18 Search Results for "Devillers, Olivier"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.42
Compressed Data Structures for Heegaard Splitting

Authors: Henrique Ennes and Clément Maria

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Heegaard splittings provide a natural representation of closed 3-manifolds by gluing handlebodies along a common surface. These splittings can be equivalently given by two finite sets of meridians lying on the surface, which define a Heegaard diagram. We present a data structure to effectively represent Heegaard diagrams as normal curves with respect to triangulations of a surface of complexity measured by the space required to express the normal coordinates' vectors in binary. This structure can be significantly more compressed than triangulations of 3-manifolds, giving exponential gains for some families. Even with this succinct definition of complexity, we establish polynomial-time algorithms for comparing and manipulating diagrams, performing stabilizations, detecting trivial stabilizations and reductions, and computing topological invariants of the underlying manifolds, such as their fundamental and homology groups. We also contrast early implementations of our techniques with standard software programs for 3-manifolds, achieving faster algorithms for the average cases and exponential gains in speed for some particular presentations of the inputs.
Cite as

Henrique Ennes and Clément Maria. Compressed Data Structures for Heegaard Splitting. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 42:1-42:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{ennes_et_al:LIPIcs.SoCG.2026.42,
  author =	{Ennes, Henrique and Maria, Cl\'{e}ment},
  title =	{{Compressed Data Structures for Heegaard Splitting}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{42:1--42:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.42},
  URN =		{urn:nbn:de:0030-drops-258484},
  doi =		{10.4230/LIPIcs.SoCG.2026.42},
  annote =	{Keywords: 3-manifold, Heegaard splitting, curves on surfaces, surface theory, data structure, computational topology}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.45
Line Segment Visibility in Simple Polygons: Exact, Robust, Scalable Computation and Applications

Authors: Sándor P. Fekete, Prahlad Narasimhan Kasthurirangan, Phillip Keldenich, Fabian Kollhoff, Chek-Manh Loi, and Michael Perk

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
The weak visibility polygon of a line segment s inside a simple polygon P, denoted by V_P(s), is the region of the polygon that is visible from at least one point on s. Given its fundamental nature in computational geometry, several algorithms have been proposed to compute weak visibility polygons efficiently, each with different trade-offs in terms of preprocessing time, query time, and space complexity. Although there are many applications that require computing these polygons such as computer graphics, robot motion planning, and network communication systems, there is a lack of any implementations of these algorithms in the literature - not to mention one that is exact, robust, and scalable. Furthermore, weak segment visibility polygons are used as basic building blocks in several other algorithms, such as in minimum-link path computation. In this work, we present an implementation of an optimal linear-time algorithm for computing the weak visibility polygon of a segment inside a triangulated simple polygon. Our implementation provides exact, robust geometric primitives and optimizations to handle large inputs with more than 18,000,000 vertices. We demonstrate two concrete applications: (1) construction of window partitions, a standard data structure in visibility algorithms, and (2) support for optimal minimum-link path queries between two points in a simple polygon, the latter serving as a direct use case of the former. Experimental results on a variety of polygon families confirm that the end-to-end running time scales linearly with the size of the polygon and is dominated by the cost of computing the triangulation, validating the practicality and scalability of the approach. The implementation is released as open source in the format of a CGAL package to support reproducibility and further research.
Cite as

Sándor P. Fekete, Prahlad Narasimhan Kasthurirangan, Phillip Keldenich, Fabian Kollhoff, Chek-Manh Loi, and Michael Perk. Line Segment Visibility in Simple Polygons: Exact, Robust, Scalable Computation and Applications. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{fekete_et_al:LIPIcs.SoCG.2026.45,
  author =	{Fekete, S\'{a}ndor P. and Kasthurirangan, Prahlad Narasimhan and Keldenich, Phillip and Kollhoff, Fabian and Loi, Chek-Manh and Perk, Michael},
  title =	{{Line Segment Visibility in Simple Polygons: Exact, Robust, Scalable Computation and Applications}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{45:1--45:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.45},
  URN =		{urn:nbn:de:0030-drops-258516},
  doi =		{10.4230/LIPIcs.SoCG.2026.45},
  annote =	{Keywords: Visibility, line segments, link distance, window partition, computation, implementation, robustness, scalability, exactness, CGAL}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.5
Bifunction and Interlevel Delaunay Trifiltrations

