23 Search Results for "Scheucher, Manfred"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.22
Disproving Two Conjectures on the Hamiltonicity of Venn Diagrams

Authors: Sofia Brenner, Linda Kleist, Torsten Mütze, Christian Rieck, and Francesco Verciani

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

Abstract
In 1984, Winkler conjectured that every simple Venn diagram with n curves can be extended to a simple Venn diagram with n+1 curves. This conjecture is equivalent to the statement that the dual graph of any simple Venn diagram has a Hamilton cycle. In this work, we construct counterexamples to Winkler’s conjecture for all n ≥ 6. As part of this proof, we computed all 3.430.404 simple Venn diagrams with n = 6 curves (even their number was not previously known), among which we found 72 counterexamples. We also disprove another conjecture about the Hamiltonicity of the arrangement graph of a Venn diagram. Specifically, while working on Winkler’s conjecture, Pruesse and Ruskey proved that this graph has a Hamilton cycle for every simple Venn diagram with n curves, and conjectured that this also holds for non-simple diagrams. We construct counterexamples to this conjecture for all n ≥ 4.
Cite as

Sofia Brenner, Linda Kleist, Torsten Mütze, Christian Rieck, and Francesco Verciani. Disproving Two Conjectures on the Hamiltonicity of Venn Diagrams. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{brenner_et_al:LIPIcs.SoCG.2026.22,
  author =	{Brenner, Sofia and Kleist, Linda and M\"{u}tze, Torsten and Rieck, Christian and Verciani, Francesco},
  title =	{{Disproving Two Conjectures on the Hamiltonicity of Venn Diagrams}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{22:1--22:16},
  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.2026.22},
  URN =		{urn:nbn:de:0030-drops-258285},
  doi =		{10.4230/LIPIcs.SoCG.2026.22},
  annote =	{Keywords: Venn diagram, Winkler’s conjecture, Hamilton cycle, perfect matching, hypercube}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.26
Finding a Fair Scoring Function for Top-k Selection: From Hardness to Practice

Authors: Guangya Cai

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

Abstract
We study the problem of finding a fair linear scoring function over (numerical) attributes for top-k selection, ensuring fairness through a proportional representation constraint on the protected group. Existing algorithms do not scale efficiently, particularly in higher dimensions. Our hardness analysis shows that in more than two dimensions, no algorithm is likely to scale efficiently with respect to dataset size, and the computational complexity is likely to grow rapidly with dimensionality. However, the hardness results also provide key insights guiding algorithm design, leading to our two-pronged solution: (1) For small k, our analysis reveals a gap in the hardness barrier. By addressing various engineering challenges, including achieving efficient parallelism, we turn this potential of efficiency into an optimized geometry-based algorithm delivering substantial performance gains. (2) For large k, where the hardness is robust, we employ a practically efficient optimization-based algorithm which, despite being theoretically worse, achieves superior real-world performance. Experimental evaluations on real-world datasets then explore scenarios where worst-case behavior does not manifest, identifying areas critical to practical performance. Our solution achieves speedups of up to several orders of magnitude compared to the state of the art, an efficiency made possible through a tight integration of hardness analysis, algorithm design, practical engineering, and empirical evaluation.
Cite as

Guangya Cai. Finding a Fair Scoring Function for Top-k Selection: From Hardness to Practice. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cai:LIPIcs.SoCG.2026.26,
  author =	{Cai, Guangya},
  title =	{{Finding a Fair Scoring Function for Top-k Selection: From Hardness to Practice}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{26:1--26:17},
  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.2026.26},
  URN =		{urn:nbn:de:0030-drops-258320},
  doi =		{10.4230/LIPIcs.SoCG.2026.26},
  annote =	{Keywords: Fairness, Top-k, Integration}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.15
Euclidean Noncrossing Steiner Spanners of Nearly Optimal Sparsity

Authors: Sujoy Bhore, Sándor Kisfaludi‑Bak, Lazar Milenković, Csaba D. Tóth, Karol Węgrzycki, and Sampson Wong

