24 Search Results for "Verbeek, Kevin"

Document
DOI: 10.4230/LIPIcs.SEA.2026.6
A Practical Algorithm for (Geometry-Aware) Interleavings Between Merge Trees

Authors: Thijs Beurskens, Emil Toftegaard Gæde, Tim Ophelders, Willem Sonke, Bettina Speckmann, and Kevin Verbeek

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
Merge trees are a popular topological descriptor for scalar field data. A common measure to compare two merge trees is the interleaving distance, which relies on a mapping between the two merge trees, also referred to as an interleaving. Despite its desirable properties, the interleaving distance has not been used much in practice, largely due to the fact that computing the exact interleaving distance is NP-hard. In this paper, we show that the exact interleaving distance can be computed efficiently for merge trees encountered in practice: we present the first implementation of the exact fixed-parameter tractable (FPT) algorithm by Touli and Wang [Touli and Wang, 2022]. This algorithm uses a dynamic program to test if a specific interleaving distance δ is feasible. They bound the running time using a parameter τ that captures the number of mapping options between the two merge trees for the output distance δ. Our experiments show that, even though τ can become quite large for real-world merge trees, the running time of our implementation does not depend very heavily on τ. Furthermore, we modify the FPT algorithm into a sweepline algorithm that runs much faster in practice. Finally, we introduce a natural restriction for the interleaving distance capturing the geometric similarity between the underlying scalar fields. This restricted interleaving distance can be computed more efficiently and can, in some settings, also result in more meaningful interleavings. We extend our implementations to support these restrictions and demonstrate their effect on the running time of the algorithms.
Cite as

Thijs Beurskens, Emil Toftegaard Gæde, Tim Ophelders, Willem Sonke, Bettina Speckmann, and Kevin Verbeek. A Practical Algorithm for (Geometry-Aware) Interleavings Between Merge Trees. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{beurskens_et_al:LIPIcs.SEA.2026.6,
  author =	{Beurskens, Thijs and G{\ae}de, Emil Toftegaard and Ophelders, Tim and Sonke, Willem and Speckmann, Bettina and Verbeek, Kevin},
  title =	{{A Practical Algorithm for (Geometry-Aware) Interleavings Between Merge Trees}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.6},
  URN =		{urn:nbn:de:0030-drops-260100},
  doi =		{10.4230/LIPIcs.SEA.2026.6},
  annote =	{Keywords: interleaving distance, geometry-aware, exact algorithm, implementation}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.24
Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support

Authors: Reilly Browne and Hsien-Chih Chang

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

Abstract
Given an unweighted graph G, the minimum r-dominating set problem asks for a subset of vertices S of the smallest cardinality, such that every vertex in G is within radius r to some vertex in S. While the r-dominating set problem on planar graph admits PTAS from Baker’s shifting/layering technique when r is a constant, the problem becomes significantly harder when r can depend on n. In fact, under Exponential-Time Hypothesis, Fox-Epstein ηl [SODA 2019] observed that no efficient PTAS can exist for the unbounded r-dominating set problem on planar graphs. One may consider even harder weighted-variant known as the vertex-weighted metric r-dominating set, where edges are associated with lengths, and every vertex is associated with a positive-valued weight, and the goal is to compute an r-dominating set with minimum total weight. As a result, people resorted to bicriteria algorithms by allowing the returned solution to use radius-(1+ε)r balls instead, in addition to the total weight being a 1+ε approximation to the optimal value. We establish the first single-criteria polynomial-time O(1)-approximation algorithm for the vertex-weighted metric r-dominating set problem on planar graphs when r is part of the input, and can be arbitrarily large compared to n. Our new (single-criteria) O(1)-approximation algorithm uses the quasi-uniformity sampling technique of Chan et al. [SODA 2012] by bounding the shallow cell complexity of the (unbounded) radius-r ball system to be linear in n. To this end we have two technical innovations: 1) The discrete ball system on planar graphs are neither pseudodisks nor have well-defined boundaries for standard union-complexity arguments. We construct a support graph for arbitrary distance ball systems as contractions of Voronoi cells; the sparseness comes as a byproduct. 2) We present an assignment of each depth-(≥3) cell to a unique 3-tuple of ball centers. This allows us to use standard Clarkson-Shor techniques to reduce the counting to cells of depth exactly 3, which we prove to be size O(n) by a novel geometric argument based on our support being a Voronoi contraction.
Cite as