Authors: Ángel Javier Alonso, Michael Kerber, Tung Lam, Michael Lesnick, and Abhishek Rathod

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
A key property of the Delaunay filtration is that it is topologically (i.e., weakly) equivalent to the offset (union-of-balls) filtration. Recently, this filtration has been extended to point clouds equipped with an ℝ-valued function, yielding a computable 2-parameter filtration that satisfies an analogous weak equivalence. Motivated in part by the study of time-varying data, we introduce a 3-parameter extension of the Delaunay filtration for point clouds equipped with an ℝ²-valued function, also satisfying an analogous weak equivalence. For a point cloud X ⊂ ℝ^d, our trifiltration has size O(|X|^{⌈(d+1)/2⌉+1}). We present an algorithm that computes this trifiltration in time O(|X|^{⌈d/2⌉+2}), together with an implementation. Our experiments demonstrate that the implementation can handle thousands of points in ℝ³, with memory growth that is nearly linear.
Cite as

Ángel Javier Alonso, Michael Kerber, Tung Lam, Michael Lesnick, and Abhishek Rathod. Bifunction and Interlevel Delaunay Trifiltrations. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{alonso_et_al:LIPIcs.SoCG.2026.5,
  author =	{Alonso, \'{A}ngel Javier and Kerber, Michael and Lam, Tung and Lesnick, Michael and Rathod, Abhishek},
  title =	{{Bifunction and Interlevel Delaunay Trifiltrations}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.5},
  URN =		{urn:nbn:de:0030-drops-258118},
  doi =		{10.4230/LIPIcs.SoCG.2026.5},
  annote =	{Keywords: Delaunay triangulation, Multiparameter persistent homology, Interlevel, Bowyer-Watson}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.31
Delaunay Triangulations with Predictions

Authors: Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set P of n points in the plane and a triangulation G that serves as a "prediction" of the Delaunay triangulation, we would like to use G to compute the correct Delaunay triangulation DT(P) more quickly when G is "close" to DT(P). We obtain a variety of results of this type, under different deterministic and probabilistic settings, including the following: 1) Define D to be the number of edges in G that are not in DT(P). We present a deterministic algorithm to compute DT(P) from G in O(n + Dlog³ n) time, and a randomized algorithm in O(n+Dlog n) expected time, the latter of which is optimal in terms of D. 2) Let R be a random subset of the edges of DT(P), where each edge is chosen independently with probability ρ. Suppose G is any triangulation of P that contains R. We present an algorithm to compute DT(P) from G in O(nlog log n + nlog(1/ρ)) time with high probability. 3) Define d_{vio} to be the maximum number of points of P strictly inside the circumcircle of a triangle in G (the number is 0 if G is equal to DT(P)). We present a deterministic algorithm to compute DT(P) from G in O(nlog^*n + nlog d_{vio}) time. We also obtain results in similar settings for related problems such as 2D Euclidean minimum spanning trees, and hope that our work will open up a fruitful line of future research.
Cite as

Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos. Delaunay Triangulations with Predictions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{cabello_et_al:LIPIcs.ITCS.2026.31,
  author =	{Cabello, Sergio and Chan, Timothy M. and Giannopoulos, Panos},
  title =	{{Delaunay Triangulations with Predictions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{31:1--31:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.31},
  URN =		{urn:nbn:de:0030-drops-253186},
  doi =		{10.4230/LIPIcs.ITCS.2026.31},
  annote =	{Keywords: Delaunay Triangulation, Minimum Spanning Tree, Algorithms with Predictions}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.29
Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings

Authors: Michael Elberfeld, Frank Kammer, and Johannes Meintrup

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
We call a graph G separable if a balanced separator can be computed for G of size O(n^ε) with ε < 1. Many real-world graphs are separable such as graphs of bounded genus, graphs of constant treewidth, and graphs excluding a fixed minor. In particular, the well-known planar graphs are separable. We present a succinct encoding of separable graphs G such that, after the encoding is computed, any number of depth-first searches (DFS) can be performed from any given start vertex, each in o(n) time and o(n) bits in the word RAM model. After the execution of a DFS, the succinct encoding of G is augmented such that the DFS tree is encoded inside the encoding while maintaining succinctness. Afterward, the encoding provides common DFS-related queries in constant time. These queries include queries such as lowest-common ancestor of two given vertices in the DFS tree or queries that output the lowpoint of a given vertex in the DFS tree. Furthermore, for planar graphs, we show that the succinct encoding can be computed in O(n) bits and expected linear time, and a compact variant can be constructed in O(n) time and bits. For other separable graph classes 𝒢 the runtime and space usage depends on the specific algorithms used to find balanced separators in graphs of 𝒢.
Cite as

Michael Elberfeld, Frank Kammer, and Johannes Meintrup. Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{elberfeld_et_al:LIPIcs.ISAAC.2025.29,
  author =	{Elberfeld, Michael and Kammer, Frank and Meintrup, Johannes},
  title =	{{Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.29},
  URN =		{urn:nbn:de:0030-drops-249379},
  doi =		{10.4230/LIPIcs.ISAAC.2025.29},
  annote =	{Keywords: Depth-First Search, Succinct, Space Efficient, Separable Graphs, Planar Graphs, Table Lookup, r-Division}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.25
Instance-Optimal Imprecise Convex Hull

Authors: Sarita de Berg, Ivor van der Hoog, Eva Rotenberg, Daniel Rutschmann, and Sampson Wong

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Imprecise measurements of a point set P = (p₁, …, p_n) can be modelled by a family of regions F = (R₁, …, R_n), where each imprecise region R_i ∈ F contains a unique point p_i ∈ P. A retrieval models an accurate measurement by replacing an imprecise region R_i with its corresponding point p_i. We construct the convex hull of an imprecise point set in the plane, by determining the cyclic ordering of the convex hull vertices of P as efficiently as possible. Efficiency is interpreted in two ways: (i) minimising the number of retrievals, and (ii) the computation time to determine the set of regions that must be retrieved. Previous works focused on only one of these two aspects: either minimising retrievals or optimising algorithmic runtime. Our contribution is the first to simultaneously achieve both. Let r(F, P) denote the minimal number of retrievals required by any algorithm to determine the convex hull of P for a given instance (F, P). For a family F of n constant-complexity polygons, our main result is a reconstruction algorithm that performs Θ(r(F, P)) retrievals in O(r(F, P) log³ n) time. Compared to previous approaches that achieve optimal retrieval counts, we improve the runtime per retrieval from polynomial to polylogarithmic. We extend the generality of previous results to simple k-gons, to pairwise disjoint disks with radii in [1,k], and to unit disks where at most k disks overlap in a single point. Our runtime scales linearly with k.
Cite as

Sarita de Berg, Ivor van der Hoog, Eva Rotenberg, Daniel Rutschmann, and Sampson Wong. Instance-Optimal Imprecise Convex Hull. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{deberg_et_al:LIPIcs.ESA.2025.25,
  author =	{de Berg, Sarita and van der Hoog, Ivor and Rotenberg, Eva and Rutschmann, Daniel and Wong, Sampson},
  title =	{{Instance-Optimal Imprecise Convex Hull}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{25:1--25:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.25},
  URN =		{urn:nbn:de:0030-drops-244932},
  doi =		{10.4230/LIPIcs.ESA.2025.25},
  annote =	{Keywords: convex hull, imprecise geometry preprocessing model, partial information}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.61
ε-Net Algorithm Implementation on Hyperbolic Surfaces