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

Abstract
A Euclidean noncrossing Steiner (1+ε)-spanner for a point set P ⊂ ℝ² is a planar straight-line graph that, for any two points a, b ∈ P, contains a path whose length is at most 1+ε times the Euclidean distance between a and b. We construct a Euclidean noncrossing Steiner (1+ε)-spanner with O(n/ε^{3/2}) edges for any set of n points in the plane. This result improves upon the previous best upper bound of O(n/ε⁴) obtained nearly three decades ago. We also establish an almost matching lower bound: There exist n points in the plane for which any Euclidean noncrossing Steiner (1+ε)-spanner has Ω_μ(n/ε^{3/2-μ}) edges for any μ > 0. Our lower bound uses recent generalizations of the Szemerédi-Trotter theorem to disk-tube incidences in geometric measure theory.
Cite as

Sujoy Bhore, Sándor Kisfaludi‑Bak, Lazar Milenković, Csaba D. Tóth, Karol Węgrzycki, and Sampson Wong. Euclidean Noncrossing Steiner Spanners of Nearly Optimal Sparsity. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhore_et_al:LIPIcs.SoCG.2026.15,
  author =	{Bhore, Sujoy and Kisfaludi‑Bak, S\'{a}ndor and Milenkovi\'{c}, Lazar and T\'{o}th, Csaba D. and W\k{e}grzycki, Karol and Wong, Sampson},
  title =	{{Euclidean Noncrossing Steiner Spanners of Nearly Optimal Sparsity}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{15:1--15:18},
  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.2026.15},
  URN =		{urn:nbn:de:0030-drops-258210},
  doi =		{10.4230/LIPIcs.SoCG.2026.15},
  annote =	{Keywords: geometric network design, spanners, crossing number, incidences}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.25
Characterizing and Recognizing Twistedness

Authors: Oswin Aichholzer, Alfredo García, Javier Tejel, Birgit Vogtenhuber, and Alexandra Weinberger

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
In a simple drawing of a graph, any two edges intersect in at most one point (either a common endpoint or a proper crossing). A simple drawing is generalized twisted if it fulfills certain rather specific constraints on how the edges are drawn. An abstract rotation system of a graph assigns to each vertex a cyclic order of its incident edges. A realizable rotation system is one that admits a simple drawing such that at each vertex, the edges emanate in that cyclic order, and a generalized twisted rotation system can be realized as a generalized twisted drawing. Generalized twisted drawings have initially been introduced to obtain improved bounds on the size of plane substructures in any simple drawing of K_n. They have since gained independent interest due to their surprising properties. However, the definition of generalized twisted drawings is very geometric and drawing-specific. In this paper, we develop characterizations of generalized twisted drawings that enable a purely combinatorial view on these drawings and lead to efficient recognition algorithms. Concretely, we show that for any n ≥ 7, an abstract rotation system of K_n is generalized twisted if and only if all subrotation systems induced by five vertices are generalized twisted. This implies a drawing-independent and concise characterization of generalized twistedness. Besides, the result yields a simple O(n⁵)-time algorithm to decide whether an abstract rotation system is generalized twisted and sheds new light on the structural features of simple drawings. We further develop a characterization via the rotations of a pair of vertices in a drawing, which we then use to derive an O(n²)-time algorithm to decide whether a realizable rotation system is generalized twisted.
Cite as

Oswin Aichholzer, Alfredo García, Javier Tejel, Birgit Vogtenhuber, and Alexandra Weinberger. Characterizing and Recognizing Twistedness. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aichholzer_et_al:LIPIcs.GD.2025.25,
  author =	{Aichholzer, Oswin and Garc{\'\i}a, Alfredo and Tejel, Javier and Vogtenhuber, Birgit and Weinberger, Alexandra},
  title =	{{Characterizing and Recognizing Twistedness}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.25},
  URN =		{urn:nbn:de:0030-drops-250116},
  doi =		{10.4230/LIPIcs.GD.2025.25},
  annote =	{Keywords: generalized twisted drawings, simple drawings, rotation systems, recognition, combinatorial characterization, efficient algorithms}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.35
A Walk on the Wild Side: A Shape-First Methodology for Orthogonal Drawings

Authors: Giordano Andreola, Susanna Caroppo, Giuseppe Di Battista, Fabrizio Grosso, Maurizio Patrignani, and Allegra Strippoli

