chimani, Markus and Cornelsen, Sabine and Da Lozzo, Giordano and Hong, Seok-Hee and Liotta, Giuseppe and Patrignani, Maurizio and Pupyrev, Sergey and Rutter, Ignaz and Wolff, Alexander},
  title =	{{The Price of Upwardness}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.13},
  URN =		{urn:nbn:de:0030-drops-212977},
  doi =		{10.4230/LIPIcs.GD.2024.13},
  annote =	{Keywords: upward drawings, beyond planarity, upward k-planarity, upward outer-1-planarity}
}
Document
DOI: 10.4230/LIPIcs.GD.2024.19
Weakly Leveled Planarity with Bounded Span

Authors: Michael A. Bekos, Giordano Da Lozzo, Fabrizio Frati, Siddharth Gupta, Philipp Kindermann, Giuseppe Liotta, Ignaz Rutter, and Ioannis G. Tollis

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

Abstract
This paper studies planar drawings of graphs in which each vertex is represented as a point along a sequence of horizontal lines, called levels, and each edge is either a horizontal segment or a strictly y-monotone curve. A graph is s-span weakly leveled planar if it admits such a drawing where the edges have span at most s; the span of an edge is the number of levels it touches minus one. We investigate the problem of computing s-span weakly leveled planar drawings from both the computational and the combinatorial perspectives. We prove the problem to be para-NP-hard with respect to its natural parameter s and investigate its complexity with respect to widely used structural parameters. We show the existence of a polynomial-size kernel with respect to vertex cover number and prove that the problem is FPT when parameterized by treedepth. We also present upper and lower bounds on the span for various graph classes. Notably, we show that cycle trees, a family of 2-outerplanar graphs generalizing Halin graphs, are Θ(log n)-span weakly leveled planar and 4-span weakly leveled planar when 3-connected. As a byproduct of these combinatorial results, we obtain improved bounds on the edge-length ratio of the graph families under consideration.
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Michael A. Bekos, Giordano Da Lozzo, Fabrizio Frati, Siddharth Gupta, Philipp Kindermann, Giuseppe Liotta, Ignaz Rutter, and Ioannis G. Tollis. Weakly Leveled Planarity with Bounded Span. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bekos_et_al:LIPIcs.GD.2024.19,
  author =	{Bekos, Michael A. and Da Lozzo, Giordano and Frati, Fabrizio and Gupta, Siddharth and Kindermann, Philipp and Liotta, Giuseppe and Rutter, Ignaz and Tollis, Ioannis G.},
  title =	{{Weakly Leveled Planarity with Bounded Span}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.19},
  URN =		{urn:nbn:de:0030-drops-213035},
  doi =		{10.4230/LIPIcs.GD.2024.19},
  annote =	{Keywords: Leveled planar graphs, edge span, graph drawing, edge-length ratio}
}
Document
DOI: 10.4230/LIPIcs.GD.2024.23
Intersection Graphs with and Without Product Structure

Authors: Laura Merker, Lena Scherzer, Samuel Schneider, and Torsten Ueckerdt

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

Abstract
A graph class 𝒢 admits product structure if there exists a constant k such that every G ∈ 𝒢 is a subgraph of H ⊠ P for a path P and some graph H of treewidth k. Famously, the class of planar graphs, as well as many beyond-planar graph classes are known to admit product structure. However, we have only few tools to prove the absence of product structure, and hence know of only a few interesting examples of classes. Motivated by the transition between product structure and no product structure, we investigate subclasses of intersection graphs in the plane (e.g., disk intersection graphs) and present necessary and sufficient conditions for these to admit product structure. Specifically, for a set S ⊂ ℝ² (e.g., a disk) and a real number α ∈ [0,1], we consider intersection graphs of α-free homothetic copies of S. That is, each vertex v is a homothetic copy of S of which at least an α-portion is not covered by other vertices, and there is an edge between u and v if and only if u ∩ v ≠ ∅. For α = 1 we have contact graphs, which are in most cases planar, and hence admit product structure. For α = 0 we have (among others) all complete graphs, and hence no product structure. In general, there is a threshold value α^*(S) ∈ [0,1] such that α-free homothetic copies of S admit product structure for all α > α^*(S) and do not admit product structure for all α < α^*(S). We show for a large family of sets S, including all triangles and all trapezoids, that it holds α^*(S) = 1, i.e., we have no product structure, except for the contact graphs (when α = 1). For other sets S, including regular n-gons for infinitely many values of n, we show that 0 < α^*(S) < 1 by proving upper and lower bounds.
Cite as

Laura Merker, Lena Scherzer, Samuel Schneider, and Torsten Ueckerdt. Intersection Graphs with and Without Product Structure. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{merker_et_al:LIPIcs.GD.2024.23,
  author =	{Merker, Laura and Scherzer, Lena and Schneider, Samuel and Ueckerdt, Torsten},
  title =	{{Intersection Graphs with and Without Product Structure}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.23},
  URN =		{urn:nbn:de:0030-drops-213070},
  doi =		{10.4230/LIPIcs.GD.2024.23},
  annote =	{Keywords: Product structure, intersection graphs, linear local treewidth}
}
Document
DOI: 10.4230/LIPIcs.GD.2024.25
Parameterized Algorithms for Beyond-Planar Crossing Numbers

Authors: Miriam Münch and Ignaz Rutter

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

Abstract
Beyond-planar graph classes are usually defined via forbidden configurations or patterns in a drawing. In this paper, we formalize these concepts on a combinatorial level and show that, for any fixed family ℱ of crossing patterns, deciding whether a given graph G admits a drawing that avoids all patterns in F and that has at most c crossings is FPT w.r.t. c. In particular, we show that for any fixed k, deciding whether a graph is k-planar, k-quasi-planar, fan-crossing, fan-crossing-free or min-k-planar, respectively, is FPT with respect to the corresponding beyond-planar crossing number.
Cite as

Miriam Münch and Ignaz Rutter. Parameterized Algorithms for Beyond-Planar Crossing Numbers. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{munch_et_al:LIPIcs.GD.2024.25,
  author =	{M\"{u}nch, Miriam and Rutter, Ignaz},
  title =	{{Parameterized Algorithms for Beyond-Planar Crossing Numbers}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.25},
  URN =		{urn:nbn:de:0030-drops-213096},
  doi =		{10.4230/LIPIcs.GD.2024.25},
  annote =	{Keywords: FPT, Beyond-planarity, Crossing-number, Crossing Patterns}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.28
A Faster Algorithm for the Fréchet Distance in 1D for the Imbalanced Case

Authors: Lotte Blank and Anne Driemel

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
The fine-grained complexity of computing the {Fréchet distance } has been a topic of much recent work, starting with the quadratic SETH-based conditional lower bound by Bringmann from 2014. Subsequent work established largely the same complexity lower bounds for the {Fréchet distance } in 1D. However, the imbalanced case, which was shown by Bringmann to be tight in dimensions d ≥ 2, was still left open. Filling in this gap, we show that a faster algorithm for the {Fréchet distance } in the imbalanced case is possible: Given two 1-dimensional curves of complexity n and n^{α} for some α ∈ (0,1), we can compute their {Fréchet distance } in O(n^{2α} log² n + n log n) time. This rules out a conditional lower bound of the form O((nm)^{1-ε}) that Bringmann showed for d ≥ 2 and any ε > 0 in turn showing a strict separation with the setting d = 1. At the heart of our approach lies a data structure that stores a 1-dimensional curve P of complexity n, and supports queries with a curve Q of complexity m for the continuous {Fréchet distance } between P and Q. The data structure has size in 𝒪(nlog n) and uses query time in 𝒪(m² log² n). Our proof uses a key lemma that is based on the concept of visiting orders and may be of independent interest. We demonstrate this by substantially simplifying the correctness proof of a clustering algorithm by Driemel, Krivošija and Sohler from 2015.
Cite as

Lotte Blank and Anne Driemel. A Faster Algorithm for the Fréchet Distance in 1D for the Imbalanced Case. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blank_et_al:LIPIcs.ESA.2024.28,
  author =	{Blank, Lotte and Driemel, Anne},
  title =	{{A Faster Algorithm for the Fr\'{e}chet Distance in 1D for the Imbalanced Case}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.28},
  URN =		{urn:nbn:de:0030-drops-210999},
  doi =		{10.4230/LIPIcs.ESA.2024.28},
  annote =	{Keywords: \{Fr\'{e}chet distance\}, distance oracle, data structures, time series}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.51
Better Diameter Algorithms for Bounded VC-Dimension Graphs and Geometric Intersection Graphs

Authors: Lech Duraj, Filip Konieczny, and Krzysztof Potępa

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We develop a framework for algorithms finding the diameter in graphs of bounded distance Vapnik-Chervonenkis dimension, in (parameterized) subquadratic time complexity. The class of bounded distance VC-dimension graphs is wide, including, e.g. all minor-free graphs. We build on the work of Ducoffe et al. [SODA'20, SIGCOMP'22], improving their technique. With our approach the algorithms become simpler and faster, working in 𝒪{(k ⋅ n^{1-1/d} ⋅ m ⋅ polylog(n))} time complexity for the graph on n vertices and m edges, where k is the diameter and d is the distance VC-dimension of the graph. Furthermore, it allows us to use the improved technique in more general setting. In particular, we use this framework for geometric intersection graphs, i.e. graphs where vertices are identical geometric objects on a plane and the adjacency is defined by intersection. Applying our approach for these graphs, we partially answer a question posed by Bringmann et al. [SoCG'22], finding an 𝒪{(n^{7/4} ⋅ polylog(n))} parameterized diameter algorithm for unit square intersection graph of size n, as well as a more general algorithm for convex polygon intersection graphs.
Cite as

Lech Duraj, Filip Konieczny, and Krzysztof Potępa. Better Diameter Algorithms for Bounded VC-Dimension Graphs and Geometric Intersection Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{duraj_et_al:LIPIcs.ESA.2024.51,
  author =	{Duraj, Lech and Konieczny, Filip and Pot\k{e}pa, Krzysztof},
  title =	{{Better Diameter Algorithms for Bounded VC-Dimension Graphs and Geometric Intersection Graphs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.51},
  URN =		{urn:nbn:de:0030-drops-211229},
  doi =		{10.4230/LIPIcs.ESA.2024.51},
  annote =	{Keywords: Graph Diameter, Geometric Intersection Graphs, Vapnik-Chervonenkis Dimension}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.66
Shortest Path Separators in Unit Disk Graphs

Authors: Elfarouk Harb, Zhengcheng Huang, and Da Wei Zheng

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths combined with the 1-hop neighbours of those paths and two other vertices. This answers an open problem of Yan, Xiang and Dragan [CGTA '12] and improves their result that requires removing the 3-hop neighbourhood of two shortest paths. Our proof uses very different ideas, including Delaunay triangulations and a generalization of the celebrated balanced separator theorem of Lipton and Tarjan [J. Appl. Math. '79] to systems of non-intersecting paths.
Cite as

Elfarouk Harb, Zhengcheng Huang, and Da Wei Zheng. Shortest Path Separators in Unit Disk Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 66:1-66:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{harb_et_al:LIPIcs.ESA.2024.66,
  author =	{Harb, Elfarouk and Huang, Zhengcheng and Zheng, Da Wei},
  title =	{{Shortest Path Separators in Unit Disk Graphs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{66:1--66:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.66},
  URN =		{urn:nbn:de:0030-drops-211375},
  doi =		{10.4230/LIPIcs.ESA.2024.66},
  annote =	{Keywords: Balanced shortest path separators, unit disk graphs, crossings}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.26
Structure-Guided Local Improvement for Maximum Satisfiability

Authors: André Schidler and Stefan Szeider

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
The enhanced performance of today’s MaxSAT solvers has elevated their appeal for many large-scale applications, notably in software analysis and computer-aided design. Our research delves into refining anytime MaxSAT solving by repeatedly identifying and solving with an exact solver smaller subinstances that are chosen based on the graphical structure of the instance. We investigate various strategies to pinpoint these subinstances. This structure-guided selection of subinstances provides an exact solver with a high potential for improving the current solution. Our exhaustive experimental analyses contrast our methodology as instantiated in our tool MaxSLIM with previous studies and benchmark it against leading-edge MaxSAT solvers.
Cite as

André Schidler and Stefan Szeider. Structure-Guided Local Improvement for Maximum Satisfiability. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 26:1-26:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{schidler_et_al:LIPIcs.CP.2024.26,
  author =	{Schidler, Andr\'{e} and Szeider, Stefan},
  title =	{{Structure-Guided Local Improvement for Maximum Satisfiability}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{26:1--26:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.26},
  URN =		{urn:nbn:de:0030-drops-207112},
  doi =		{10.4230/LIPIcs.CP.2024.26},
  annote =	{Keywords: maximum satisfiability, large neighborhood search (LNS), SAT-based local improvement (SLIM), incomplete MaxSAT, graphical structure, metaheuristic}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.23
Engineering A* Search for the Flip Distance of Plane Triangulations

Authors: Philip Mayer and Petra Mutzel

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
The flip distance for two triangulations of a point set is defined as the smallest number of edge flips needed to transform one triangulation into another, where an edge flip is the act of replacing an edge of a triangulation by a different edge such that the result remains a triangulation. We adapt and engineer a sophisticated A* search algorithm acting on the so-called flip graph. In particular, we prove that previously proposed lower bounds for the flip distance form consistent heuristics for A* and show that they can be computed efficiently using dynamic algorithms. As an alternative approach, we present an integer linear program (ILP) for the flip distance problem. We experimentally evaluate our approaches on a new real-world benchmark data set based on an application in geodesy, namely sea surface reconstruction. Our evaluation reveals that A* search consistently outperforms our ILP formulation as well as a naive baseline, which is bidirectional breadth-first search. In particular, the runtime of our approach improves upon the baseline by more than two orders of magnitude. Furthermore, our A* search successfully solves most of the considered sea surface instances with up to 41 points. This is a substantial improvement compared to the baseline, which struggles with subsets of the real-world data of size 25. Lastly, to allow the consideration of global sea level data, we developed a decomposition-based heuristic for the flip distance. In our experiments it yields optimal flip distance values for most of the considered sea level data and it can be applied to large data sets due to its fast runtime.
Cite as

Philip Mayer and Petra Mutzel. Engineering A* Search for the Flip Distance of Plane Triangulations. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mayer_et_al:LIPIcs.SEA.2024.23,
  author =	{Mayer, Philip and Mutzel, Petra},
  title =	{{Engineering A* Search for the Flip Distance of Plane Triangulations}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.23},
  URN =		{urn:nbn:de:0030-drops-203887},
  doi =		{10.4230/LIPIcs.SEA.2024.23},
  annote =	{Keywords: Computational Geometry, Triangulations, Flip Distance, A-star Search, Integer Linear Programming}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.23
A Canonical Tree Decomposition for Chirotopes

Authors: Mathilde Bouvel, Valentin Feray, Xavier Goaoc, and Florent Koechlin

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

Abstract
We introduce and study a notion of decomposition of planar point sets (or rather of their chirotopes) as trees decorated by smaller chirotopes. This decomposition is based on the concept of mutually avoiding sets, and adapts in some sense the modular decomposition of graphs in the world of chirotopes. The associated tree always exists and is unique up to some appropriate constraints. We also show how to compute the number of triangulations of a chirotope efficiently, starting from its tree and the (weighted) numbers of triangulations of its parts.
Cite as

Mathilde Bouvel, Valentin Feray, Xavier Goaoc, and Florent Koechlin. A Canonical Tree Decomposition for Chirotopes. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bouvel_et_al:LIPIcs.SoCG.2024.23,
  author =	{Bouvel, Mathilde and Feray, Valentin and Goaoc, Xavier and Koechlin, Florent},
  title =	{{A Canonical Tree Decomposition for Chirotopes}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{23:1--23:18},
  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.2024.23},
  URN =		{urn:nbn:de:0030-drops-199680},
  doi =		{10.4230/LIPIcs.SoCG.2024.23},
  annote =	{Keywords: Order type, modular decomposition, counting triangulations, mutually avoiding point sets, generating functions, rewriting systems}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.SoCG.2022
LIPIcs, Volume 224, SoCG 2022, Complete Volume

Authors: Xavier Goaoc and Michael Kerber

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

Abstract
LIPIcs, Volume 224, SoCG 2022, Complete Volume
Cite as

38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 1-1110, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Proceedings{goaoc_et_al:LIPIcs.SoCG.2022,
  title =	{{LIPIcs, Volume 224, SoCG 2022, Complete Volume}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{1--1110},
  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},
  URN =		{urn:nbn:de:0030-drops-160075},
  doi =		{10.4230/LIPIcs.SoCG.2022},
  annote =	{Keywords: LIPIcs, Volume 224, SoCG 2022, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.SoCG.2022.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Xavier Goaoc and Michael Kerber

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

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{goaoc_et_al:LIPIcs.SoCG.2022.0,
  author =	{Goaoc, Xavier and Kerber, Michael},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{0:i--0:xx},
  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.2022.0},
  URN =		{urn:nbn:de:0030-drops-160087},
  doi =		{10.4230/LIPIcs.SoCG.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.1
Tiling with Squares and Packing Dominos in Polynomial Time

Authors: Anders Aamand, Mikkel Abrahamsen, Thomas Ahle, and Peter M. R. Rasmussen

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

Abstract
A polyomino is a polygonal region with axis-parallel edges and corners of integral coordinates, which may have holes. In this paper, we consider planar tiling and packing problems with polyomino pieces and a polyomino container P. We give polynomial-time algorithms for deciding if P can be tiled with k× k squares for any fixed k which can be part of the input (that is, deciding if P is the union of a set of non-overlapping k× k squares) and for packing P with a maximum number of non-overlapping and axis-parallel 2× 1 dominos, allowing rotations by 90^∘. As packing is more general than tiling, the latter algorithm can also be used to decide if P can be tiled by 2× 1 dominos. These are classical problems with important applications in VLSI design, and the related problem of finding a maximum packing of 2× 2 squares is known to be NP-hard [J. Algorithms 1990]. For our three problems there are known pseudo-polynomial-time algorithms, that is, algorithms with running times polynomial in the area or perimeter of P. However, the standard, compact way to represent a polygon is by listing the coordinates of the corners in binary. We use this representation, and thus present the first polynomial-time algorithms for the problems. Concretely, we give a simple O(nlog n)-time algorithm for tiling with squares, where n is the number of corners of P. We then give a more involved algorithm that reduces the problems of packing and tiling with dominos to finding a maximum and perfect matching in a graph with O(n³) vertices. This leads to algorithms with running times O(n³(log³ n)/(log²log n)) and O(n³(log² n)/(log log n)), respectively.
Cite as

Anders Aamand, Mikkel Abrahamsen, Thomas Ahle, and Peter M. R. Rasmussen. Tiling with Squares and Packing Dominos in Polynomial Time. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{aamand_et_al:LIPIcs.SoCG.2022.1,
  author =	{Aamand, Anders and Abrahamsen, Mikkel and Ahle, Thomas and Rasmussen, Peter M. R.},
  title =	{{Tiling with Squares and Packing Dominos in Polynomial Time}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{1:1--1:17},
  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.2022.1},
  URN =		{urn:nbn:de:0030-drops-160096},
  doi =		{10.4230/LIPIcs.SoCG.2022.1},
  annote =	{Keywords: packing, tiling, polyominos}
}
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