Authors: Vincent Despré, Camille Lanuel, Marc Pouget, and Monique Teillaud

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We propose an implementation, using the CGAL library, of an algorithm to compute ε-nets on hyperbolic surfaces proposed by Despré, Lanuel and Teillaud [Despré et al., 2024]. We describe the data structure, detail the implemented algorithm and report experimental results on hyperbolic surfaces of genus 2. The implementation differs from the cited algorithm on several aspects. In particular, we use a different data structure, based on combinatorial maps, to represent a triangulation of a surface. We explain how to generate fundamental polygons to represent our input hyperbolic surfaces and the arithmetic issues related to the number type of the coordinates of their vertices.
Cite as

Vincent Despré, Camille Lanuel, Marc Pouget, and Monique Teillaud. ε-Net Algorithm Implementation on Hyperbolic Surfaces. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 61:1-61:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{despre_et_al:LIPIcs.ESA.2025.61,
  author =	{Despr\'{e}, Vincent and Lanuel, Camille and Pouget, Marc and Teillaud, Monique},
  title =	{{\epsilon-Net Algorithm Implementation on Hyperbolic Surfaces}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{61:1--61:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.61},
  URN =		{urn:nbn:de:0030-drops-245296},
  doi =		{10.4230/LIPIcs.ESA.2025.61},
  annote =	{Keywords: Hyperbolic surface, Delaunay triangulation, Data structure, Combinatorial map, Implementation, CGAL}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.46
Non-Euclidean Erdős-Anning Theorems

Authors: David Eppstein

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
The Erdős-Anning theorem states that every point set in the Euclidean plane with integer distances must be either collinear or finite. More strongly, for any (non-degenerate) triangle of diameter δ, at most O(δ²) points can have integer distances from all three triangle vertices. We prove the same results for any strictly convex distance function on the plane, and analogous results for every two-dimensional complete Riemannian manifold of bounded genus and for geodesic distance on the boundary of every three-dimensional Euclidean convex set. As a consequence, we resolve a 1983 question of Richard Guy on the equilateral dimension of Riemannian manifolds. Our proofs are based on the properties of additively weighted Voronoi diagrams of these distances.
Cite as

David Eppstein. Non-Euclidean Erdős-Anning Theorems. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{eppstein:LIPIcs.SoCG.2025.46,
  author =	{Eppstein, David},
  title =	{{Non-Euclidean Erd\H{o}s-Anning Theorems}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{46:1--46:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.46},
  URN =		{urn:nbn:de:0030-drops-231983},
  doi =		{10.4230/LIPIcs.SoCG.2025.46},
  annote =	{Keywords: integer distances, additively weighted Voronoi diagrams, convex distance functions, Riemannian manifolds, geodesic distance}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.31
A Linear Time Algorithm for the Maximum Overlap of Two Convex Polygons Under Translation

Authors: Timothy M. Chan and Isaac M. Hair

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Given two convex polygons P and Q with n and m edges, the maximum overlap problem is to find a translation of P that maximizes the area of its intersection with Q. We give the first randomized algorithm for this problem with linear running time. Our result improves the previous two-and-a-half-decades-old algorithm by de Berg, Cheong, Devillers, van Kreveld, and Teillaud (1998), which ran in O((n+m)log(n+m)) time, as well as multiple recent algorithms given for special cases of the problem.
Cite as