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
Several algorithms for the construction of orthogonal drawings of graphs, including those based on the Topology-Shape-Metrics (TSM) paradigm, tend to prioritize the minimization of crossings. This emphasis has two notable side effects: some edges are drawn with unnecessarily long sequences of segments and bends, and the overall drawing area may become excessively large. As a result, the produced drawings often lack geometric uniformity. Moreover, orthogonal crossings are known to have a limited impact on readability, suggesting that crossing minimization may not always be the optimal goal. In this paper, we introduce a methodology that "subverts" the traditional TSM pipeline by focusing on minimizing bends. Given a graph G, we ideally seek to construct a rectilinear drawing of G, that is, an orthogonal drawing with no bends. When not possible, we incrementally subdivide the edges of G by introducing dummy vertices that will (possibly) correspond to bends in the final drawing. This process continues until a rectilinear drawing of a subdivision of the graph is found, after which the final coordinates are computed. We tackle the (NP-complete) rectilinear drawability problem by encoding it as a SAT formula and solving it with state-of-the-art SAT solvers. If the SAT formula is unsatisfiable, we use the solver’s proof to determine which edge to subdivide. Our implementation, domus, which is fairly simple, is evaluated through extensive experiments on small- to medium-sized graphs. The results show that it consistently outperforms ogdf’s TSM-based approach across most standard graph drawing metrics.
Cite as

Giordano Andreola, Susanna Caroppo, Giuseppe Di Battista, Fabrizio Grosso, Maurizio Patrignani, and Allegra Strippoli. A Walk on the Wild Side: A Shape-First Methodology for Orthogonal Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{andreola_et_al:LIPIcs.GD.2025.35,
  author =	{Andreola, Giordano and Caroppo, Susanna and Di Battista, Giuseppe and Grosso, Fabrizio and Patrignani, Maurizio and Strippoli, Allegra},
  title =	{{A Walk on the Wild Side: A Shape-First Methodology for Orthogonal Drawings}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{35:1--35:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.35},
  URN =		{urn:nbn:de:0030-drops-250218},
  doi =		{10.4230/LIPIcs.GD.2025.35},
  annote =	{Keywords: Non-planar Orthogonal Drawings, SAT Solver, Experimental Comparison}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.29
Stabbing Faces by a Convex Curve

Authors: David Eppstein

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
We prove that, for every plane graph G and every smooth convex curve C not on a single line, there exists a straight-line drawing of G for which every face is crossed by C.
Cite as

David Eppstein. Stabbing Faces by a Convex Curve. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 29:1-29:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eppstein:LIPIcs.GD.2025.29,
  author =	{Eppstein, David},
  title =	{{Stabbing Faces by a Convex Curve}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{29:1--29:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.29},
  URN =		{urn:nbn:de:0030-drops-250155},
  doi =		{10.4230/LIPIcs.GD.2025.29},
  annote =	{Keywords: planar graphs, convex curves, stabbing, transversal}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.16
Isometric-Universal Graphs for Trees

Authors: Edgar Baucher, François Dross, and Cyril Gavoille

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

Abstract
We consider the problem of finding the smallest graph that contains two input trees each with at most n vertices preserving their distances. In other words, we look for an isometric-universal graph with the minimum number of vertices for two given trees. We prove that this problem can be solved in time O(n^{5/2}log{n}). We extend this result to forests instead of trees, and propose an algorithm with running time O(n^{7/2}log{n}). As a key ingredient, we show that a smallest isometric-universal graph of two trees essentially is a tree. Furthermore, we prove that these results cannot be extended. Firstly, we show that deciding whether there exists an isometric-universal graph with t vertices for three forests is NP-complete. Secondly, we show that any smallest isometric-universal graph cannot be a tree for some families of three trees. This latter result has implications for greedy strategies solving the smallest isometric-universal graph problem.
Cite as

Edgar Baucher, François Dross, and Cyril Gavoille. Isometric-Universal Graphs for Trees. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baucher_et_al:LIPIcs.MFCS.2025.16,
  author =	{Baucher, Edgar and Dross, Fran\c{c}ois and Gavoille, Cyril},
  title =	{{Isometric-Universal Graphs for Trees}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{16:1--16:16},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-241237},
  doi =		{10.4230/LIPIcs.MFCS.2025.16},
  annote =	{Keywords: tree, forest, isometric subgraph, universal graph, distance-preserving}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.15
RustSAT: A Library for SAT Solving in Rust