Reilly Browne and Hsien-Chih Chang. Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{browne_et_al:LIPIcs.SoCG.2026.24,
  author =	{Browne, Reilly and Chang, Hsien-Chih},
  title =	{{Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{24:1--24:17},
  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.2026.24},
  URN =		{urn:nbn:de:0030-drops-258300},
  doi =		{10.4230/LIPIcs.SoCG.2026.24},
  annote =	{Keywords: Minimum dominating set, planar graphs, shallow cell complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.64
Gap-ETH-Tight Algorithms for Hyperbolic TSP and Steiner Tree

Authors: Sándor Kisfaludi-Bak, Saeed Odak, Satyam Singh, and Geert van Wordragen

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

Abstract
We give an approximation scheme for the TSP in d-dimensional hyperbolic space that has optimal dependence on ε under Gap-ETH. For any fixed dimension d ≥ 2 and for any ε > 0 our randomized algorithm gives a (1+ε)-approximation in time 2^O(1/ε^{d-1}) n^{1+o(1)}. We also provide an algorithm for the hyperbolic Steiner tree problem with the same running time. Our algorithm is an Arora-style dynamic program based on a randomly shifted hierarchical decomposition. However, we introduce a new hierarchical decomposition called the hybrid hyperbolic quadtree to achieve the desired large-scale structure, which deviates significantly from the recently proposed hyperbolic quadtree of Kisfaludi-Bak and Van Wordragen (JoCG'25). Moreover, we have a new non-uniform portal placement, and our structure theorem employs a new weighted crossing analysis. We believe that these techniques could form the basis for further developments in geometric optimization in curved spaces.
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Sándor Kisfaludi-Bak, Saeed Odak, Satyam Singh, and Geert van Wordragen. Gap-ETH-Tight Algorithms for Hyperbolic TSP and Steiner Tree. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 64:1-64:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kisfaludibak_et_al:LIPIcs.SoCG.2026.64,
  author =	{Kisfaludi-Bak, S\'{a}ndor and Odak, Saeed and Singh, Satyam and van Wordragen, Geert},
  title =	{{Gap-ETH-Tight Algorithms for Hyperbolic TSP and Steiner Tree}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{64:1--64:17},
  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.2026.64},
  URN =		{urn:nbn:de:0030-drops-258710},
  doi =		{10.4230/LIPIcs.SoCG.2026.64},
  annote =	{Keywords: Hyperbolic traveling salesman problem, TSP, Hyperbolic Steiner tree problem, Approximation scheme, Banyan, Hyperbolic geometry}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.65
Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces

Authors: Sándor Kisfaludi-Bak and Geert van Wordragen

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

Abstract
We consider Steiner spanners in Euclidean and non-Euclidean geometries. In the Euclidean setting, a recent line of work initiated by Le and Solomon [FOCS'19] and further improved by Chang et al. [SoCG'24] obtained Steiner (1+ε)-spanners of size O_d(ε^{(1-d)/2} log(1/ε) n), nearly matching the lower bound Ω_d(ε^{(1-d)/2} n) of Bhore and Tóth [SIDMA'22]. We obtain Steiner (1+ε)-spanners of size O_d(ε^{(1-d)/2} log(1/ε)n) not only in d-dimensional Euclidean space, but also in d-dimensional spherical and hyperbolic space. For any fixed dimension d, the obtained edge count is optimal up to an O(log(1/ε)) factor in each of these spaces. Unlike earlier constructions, our Steiner spanners are based on simple quadtrees, and they can be dynamically maintained, leading to efficient data structures for dynamic approximate nearest neighbours and bichromatic closest pair. In the hyperbolic setting, we also show that 2-spanners in the hyperbolic plane must have Ω(nlog n) edges, and we obtain a 2-spanner of size O_d(nlog n) in d-dimensional hyperbolic space, matching our lower bound for any constant d. Finally, we give a Steiner spanner with additive error ε in hyperbolic space with O_d(ε^{(1-d)/2} log(α(n)/ε)n) edges, where α(n) is the inverse Ackermann function. Our techniques generalize to closed orientable surfaces of constant curvature as well as to some other quotient spaces.
Cite as