Timothy M. Chan and Isaac M. Hair. A Linear Time Algorithm for the Maximum Overlap of Two Convex Polygons Under Translation. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chan_et_al:LIPIcs.SoCG.2025.31,
  author =	{Chan, Timothy M. and Hair, Isaac M.},
  title =	{{A Linear Time Algorithm for the Maximum Overlap of Two Convex Polygons Under Translation}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.31},
  URN =		{urn:nbn:de:0030-drops-231832},
  doi =		{10.4230/LIPIcs.SoCG.2025.31},
  annote =	{Keywords: Convex polygons, shape matching, prune-and-search, parametric search}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.30
Computation of Toroidal Schnyder Woods Made Simple and Fast: From Theory to Practice

Authors: Luca Castelli Aleardi, Eric Fusy, Jyh-Chwen Ko, and Razvan-Stefan Puscasu

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We consider the problem of computing Schnyder woods for graphs embedded on the torus. We design simple linear-time algorithms based on canonical orderings that compute toroidal Schnyder woods for simple toroidal triangulations. The Schnyder woods computed by one of our algorithm are crossing and satisfy an additional structural property: at least two of the mono-chromatic components of the Schnyder wood are connected. We also exhibit experimental results empirically confirming three conjectures involving the structure of toroidal and higher genus Schnyder woods.
Cite as

Luca Castelli Aleardi, Eric Fusy, Jyh-Chwen Ko, and Razvan-Stefan Puscasu. Computation of Toroidal Schnyder Woods Made Simple and Fast: From Theory to Practice. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{castellialeardi_et_al:LIPIcs.SoCG.2025.30,
  author =	{Castelli Aleardi, Luca and Fusy, Eric and Ko, Jyh-Chwen and Puscasu, Razvan-Stefan},
  title =	{{Computation of Toroidal Schnyder Woods Made Simple and Fast: From Theory to Practice}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.30},
  URN =		{urn:nbn:de:0030-drops-231825},
  doi =		{10.4230/LIPIcs.SoCG.2025.30},
  annote =	{Keywords: Schnyder woods, toroidal triangulations, canonical ordering}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.59
Incremental Planar Nearest Neighbor Queries with Optimal Query Time

Authors: John Iacono and Yakov Nekrich

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
In this paper we show that two-dimensional nearest neighbor queries can be answered in optimal O(log n) time while supporting insertions in O(log^{1+ε} n) time. No previous data structure was known that supports O(log n)-time queries and polylog-time insertions. In order to achieve logarithmic queries our data structure uses a new technique related to fractional cascading that leverages the inherent geometry of this problem. Our method can be also used in other semi-dynamic scenarios.
Cite as

John Iacono and Yakov Nekrich. Incremental Planar Nearest Neighbor Queries with Optimal Query Time. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 59:1-59:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{iacono_et_al:LIPIcs.SoCG.2025.59,
  author =	{Iacono, John and Nekrich, Yakov},
  title =	{{Incremental Planar Nearest Neighbor Queries with Optimal Query Time}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{59:1--59:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.59},
  URN =		{urn:nbn:de:0030-drops-232117},
  doi =		{10.4230/LIPIcs.SoCG.2025.59},
  annote =	{Keywords: Data Structures, Dynamic Data Structures, Nearest Neighbor Queries}
}
Document
CG Challenge
DOI: 10.4230/LIPIcs.SoCG.2025.79
Computing Non-Obtuse Triangulations with Few Steiner Points (CG Challenge)

Authors: Mikkel Abrahamsen, Florestan Brunck, Jacobus Conradi, Benedikt Kolbe, and André Nusser

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We present the winning implementation of the Seventh Computational Geometry Challenge (CG:SHOP 2025). The task in this challenge was to find non-obtuse triangulations for given planar regions, respecting a given set of constraints consisting of extra vertices and edges that must be part of the triangulation. The goal was to minimize the number of introduced Steiner points. Our approach is to maintain a constrained Delaunay triangulation, for which we repeatedly remove, relocate, or add Steiner points. We use local search to choose the action that improves the triangulation the most, until the resulting triangulation is non-obtuse.
Cite as