Authors: Christoph Jabs

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
State-of-the-art Boolean satisfiability (SAT) solvers constitute a practical and competitive approach for solving various real-world problems. To encourage their widespread adoption, the relatively high barrier of entry following from the low level syntax of SAT and the expert knowledge required to achieve tight integration with SAT solvers should be further reduced. We present RustSAT, a library with the aim of making SAT solving technology readily available in the Rust programming language. RustSAT provides functionality for helping with generating (Max)SAT instances, writing them to, or reading them from files. Furthermore, RustSAT includes interfaces to various state-of-the-art SAT solvers available with a unified Rust API. Lastly, RustSAT implements several encodings for higher level constraints (at-most-one, cardinality, and pseudo-Boolean), which are also available via a C and Python API.
Cite as

Christoph Jabs. RustSAT: A Library for SAT Solving in Rust. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 15:1-15:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jabs:LIPIcs.SAT.2025.15,
  author =	{Jabs, Christoph},
  title =	{{RustSAT: A Library for SAT Solving in Rust}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{15:1--15:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.15},
  URN =		{urn:nbn:de:0030-drops-237498},
  doi =		{10.4230/LIPIcs.SAT.2025.15},
  annote =	{Keywords: Rust, library, SAT solvers, constraint encodings}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.3
Problem Partitioning via Proof Prefixes

Authors: Zachary Battleman, Joseph E. Reeves, and Marijn J. H. Heule

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
Satisfiability solvers have been instrumental in tackling hard problems, including mathematical challenges that require years of computation. A key obstacle in efficiently solving such problems lies in effectively partitioning them into many, frequently millions of subproblems. Existing automated partitioning techniques, primarily based on lookahead methods, perform well on some instances but fail to generate effective partitions for many others. This paper introduces a powerful partitioning approach that leverages prefixes of proofs derived from conflict-driven clause-learning solvers. This method enables non-experts to harness the power of massively parallel SAT solving for their problems. We also propose a semantically-driven partitioning technique tailored for problems with large cardinality constraints, which frequently arise in optimization tasks. We evaluate our methods on diverse benchmarks, including combinatorial problems and formulas from SAT and MaxSAT competitions. Our results demonstrate that these techniques outperform existing partitioning strategies in many cases, offering improved scalability and efficiency.
Cite as

Zachary Battleman, Joseph E. Reeves, and Marijn J. H. Heule. Problem Partitioning via Proof Prefixes. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{battleman_et_al:LIPIcs.SAT.2025.3,
  author =	{Battleman, Zachary and Reeves, Joseph E. and Heule, Marijn J. H.},
  title =	{{Problem Partitioning via Proof Prefixes}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.3},
  URN =		{urn:nbn:de:0030-drops-237378},
  doi =		{10.4230/LIPIcs.SAT.2025.3},
  annote =	{Keywords: Satisfiability solving, parallel computing, problem partitioning}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.85
Towards the Proximity Conjecture on Group-Labeled Matroids

Authors: Dániel Garamvölgyi, Ryuhei Mizutani, Taihei Oki, Tamás Schwarcz, and Yutaro Yamaguchi

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

Abstract
Consider a matroid M whose ground set is equipped with a labeling to an abelian group. A basis of M is called F-avoiding if the sum of the labels of its elements is not in a forbidden label set F. Hörsch, Imolay, Mizutani, Oki, and Schwarcz (2024) conjectured that if an F-avoiding basis exists, then any basis can be transformed into an F-avoiding basis by exchanging at most |F| elements. This proximity conjecture is known to hold for certain specific groups; in the case where |F| ≤ 2; or when the matroid is subsequence-interchangeably base orderable (SIBO), which is a weakening of the so-called strongly base orderable (SBO) property. In this paper, we settle the proximity conjecture for sparse paving matroids or in the case where |F| ≤ 4. Related to the latter result, we present the first known example of a non-SIBO matroid. We further address the setting of multiple group-label constraints, showing proximity results for the cases of two labelings, SIBO matroids, matroids representable over a fixed, finite field, and sparse paving matroids.
Cite as

Dániel Garamvölgyi, Ryuhei Mizutani, Taihei Oki, Tamás Schwarcz, and Yutaro Yamaguchi. Towards the Proximity Conjecture on Group-Labeled Matroids. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 85:1-85:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garamvolgyi_et_al:LIPIcs.ICALP.2025.85,
  author =	{Garamv\"{o}lgyi, D\'{a}niel and Mizutani, Ryuhei and Oki, Taihei and Schwarcz, Tam\'{a}s and Yamaguchi, Yutaro},
  title =	{{Towards the Proximity Conjecture on Group-Labeled Matroids}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{85:1--85:17},
  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.2025.85},
  URN =		{urn:nbn:de:0030-drops-234628},
  doi =		{10.4230/LIPIcs.ICALP.2025.85},
  annote =	{Keywords: sparse paving matroid, subsequence-interchangeable base orderability, congruency constraint, multiple labelings}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.16
Signotopes with Few Plus Signs