Sándor Kisfaludi-Bak and Geert van Wordragen. Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 65:1-65:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kisfaludibak_et_al:LIPIcs.SoCG.2026.65,
  author =	{Kisfaludi-Bak, S\'{a}ndor and van Wordragen, Geert},
  title =	{{Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{65:1--65:17},
  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.2026.65},
  URN =		{urn:nbn:de:0030-drops-258728},
  doi =		{10.4230/LIPIcs.SoCG.2026.65},
  annote =	{Keywords: hyperbolic geometry, Steiner spanner, dynamic approximate nearest neighbours}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.11
Locally Correct Interleavings Between Merge Trees

Authors: Thijs Beurskens, Tim Ophelders, Bettina Speckmann, and Kevin Verbeek

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

Abstract
Merge trees are typically used as a topological summary of scalar fields. To analyze e.g. a time-varying scalar field via its merge tree representation, one needs a suitable method to match and compare two merge trees. We consider the interleaving distance as a method to match and compare merge trees. An interleaving between two merge trees consists of two maps, one in each direction. These maps must satisfy ancestor relations and hence introduce a "shift" between points and their image. An optimal interleaving minimizes the maximum shift; the interleaving distance is the value of this shift. However, to study the evolution of merge trees, we need not only a number but also a meaningful matching between the two trees. The two maps of an optimal interleaving induce a matching, but due to the bottleneck nature of the interleaving distance, this matching fails to capture local similarities between the trees. In this paper we hence propose a notion of local optimality for interleavings. To do so, we define the residual interleaving distance, a generalization of the interleaving distance that allows additional constraints on the maps. This allows us to define locally correct interleavings, which use a range of shifts across the two merge trees that reflect the local similarity well. We give a constructive proof that a locally correct interleaving always exists.
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Thijs Beurskens, Tim Ophelders, Bettina Speckmann, and Kevin Verbeek. Locally Correct Interleavings Between Merge Trees. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{beurskens_et_al:LIPIcs.SoCG.2026.11,
  author =	{Beurskens, Thijs and Ophelders, Tim and Speckmann, Bettina and Verbeek, Kevin},
  title =	{{Locally Correct Interleavings Between Merge Trees}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{11:1--11:15},
  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.2026.11},
  URN =		{urn:nbn:de:0030-drops-258173},
  doi =		{10.4230/LIPIcs.SoCG.2026.11},
  annote =	{Keywords: Interleaving distance, merge trees, local correctness, matchings, topological data analysis}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.67
Compact Representation of Semilinear and Terrain-Like Graphs

Authors: Jean Cardinal and Yelena Yuditsky

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

Abstract
We consider the existence and construction of biclique covers of graphs, consisting of coverings of their edge sets by complete bipartite graphs. The size of such a cover is the sum of the sizes of the bicliques. Small-size biclique covers of graphs are ubiquitous in computational geometry, and have been shown to be useful compact representations of graphs. We give a brief survey of classical and recent results on biclique covers and their applications, and give new families of graphs having biclique covers of near-linear size. In particular, we show that semilinear graphs, whose edges are defined by linear relations in bounded dimensional space, always have biclique covers of size O(npolylog n). This generalizes many previously known results on special classes of graphs including interval graphs, permutation graphs, and graphs of bounded boxicity, but also new classes such as intersection graphs of L-shapes in the plane. It also directly implies the bounds for Zarankiewicz’s problem derived by Basit, Chernikov, Starchenko, Tao, and Tran (Forum Math. Sigma, 2021). We also consider capped graphs, also known as terrain-like graphs, defined as ordered graphs forbidding a certain ordered pattern on four vertices. Terrain-like graphs contain the induced subgraphs of terrain visibility graphs. We give an elementary proof that these graphs admit biclique partitions of size O(nlog³ n). This provides a simple combinatorial analogue of a classical result from Agarwal, Alon, Aronov, and Suri on polygon visibility graphs (Discrete Comput. Geom. 1994). Finally, we prove that there exists families of unit disk graphs on n vertices that do not admit biclique coverings of size o(n^{4/3}), showing that we are unlikely to improve on Szemerédi-Trotter type incidence bounds for higher-degree semialgebraic graphs.
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Jean Cardinal and Yelena Yuditsky. Compact Representation of Semilinear and Terrain-Like Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 67:1-67:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cardinal_et_al:LIPIcs.ESA.2025.67,
  author =	{Cardinal, Jean and Yuditsky, Yelena},
  title =	{{Compact Representation of Semilinear and Terrain-Like Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{67:1--67:19},
  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.2025.67},
  URN =		{urn:nbn:de:0030-drops-245359},
  doi =		{10.4230/LIPIcs.ESA.2025.67},
  annote =	{Keywords: Biclique covers, intersection graphs, visibility graphs, Zarankiewicz’s problem}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.2
Covering Simple Orthogonal Polygons with Rectangles