Mikkel Abrahamsen, Florestan Brunck, Jacobus Conradi, Benedikt Kolbe, and André Nusser. Computing Non-Obtuse Triangulations with Few Steiner Points (CG Challenge). In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 79:1-79:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2025.79,
  author =	{Abrahamsen, Mikkel and Brunck, Florestan and Conradi, Jacobus and Kolbe, Benedikt and Nusser, Andr\'{e}},
  title =	{{Computing Non-Obtuse Triangulations with Few Steiner Points}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{79:1--79:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.79},
  URN =		{urn:nbn:de:0030-drops-232311},
  doi =		{10.4230/LIPIcs.SoCG.2025.79},
  annote =	{Keywords: non-obtuse triangulation, local search, competition}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.4
A Subquadratic Algorithm for Computing the L₁-Distance Between Two Terrains

Authors: Pankaj K. Agarwal, Boris Aronov, Olivier Devillers, Christian Knauer, and Guillaume Moroz

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We study the problem of computing the L₁-distance between two piecewise-linear bivariate functions f and g, defined over a bounded polygonal domain 𝕄 ⊂ ℝ², that is, computing the quantity ‖f-g‖₁ = ∫_𝕄 |f(x,y)-g(x,y)| dx dy. If f and g are defined by linear interpolation over triangulations 𝐓_f and 𝐓_g, respectively, of 𝕄 with a total of n triangles, we show that ‖f-g‖₁ can be computed in Õ(n^α) time, where α = max{(ω+1)/2, 8/5}, ω is the matrix multiplication exponent, and Õ notation hides factors of the form n^ε for any ε > 0. This bound holds for the currently best known value of ω, which is approximately 2.37. More generally, if the complexity of the overlay of 𝐓_f and 𝐓_g is κ, then the runtime of our algorithm is Õ(κ^{α-1}n^{2-α}).
Cite as

Pankaj K. Agarwal, Boris Aronov, Olivier Devillers, Christian Knauer, and Guillaume Moroz. A Subquadratic Algorithm for Computing the L₁-Distance Between Two Terrains. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{agarwal_et_al:LIPIcs.SoCG.2025.4,
  author =	{Agarwal, Pankaj K. and Aronov, Boris and Devillers, Olivier and Knauer, Christian and Moroz, Guillaume},
  title =	{{A Subquadratic Algorithm for Computing the L₁-Distance Between Two Terrains}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{4:1--4:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.4},
  URN =		{urn:nbn:de:0030-drops-231561},
  doi =		{10.4230/LIPIcs.SoCG.2025.4},
  annote =	{Keywords: Terrain similarity, volume computation, polynomial interpolation, geometric cuttings, bivariate multipoint evaluation}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.32
SCARST: Schnyder Compact and Regularity Sensitive Triangulation Data Structure

Authors: Luca Castelli Aleardi and Olivier Devillers

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

Abstract
We consider the design of fast and compact representations of the connectivity information of triangle meshes. Although traditional data structures (Half-Edge, Corner Table) are fast and user-friendly, they tend to be memory-expensive. On the other hand, compression schemes, while meeting information-theoretic lower bounds, do not support navigation within the mesh structure. Compact representations provide an advantageous balance for representing large meshes, enabling a judicious compromise between memory consumption and fast implementation of navigational operations. We propose new representations that are sensitive to the regularity of the graph while still having worst case guarantees. For all our data structures we have both an interesting storage cost, typically 2 or 3 r.p.v. (references per vertex) in the case of very regular triangulations, and provable upper bounds in the worst case scenario. One of our solutions has a worst case cost of 3.33 r.p.v., which is currently the best-known bound improving the previous 4 r.p.v. [Castelli et al. 2018]. Our representations have slightly slower running times (factors 1.5 to 4) than classical data structures. In our experiments we compare on various meshes runtime and memory performance of our representations with those of the most efficient existing solutions.
Cite as