Authors: Helena Bergold, Lukas Egeling, and Hung P. Hoang

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

Abstract
Arrangements of pseudohyperplanes are widely studied in computational geometry. A rich subclass of pseudohyerplane arrangements, which has gained more attention in recent years, is the so-called signotopes. Introduced by Manin and Schechtman (1989), the higher Bruhat order is a natural order of r-signotopes on n elements, with the signotope corresponding to the cyclic arrangement as the minimal element. In this paper, we show that the lower (and by symmetry upper) levels of this higher Bruhat order contain the same number of elements for a fixed difference n-r. This result implies that given the difference d = n-r and p, the number of one-element extensions of the cyclic arrangement of n hyperplanes in ℝ^d with at most p points on one side of the extending pseudohyperplane does not depend on n, as long as n ≥ d + p.
Cite as

Helena Bergold, Lukas Egeling, and Hung P. Hoang. Signotopes with Few Plus Signs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bergold_et_al:LIPIcs.SoCG.2025.16,
  author =	{Bergold, Helena and Egeling, Lukas and Hoang, Hung P.},
  title =	{{Signotopes with Few Plus Signs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{16:1--16:14},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-231681},
  doi =		{10.4230/LIPIcs.SoCG.2025.16},
  annote =	{Keywords: flip graph, higher Bruhat order, signotope, counting, Ferrers diagram, one-element extension}
}
Document
DOI: 10.4230/LIPIcs.GD.2024.5
Holes in Convex and Simple Drawings

Authors: Helena Bergold, Joachim Orthaber, Manfred Scheucher, and Felix Schröder

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

Abstract
Gons and holes in point sets have been extensively studied in the literature. For simple drawings of the complete graph a generalization of the Erdős-Szekeres theorem is known and empty triangles have been investigated. We introduce a notion of k-holes for simple drawings and study their existence with respect to the convexity hierarchy. We present a family of simple drawings without 4-holes and prove a generalization of Gerken’s empty hexagon theorem for convex drawings. A crucial intermediate step will be the structural investigation of pseudolinear subdrawings in convex drawings.
Cite as

Helena Bergold, Joachim Orthaber, Manfred Scheucher, and Felix Schröder. Holes in Convex and Simple Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 5:1-5:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bergold_et_al:LIPIcs.GD.2024.5,
  author =	{Bergold, Helena and Orthaber, Joachim and Scheucher, Manfred and Schr\"{o}der, Felix},
  title =	{{Holes in Convex and Simple Drawings}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{5:1--5:9},
  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.2024.5},
  URN =		{urn:nbn:de:0030-drops-212895},
  doi =		{10.4230/LIPIcs.GD.2024.5},
  annote =	{Keywords: simple topological graph, convexity hierarchy, k-gon, k-hole, empty k-cycle, Erd\H{o}s-Szekeres theorem, Empty Hexagon theorem, planar point set, pseudolinear drawing}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.18
Plane Hamiltonian Cycles in Convex Drawings

Authors: Helena Bergold, Stefan Felsner, Meghana M. Reddy, Joachim Orthaber, and Manfred Scheucher

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

Abstract
A conjecture by Rafla from 1988 asserts that every simple drawing of the complete graph K_n admits a plane Hamiltonian cycle. It turned out that already the existence of much simpler non-crossing substructures in such drawings is hard to prove. Recent progress was made by Aichholzer et al. and by Suk and Zeng who proved the existence of a plane path of length Ω(log n / log log n) and of a plane matching of size Ω(n^{1/2}) in every simple drawing of K_n. Instead of studying simpler substructures, we prove Rafla’s conjecture for the subclass of convex drawings, the most general class in the convexity hierarchy introduced by Arroyo et al. Moreover, we show that every convex drawing of K_n contains a plane Hamiltonian path between each pair of vertices (Hamiltonian connectivity) and a plane k-cycle for each 3 ≤ k ≤ n (pancyclicity), and present further results on maximal plane subdrawings.
Cite as

Helena Bergold, Stefan Felsner, Meghana M. Reddy, Joachim Orthaber, and Manfred Scheucher. Plane Hamiltonian Cycles in Convex Drawings. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bergold_et_al:LIPIcs.SoCG.2024.18,
  author =	{Bergold, Helena and Felsner, Stefan and M. Reddy, Meghana and Orthaber, Joachim and Scheucher, Manfred},
  title =	{{Plane Hamiltonian Cycles in Convex Drawings}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{18:1--18:16},
  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.2024.18},
  URN =		{urn:nbn:de:0030-drops-199630},
  doi =		{10.4230/LIPIcs.SoCG.2024.18},
  annote =	{Keywords: simple drawing, convexity hierarchy, plane pancyclicity, plane Hamiltonian connectivity, maximal plane subdrawing}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.43
An Improved Lower Bound on the Number of Pseudoline Arrangements

Authors: Fernando Cortés Kühnast, Justin Dallant, Stefan Felsner, and Manfred Scheucher

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

Abstract
Arrangements of pseudolines are classic objects in discrete and computational geometry. They have been studied with increasing intensity since their introduction almost 100 years ago. The study of the number B_n of non-isomorphic simple arrangements of n pseudolines goes back to Goodman and Pollack, Knuth, and others. It is known that B_n is in the order of 2^Θ(n²) and finding asymptotic bounds on b_n = log₂(B_n)/n² remains a challenging task. In 2011, Felsner and Valtr showed that 0.1887 ≤ b_n ≤ 0.6571 for sufficiently large n. The upper bound remains untouched but in 2020 Dumitrescu and Mandal improved the lower bound constant to 0.2083. Their approach utilizes the known values of B_n for up to n = 12. We tackle the lower bound by utilizing dynamic programming and the Lindström–Gessel–Viennot lemma. Our new bound is b_n ≥ 0.2721 for sufficiently large n. The result is based on a delicate interplay of theoretical ideas and computer assistance.
Cite as

Fernando Cortés Kühnast, Justin Dallant, Stefan Felsner, and Manfred Scheucher. An Improved Lower Bound on the Number of Pseudoline Arrangements. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 43:1-43:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{corteskuhnast_et_al:LIPIcs.SoCG.2024.43,
  author =	{Cort\'{e}s K\"{u}hnast, Fernando and Dallant, Justin and Felsner, Stefan and Scheucher, Manfred},
  title =	{{An Improved Lower Bound on the Number of Pseudoline Arrangements}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{43:1--43:18},
  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.2024.43},
  URN =		{urn:nbn:de:0030-drops-199880},
  doi =		{10.4230/LIPIcs.SoCG.2024.43},
  annote =	{Keywords: counting, pseudoline arrangement, recursive construction, bipermutation, divide and conquer, dynamic programming, computer-assisted proof}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.46
Saturation Results Around the Erdős-Szekeres Problem

Authors: Gábor Damásdi, Zichao Dong, Manfred Scheucher, and Ji Zeng

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

Abstract
In this paper, we consider saturation problems related to the celebrated Erdős-Szekeres convex polygon problem. For each n ≥ 7, we construct a planar point set of size (7/8) ⋅ 2^{n-2} which is saturated for convex n-gons. That is, the set contains no n points in convex position while the addition of any new point creates such a configuration. This demonstrates that the saturation number is smaller than the Ramsey number for the Erdős-Szekeres problem. The proof also shows that the original Erdős-Szekeres construction is indeed saturated. Our construction is based on a similar improvement for the saturation version of the cups-versus-caps theorem. Moreover, we consider the generalization of the cups-versus-caps theorem to monotone paths in ordered hypergraphs. In contrast to the geometric setting, we show that this abstract saturation number is always equal to the corresponding Ramsey number.
Cite as

Gábor Damásdi, Zichao Dong, Manfred Scheucher, and Ji Zeng. Saturation Results Around the Erdős-Szekeres Problem. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{damasdi_et_al:LIPIcs.SoCG.2024.46,
  author =	{Dam\'{a}sdi, G\'{a}bor and Dong, Zichao and Scheucher, Manfred and Zeng, Ji},
  title =	{{Saturation Results Around the Erd\H{o}s-Szekeres Problem}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{46:1--46:14},
  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.2024.46},
  URN =		{urn:nbn:de:0030-drops-199919},
  doi =		{10.4230/LIPIcs.SoCG.2024.46},
  annote =	{Keywords: Convex polygon, Cups-versus-caps, Monotone path, Saturation problem}
}
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