Authors: Aniket Basu Roy

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study the problem of Covering Orthogonal Polygons with Rectangles, focusing on three variants: covering the interior, the boundary, and the corners. While previous work provided constant-factor approximation algorithms for these problems, significant improvements had not been achieved for over two decades. The main contribution of this work is the development of a Polynomial Time Approximation Scheme (PTAS) for both the Boundary Cover and Corner Cover problems on simple polygons, using a local search algorithm. Our work advances the state of the art, improving upon the previous best-known 4-approximation for the Boundary Cover and 2-approximation for the Corner Cover problems. The technical core of our work lies in proving the existence of planar support graphs for certain geometric hypergraphs defined by the polygon and its containment-maximal rectangles. This structural insight enables the application of the local search framework to achieve the PTAS results. We also demonstrate the limitations of this approach by constructing instances where local search fails for the Interior Cover and certain dual problems, such as the Maximum Antirectangle and Hitting Set problems. Additionally, the methods yield a PTAS for a special case of the Discrete Independent Set problem for rectangles. These results not only settle longstanding open questions but also introduce new techniques that may be of independent interest within computational geometry.
Cite as

Aniket Basu Roy. Covering Simple Orthogonal Polygons with Rectangles. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{basuroy:LIPIcs.APPROX/RANDOM.2025.2,
  author =	{Basu Roy, Aniket},
  title =	{{Covering Simple Orthogonal Polygons with Rectangles}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.2},
  URN =		{urn:nbn:de:0030-drops-243686},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.2},
  annote =	{Keywords: Polygon Covering, Approximation Algorithms, Orthogonal Polygons, Rectangles, Local Search, Planar Supports}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.46
Guarding Offices with Maximum Dispersion

Authors: Sándor P. Fekete, Kai Kobbe, Dominik Krupke, Joseph S. B. Mitchell, Christian Rieck, and Christian Scheffer

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We investigate the Dispersive Art Gallery Problem with vertex guards and rectangular visibility (r-visibility) for a class of orthogonal polygons that reflect the properties of real-world floor plans: these office-like polygons consist of rectangular rooms and corridors. In the dispersive variant of the Art Gallery Problem, the objective is not to minimize the number of guards but to maximize the minimum geodesic L₁-distance between any two guards, called the dispersion distance. Our main contributions are as follows. We prove that determining whether a vertex guard set can achieve a dispersion distance of 4 in office-like polygons is NP-complete, where vertices of the polygon are restricted to integer coordinates. Additionally, we present a simple worst-case optimal algorithm that guarantees a dispersion distance of 3 in polynomial time. Our complexity result extends to polyominoes, resolving an open question posed by Rieck and Scheffer [Christian Rieck and Christian Scheffer, 2024]. When vertex coordinates are allowed to be rational, we establish analogous results, proving that achieving a dispersion distance of 2+ε is NP-hard for any ε > 0, while the classic Art Gallery Problem remains solvable in polynomial time for this class of polygons. Furthermore, we give a straightforward polynomial-time algorithm that computes worst-case optimal solutions with a dispersion distance 2. On the other hand, for the more restricted class of hole-free independent office-like polygons, we propose a dynamic programming approach that computes optimal solutions. Moreover, we demonstrate that the problem is practically tractable for arbitrary orthogonal polygons. To this end, we compare solvers based on SAT, CP, and MIP formulations. Notably, SAT solvers efficiently compute optimal solutions for randomly generated instances with up to 1600 vertices in under 15s.
Cite as

Sándor P. Fekete, Kai Kobbe, Dominik Krupke, Joseph S. B. Mitchell, Christian Rieck, and Christian Scheffer. Guarding Offices with Maximum Dispersion. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 46:1-46:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fekete_et_al:LIPIcs.MFCS.2025.46,
  author =	{Fekete, S\'{a}ndor P. and Kobbe, Kai and Krupke, Dominik and Mitchell, Joseph S. B. and Rieck, Christian and Scheffer, Christian},
  title =	{{Guarding Offices with Maximum Dispersion}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{46:1--46:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.46},
  URN =		{urn:nbn:de:0030-drops-241530},
  doi =		{10.4230/LIPIcs.MFCS.2025.46},
  annote =	{Keywords: Dispersive Art Gallery Problem, vertex guards, office-like polygons, orthogonal polygons, polyominoes, NP-completeness, worst-case optimality, dynamic programming, SAT solver}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.7
Continuous Map Matching to Paths Under Travel Time Constraints

Authors: Yannick Bosch and Sabine Storandt

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of k spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by location in the graph, such that consecutive locations can be reached from one another along the path within the timestamp difference of the respective measurements. This problem arises in public transit data processing as well as in map matching of movement trajectories to general graphs. We show that the classical approach for this problem, which relies on selecting a finite set of candidate locations in the graph for each measurement, cannot guarantee to find a consistent solution. We propose a new algorithm that can deal with an infinite set of candidate locations per measurement. We prove that our algorithm always detects a consistent map matching path (if one exists). Despite the enlarged candidate set, we also demonstrate that our algorithm has superior running time in theory and practice. For a path graph with n nodes, we show that our algorithm runs in 𝒪(k² n log {nk}) and under mild assumptions in 𝒪(k n ^λ + n log³ n) for λ ≈ 0.695. This is a significant improvement over the baseline, which runs in 𝒪(k n²) and which might not even identify a correct solution. The performance of our algorithm hinges on an efficient segment-circle intersection data structure. We describe how to design and implement such a data structure for our application. In the experimental evaluation, we demonstrate the usefulness of our novel algorithm on a diverse set of generated measurements as well as GTFS data.
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Yannick Bosch and Sabine Storandt. Continuous Map Matching to Paths Under Travel Time Constraints. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bosch_et_al:LIPIcs.SEA.2025.7,
  author =	{Bosch, Yannick and Storandt, Sabine},
  title =	{{Continuous Map Matching to Paths Under Travel Time Constraints}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.7},
  URN =		{urn:nbn:de:0030-drops-232457},
  doi =		{10.4230/LIPIcs.SEA.2025.7},
  annote =	{Keywords: Map matching, Travel time, Segment-circle intersection data structure}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.36
Faster Fréchet Distance Under Transformations

Authors: Kevin Buchin, Maike Buchin, Zijin Huang, André Nusser, and Sampson Wong

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study the problem of computing the Fréchet distance between two polygonal curves under transformations. First, we consider translations in the Euclidean plane. Given two curves π and σ of total complexity n and a threshold δ ≥ 0, we present an 𝒪̃(n^{7 + 1/3}) time algorithm to determine whether there exists a translation t ∈ ℝ² such that the Fréchet distance between π and σ + t is at most δ. This improves on the previous best result, which is an 𝒪(n⁸) time algorithm. We then generalize this result to any class of rationally parameterized transformations, which includes translation, rotation, scaling, and arbitrary affine transformations. For a class T of rationally parametrized transformations with k degrees of freedom, we show that one can determine whether there is a transformation τ ∈ T such that the Fréchet distance between π and τ(σ) is at most δ in 𝒪̃(n^{3k+4/3}) time.
Cite as

Kevin Buchin, Maike Buchin, Zijin Huang, André Nusser, and Sampson Wong. Faster Fréchet Distance Under Transformations. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{buchin_et_al:LIPIcs.ICALP.2025.36,
  author =	{Buchin, Kevin and Buchin, Maike and Huang, Zijin and Nusser, Andr\'{e} and Wong, Sampson},
  title =	{{Faster Fr\'{e}chet Distance Under Transformations}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{36:1--36:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.36},
  URN =		{urn:nbn:de:0030-drops-234137},
  doi =		{10.4230/LIPIcs.ICALP.2025.36},
  annote =	{Keywords: Fr\'{e}chet distance, curve similarity, shape matching}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.14
IsaBIL: A Framework for Verifying (In)correctness of Binaries in Isabelle/HOL

Authors: Matt Griffin, Brijesh Dongol, and Azalea Raad

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract
This paper presents IsaBIL, a binary analysis framework in Isabelle/HOL that is based on the widely used Binary Analysis Platform (BAP). Specifically, in IsaBIL, we formalise BAP’s intermediate language, called BIL and integrate it with Hoare logic (to enable proofs of correctness) as well as incorrectness logic (to enable proofs of incorrectness). IsaBIL inherits the full flexibility of BAP, allowing us to verify binaries for a wide range of languages (C, C++, Rust), toolchains (LLVM, Ghidra) and target architectures (x86, RISC-V), and can also be used when the source code for a binary is unavailable. To make verification tractable, we develop a number of big-step rules that combine BIL’s existing small-step rules at different levels of abstraction to support reuse. We develop high-level reasoning rules for RISC-V instructions (our main target architecture) to further optimise verification. Additionally, we develop Isabelle proof tactics that exploit common patterns in C binaries for RISC-V to discharge large numbers of proof goals (often in the 100s) automatically. IsaBIL includes an Isabelle/ML based parser for BIL programs, allowing one to automatically generate the associated Isabelle/HOL program locale from a BAP output. Taken together, IsaBIL provides a highly flexible proof environment for program binaries. As examples, we prove correctness of key examples from the Joint Strike Fighter coding standards and the MITRE database.
Cite as

Matt Griffin, Brijesh Dongol, and Azalea Raad. IsaBIL: A Framework for Verifying (In)correctness of Binaries in Isabelle/HOL. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 14:1-14:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{griffin_et_al:LIPIcs.ECOOP.2025.14,
  author =	{Griffin, Matt and Dongol, Brijesh and Raad, Azalea},
  title =	{{IsaBIL: A Framework for Verifying (In)correctness of Binaries in Isabelle/HOL}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{14:1--14:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2025.14},
  URN =		{urn:nbn:de:0030-drops-233070},
  doi =		{10.4230/LIPIcs.ECOOP.2025.14},
  annote =	{Keywords: Binary Analysis Platform, Isabelle/HOL, Hoare Logic, Incorrectness Logic}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.47
Shelling and Sinking Graphs on the Sphere

Authors: Jeff Erickson and Christian Howard

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

Abstract
We describe a promising approach to efficiently morph spherical graphs, extending earlier approaches of Awartani and Henderson [Trans. AMS 1987] and Kobourov and Landis [JGAA 2006]. Specifically, we describe two methods to morph shortest-path triangulations of the sphere by moving their vertices along longitudes into the southern hemisphere; we call a triangulation sinkable if such a morph exists. Our first method generalizes a longitudinal shelling construction of Awartani and Henderson; a triangulation is sinkable if a specific orientation of its dual graph is acyclic. We describe a simple polynomial-time algorithm to find a longitudinally shellable rotation of a given spherical triangulation, if one exists; we also construct a spherical triangulation that has no longitudinally shellable rotation. Our second method is based on a linear-programming characterization of sinkability. By identifying its optimal basis, we show that this linear program can be solved in O(n^{ω/2}) time, where ω is the matrix-multiplication exponent, assuming the underlying linear system is non-singular. Finally, we pose several conjectures and describe experimental results that support them.
Cite as

Jeff Erickson and Christian Howard. Shelling and Sinking Graphs on the Sphere. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 47:1-47:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{erickson_et_al:LIPIcs.SoCG.2025.47,
  author =	{Erickson, Jeff and Howard, Christian},
  title =	{{Shelling and Sinking Graphs on the Sphere}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{47:1--47:18},
  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.2025.47},
  URN =		{urn:nbn:de:0030-drops-231996},
  doi =		{10.4230/LIPIcs.SoCG.2025.47},
  annote =	{Keywords: morphing, planar graphs, spherical graph drawing, longitudinal shelling}
}
Document
Vision
DOI: 10.4230/TGDK.1.1.3
Knowledge Engineering Using Large Language Models

Authors: Bradley P. Allen, Lise Stork, and Paul Groth

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
Knowledge engineering is a discipline that focuses on the creation and maintenance of processes that generate and apply knowledge. Traditionally, knowledge engineering approaches have focused on knowledge expressed in formal languages. The emergence of large language models and their capabilities to effectively work with natural language, in its broadest sense, raises questions about the foundations and practice of knowledge engineering. Here, we outline the potential role of LLMs in knowledge engineering, identifying two central directions: 1) creating hybrid neuro-symbolic knowledge systems; and 2) enabling knowledge engineering in natural language. Additionally, we formulate key open research questions to tackle these directions.
Cite as

Bradley P. Allen, Lise Stork, and Paul Groth. Knowledge Engineering Using Large Language Models. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{allen_et_al:TGDK.1.1.3,
  author =	{Allen, Bradley P. and Stork, Lise and Groth, Paul},
  title =	{{Knowledge Engineering Using Large Language Models}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:19},
  ISSN =	{2942-7517},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.3},
  URN =		{urn:nbn:de:0030-drops-194777},
  doi =		{10.4230/TGDK.1.1.3},
  annote =	{Keywords: knowledge engineering, large language models}
}
Document
DOI: 10.4230/LIPIcs.GIScience.2023.10
Data-Spatial Layouts for Grid Maps

Authors: Nathan van Beusekom, Wouter Meulemans, Bettina Speckmann, and Jo Wood

Published in: LIPIcs, Volume 277, 12th International Conference on Geographic Information Science (GIScience 2023)

Abstract
Grid maps are a well-known technique to visualize data associated with spatial regions. A grid map assigns each region to a tile in a grid (often orthogonal or hexagonal) and then represents the associated data values within this tile. Good grid maps represent the underlying geographic space well: regions that are geographically close are close in the grid map and vice versa. Though Tobler’s law suggests that spatial proximity relates to data similarity, local variations may obscure clusters and patterns in the data. For example, there are often clear differences between urban centers and adjacent rural areas with respect to socio-economic indicators. To get a better view of the data distribution, we propose grid-map layouts that take data values into account and place regions with similar data into close proximity. In the limit, such a data layout is essentially a chart and loses all spatial meaning. We present an algorithm to create hybrid layouts, allowing for trade-offs between data values and geographic space when assigning regions to tiles. Our algorithm also handles hierarchical grid maps and allows us to focus either on data or on geographic space on different levels of the hierarchy. Leveraging our algorithm we explore the design space of (hierarchical) grid maps with a hybrid layout and their semantics.
Cite as

Nathan van Beusekom, Wouter Meulemans, Bettina Speckmann, and Jo Wood. Data-Spatial Layouts for Grid Maps. In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vanbeusekom_et_al:LIPIcs.GIScience.2023.10,
  author =	{van Beusekom, Nathan and Meulemans, Wouter and Speckmann, Bettina and Wood, Jo},
  title =	{{Data-Spatial Layouts for Grid Maps}},
  booktitle =	{12th International Conference on Geographic Information Science (GIScience 2023)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-288-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{277},
  editor =	{Beecham, Roger and Long, Jed A. and Smith, Dianna and Zhao, Qunshan and Wise, Sarah},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2023.10},
  URN =		{urn:nbn:de:0030-drops-189052},
  doi =		{10.4230/LIPIcs.GIScience.2023.10},
  annote =	{Keywords: Grid map, algorithms, trade-offs}
}
Document
DOI: 10.4230/LIPIcs.GIScience.2021.II.7
Coordinated Schematization for Visualizing Mobility Patterns on Networks

Authors: Bram Custers, Wouter Meulemans, Bettina Speckmann, and Kevin Verbeek

Published in: LIPIcs, Volume 208, 11th International Conference on Geographic Information Science (GIScience 2021) - Part II

Abstract
GPS trajectories of vehicles moving on a road network are a valuable source of traffic information. However, the sheer volume of available data makes it challenging to identify and visualize salient patterns. Meaningful visual summaries of trajectory collections require that both the trajectories and the underlying network are aggregated and simplified in a coherent manner. In this paper we propose a coordinated fully-automated pipeline for computing a schematic overview of mobility patterns from a collection of trajectories on a street network. Our pipeline utilizes well-known building blocks from GIS, automated cartography, and trajectory analysis: map matching, road selection, schematization, movement patterns, and metro-map style rendering. We showcase the results of our pipeline on two real-world trajectory collections around The Hague and Beijing.
Cite as

Bram Custers, Wouter Meulemans, Bettina Speckmann, and Kevin Verbeek. Coordinated Schematization for Visualizing Mobility Patterns on Networks. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part II. Leibniz International Proceedings in Informatics (LIPIcs), Volume 208, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{custers_et_al:LIPIcs.GIScience.2021.II.7,
  author =	{Custers, Bram and Meulemans, Wouter and Speckmann, Bettina and Verbeek, Kevin},
  title =	{{Coordinated Schematization for Visualizing Mobility Patterns on Networks}},
  booktitle =	{11th International Conference on Geographic Information Science (GIScience 2021) - Part II},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-208-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{208},
  editor =	{Janowicz, Krzysztof and Verstegen, Judith A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2021.II.7},
  URN =		{urn:nbn:de:0030-drops-147665},
  doi =		{10.4230/LIPIcs.GIScience.2021.II.7},
  annote =	{Keywords: Trajectories, Visualization, Schematization}
}
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