Luca Castelli Aleardi and Olivier Devillers. SCARST: Schnyder Compact and Regularity Sensitive Triangulation Data Structure. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{castellialeardi_et_al:LIPIcs.SoCG.2024.32,
  author =	{Castelli Aleardi, Luca and Devillers, Olivier},
  title =	{{SCARST: Schnyder Compact and Regularity Sensitive Triangulation Data Structure}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{32:1--32:19},
  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.2024.32},
  URN =		{urn:nbn:de:0030-drops-199779},
  doi =		{10.4230/LIPIcs.SoCG.2024.32},
  annote =	{Keywords: Meshes, compression, triangulations, compact representations}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.22
Randomized Incremental Construction of Delaunay Triangulations of Nice Point Sets

Authors: Jean-Daniel Boissonnat, Olivier Devillers, Kunal Dutta, and Marc Glisse

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
Randomized incremental construction (RIC) is one of the most important paradigms for building geometric data structures. Clarkson and Shor developed a general theory that led to numerous algorithms that are both simple and efficient in theory and in practice. Randomized incremental constructions are most of the time space and time optimal in the worst-case, as exemplified by the construction of convex hulls, Delaunay triangulations and arrangements of line segments. However, the worst-case scenario occurs rarely in practice and we would like to understand how RIC behaves when the input is nice in the sense that the associated output is significantly smaller than in the worst-case. For example, it is known that the Delaunay triangulations of nicely distributed points on polyhedral surfaces in E^3 has linear complexity, as opposed to a worst-case quadratic complexity. The standard analysis does not provide accurate bounds on the complexity of such cases and we aim at establishing such bounds in this paper. More precisely, we will show that, in the case of nicely distributed points on polyhedral surfaces, the complexity of the usual RIC is O(n log n), which is optimal. In other words, without any modification, RIC nicely adapts to good cases of practical value. Our proofs also work for some other notions of nicely distributed point sets, such as (epsilon, kappa)-samples. Along the way, we prove a probabilistic lemma for sampling without replacement, which may be of independent interest.
Cite as

Jean-Daniel Boissonnat, Olivier Devillers, Kunal Dutta, and Marc Glisse. Randomized Incremental Construction of Delaunay Triangulations of Nice Point Sets. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 22:1-22:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{boissonnat_et_al:LIPIcs.ESA.2019.22,
  author =	{Boissonnat, Jean-Daniel and Devillers, Olivier and Dutta, Kunal and Glisse, Marc},
  title =	{{Randomized Incremental Construction of Delaunay Triangulations of Nice Point Sets}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{22:1--22:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.22},
  URN =		{urn:nbn:de:0030-drops-111437},
  doi =		{10.4230/LIPIcs.ESA.2019.22},
  annote =	{Keywords: Randomized incremental construction, Delaunay triangulations, Voronoi diagrams, polyhedral surfaces, probabilistic analysis}
}
  • Refine by Type
  • 18 Document/PDF
  • 12 Document/HTML

  • Refine by Publication Year
  • 4 2026
  • 9 2025
  • 1 2024
  • 1 2019
  • 1 2018
  • Show More...

  • Refine by Author
  • 6 Devillers, Olivier
  • 2 Castelli Aleardi, Luca
  • 2 Chan, Timothy M.
  • 2 Glisse, Marc
  • 2 Teillaud, Monique
  • Show More...

  • Refine by Series/Journal
  • 18 LIPIcs

  • Refine by Classification
  • 14 Theory of computation → Computational geometry
  • 3 Theory of computation → Data structures design and analysis
  • 2 Mathematics of computing → Combinatoric problems
  • 2 Mathematics of computing → Geometric topology
  • 1 General and reference → Experimentation
  • Show More...

  • Refine by Keyword
  • 2 CGAL
  • 2 Delaunay triangulation
  • 1 3-manifold
  • 1 Algorithms with Predictions
  • 1 Apollonius diagram
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact