45 Search Results for "Hull, Richard"

Document
DOI: 10.4230/LIPIcs.CSL.2026.10
Disjunctions of Two Dependence Atoms

Authors: Nicolas Fröhlich, Phokion G. Kolaitis, and Arne Meier

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Dependence logic is a formalism that augments the syntax of first-order logic with dependence atoms asserting that the value of a variable is determined by the values of some other variables, i.e., dependence atoms express functional dependencies in relational databases. On finite structures, dependence logic captures NP, hence there are sentences of dependence logic whose model-checking problem is NP-complete. In fact, it is known that there are disjunctions of three dependence atoms whose model-checking problem is NP-complete. Motivated from considerations in database theory, we study the model-checking problem for disjunctions of two unary dependence atoms and establish a trichotomy theorem, namely, for every such formula, one of the following is true for the model-checking problem: (i) it is NL-complete; (ii) it is L-complete; (iii) it is first-order definable (hence, in AC⁰). Furthermore, we classify the complexity of the model-checking problem for disjunctions of two arbitrary dependence atoms, and also characterize when such a disjunction is coherent, i.e., when it satisfies a certain small-model property. Along the way, we identify a new class of 2CNF-formulas whose satisfiability problem is L-complete.
Cite as

Nicolas Fröhlich, Phokion G. Kolaitis, and Arne Meier. Disjunctions of Two Dependence Atoms. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{frohlich_et_al:LIPIcs.CSL.2026.10,
  author =	{Fr\"{o}hlich, Nicolas and Kolaitis, Phokion G. and Meier, Arne},
  title =	{{Disjunctions of Two Dependence Atoms}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.10},
  URN =		{urn:nbn:de:0030-drops-254343},
  doi =		{10.4230/LIPIcs.CSL.2026.10},
  annote =	{Keywords: Dependence logic, coherence, model-checking, complexity, functional dependencies}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.IPEC.2025.1
A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk)

Authors: Martin Koutecký

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Integer Programming (IP) is a fundamental but computationally hard problem. Still, certain efficiently solvable subclasses have been identified over time, most notably totally unimodular IPs in the 1950s, and fixed-dimension IPs in the 1980s. Starting around the year 2000, a stream of research has identified block-structured IPs as yet another tractable subclass. In this paper, we give a brief and incomplete review of this history, with a focus on several of the author’s contributions.
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Martin Koutecký. A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk). In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koutecky:LIPIcs.IPEC.2025.1,
  author =	{Kouteck\'{y}, Martin},
  title =	{{A Brief History of Parameterized Algorithms for Block-Structured Integer Programs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.1},
  URN =		{urn:nbn:de:0030-drops-251338},
  doi =		{10.4230/LIPIcs.IPEC.2025.1},
  annote =	{Keywords: Integer Programming, Parameterized Algorithm, Graver Basis, Treedepth, n-fold, tree-fold, 2-stage stochastic, multistage stochastic, Mixed-Integer Programming}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.5
Inconsistency-Tolerant Semantics Based on (Preferred) Repairs (Invited Paper)

Authors: Camille Bourgaux

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
Real-world datasets are plagued by data quality issues which may render the data inconsistent w.r.t. a set of constraints, be they given by database integrity constraints or ontologies. A prominent way to handle such inconsistent data is to use inconsistency-tolerant semantics to obtain meaningful answers to queries. Most of these semantics are based on some notion of repairs, which represent ways of restoring the data consistency. The most basic kind of repairs is that of subset repairs, which are maximal consistent subsets of the dataset. However, in many scenarios, one can define preferred repairs based on some preference information. These lecture notes present inconsistency-tolerant semantics, focusing on the repair-based ones, then review different kinds of preferred repairs that have been considered in the literature. We present in particular the relationships between different kinds of preferred repairs and other notions related to inconsistency handling, the computational complexity of reasoning with (preferred) repairs, and some implementations.
Cite as

Camille Bourgaux. Inconsistency-Tolerant Semantics Based on (Preferred) Repairs (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 5:1-5:67, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bourgaux:OASIcs.RW.2024/2025.5,
  author =	{Bourgaux, Camille},
  title =	{{Inconsistency-Tolerant Semantics Based on (Preferred) Repairs}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{5:1--5:67},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.5},
  URN =		{urn:nbn:de:0030-drops-250504},
  doi =		{10.4230/OASIcs.RW.2024/2025.5},
  annote =	{Keywords: Knowledge bases, databases, inconsistency handling, repairs, preferences}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.9
Reasoning About Time in DatalogMTL: Course Notes (Invited Paper)

Authors: Przemysław Andrzej Wałęga

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
Many real-world applications, such as those in healthcare, finance, and logistics, require reasoning over temporal data. Standard rule-based languages like Datalog, however, lack explicit mechanisms for handling time and temporal dependencies. In this chapter, we discussDatalogMTL, an extension of Datalog with operators frommetric temporal logic that allow to express complex temporal properties. We focus on reasoning algorithms for DatalogMTL, discussing bothmaterialisation, based on fixpoint applications of the immediate consequence operator, and anovel saturation-based extensionthat detects and halts infinite derivations, ensuring both completeness and termination of reasoning.
Cite as

Przemysław Andrzej Wałęga. Reasoning About Time in DatalogMTL: Course Notes (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{walega:OASIcs.RW.2024/2025.9,
  author =	{Wa{\l}\k{e}ga, Przemys{\l}aw Andrzej},
  title =	{{Reasoning About Time in DatalogMTL: Course Notes}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{9:1--9:23},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.9},
  URN =		{urn:nbn:de:0030-drops-250546},
  doi =		{10.4230/OASIcs.RW.2024/2025.9},
  annote =	{Keywords: DatalogMTL, Logic Programming, Temporal Reasoning}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.7
Modern Datalog: Concepts, Methods, Applications (Invited Paper)

Authors: Markus Krötzsch

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
Pure Datalog is arguably the most fundamental rule language, elegant and simple, but also often too limited to be useful in practice. This has motivated the introduction of many new expressive features, ranging from datatypes and related functions, over aggregates and semi-ring generalisations, to existential quantifiers and complex terms. In spite of their variety, all these approaches remain true to the nature of Datalog as a direct, pattern-based way of computing on structured data. We therefore find that a modern notion of Datalog is emerging, distinctly different from other approaches of logic programming and with its own set of related methods and applications. In this course, we introduce Datalog and its most common extensions, and explain when and how these features can be used together (which is often, but not always, safe to do). We further look at modern Datalog systems and some of their primary use cases. Hands-on work with Datalog and its extensions is done with the free Datalog engine https://knowsys.github.io/nemo-doc/. The course is accessible to all audiences and does not assume specific prior knowledge.
Cite as

Markus Krötzsch. Modern Datalog: Concepts, Methods, Applications (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 7:1-7:41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{krotzsch:OASIcs.RW.2024/2025.7,
  author =	{Kr\"{o}tzsch, Markus},
  title =	{{Modern Datalog: Concepts, Methods, Applications}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{7:1--7:41},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.7},
  URN =		{urn:nbn:de:0030-drops-250524},
  doi =		{10.4230/OASIcs.RW.2024/2025.7},
  annote =	{Keywords: Datalog, query language, knowlegde representation and reasoning, logic programming, Horn logic, SPARQL, datatypes and aggregation, lecture notes, tutorial}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.46
Realizing Metric Spaces with Convex Obstacles

Authors: Sándor Kisfaludi-Bak and Leonidas Theocharous

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

Abstract
The presence of obstacles has a significant impact on distance computation, motion-planning, and visibility. These problems have been studied extensively in the planar setting, while our understanding of these problems in 3- and higher-dimensional spaces is still rudimentary. In this paper, we study the impact of different types of obstacles on the induced geodesic metric in 3-dimensional Euclidean space. We say that a finite metric space (X, dist_X) is approximately realizable by a collection 𝒯 of obstacles in ℝ³ if for any ε > 0 it can be embedded into (ℝ³⧵⋃_{T∈𝒯} T, dist_𝒯) with worst-case multiplicative distortion 1+ε, where dist_𝒯 denotes the geodesic distance in the free space induced by 𝒯. We focus on three key geometric properties of obstacles -convexity, disjointness, and fatness- and examine how dropping each one of them affects the existence of such embeddings. Our main result concerns dropping the fatness property: we demonstrate that any finite metric space is realizable with 1+ε worst-case multiplicative distortion using a collection of convex and pairwise disjoint obstacles in ℝ³, even if the obstacles are congruent and equilateral triangles. Based on the same construction, we can also show that if we require fatness but drop any of the other two properties instead, then we can still approximately realize any finite metric space. Our results have important implications on the approximability of tsp with obstacles, a natural variant of tsp introduced recently by Alkema et al. (ESA 2022). Specifically, we use the recent results of Banerjee et al. on tsp in doubling spaces (FOCS 2024) and of Chew et al. on distances among obstacles (Inf. Process. Lett. 2002) to show that tsp with obstacles admits a PTAS if the obstacles are convex, fat, and pairwise disjoint. If any of these three properties is dropped, then our results, combined with the APX-hardness of Metric tsp, demonstrate that tsp with obstacles is APX-hard.
Cite as

Sándor Kisfaludi-Bak and Leonidas Theocharous. Realizing Metric Spaces with Convex Obstacles. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 46:1-46:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kisfaludibak_et_al:LIPIcs.ISAAC.2025.46,
  author =	{Kisfaludi-Bak, S\'{a}ndor and Theocharous, Leonidas},
  title =	{{Realizing Metric Spaces with Convex Obstacles}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{46:1--46:21},
  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.2025.46},
  URN =		{urn:nbn:de:0030-drops-249545},
  doi =		{10.4230/LIPIcs.ISAAC.2025.46},
  annote =	{Keywords: traveling salesman, geodesic distance}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.13
Separability of Witness Gabriel Drawings

Authors: Carolina Haase, Philipp Kindermann, William Lenhart, and Giuseppe Liotta

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

Abstract
A witness Gabriel drawing Γ is a straight-line drawing of a graph in which any two vertices of Γ are adjacent if and only if the disk having these vertices as antipodal points contains no element of a special set of points called witnesses. A witness Gabriel drawing is linearly separable if the vertices and the witnesses lie in opposite half-planes. We prove that every outerplanar graph has a linearly separable witness Gabriel drawing by introducing and studying a new type of drawing that we call a border parabola drawing. We then use border parabola drawings to characterize those triangle-free graphs that admit a linearly separable witness Gabriel drawing. We also consider witness Gabriel drawings where no witness lies in the interior of the convex hull of the vertex set, which we call convexly separable drawings. We construct witness Gabriel drawable graphs for which any witness Gabriel drawing must be convexly separable and that do not admit any linearly separable witness Gabriel drawing.
Cite as

Carolina Haase, Philipp Kindermann, William Lenhart, and Giuseppe Liotta. Separability of Witness Gabriel Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haase_et_al:LIPIcs.GD.2025.13,
  author =	{Haase, Carolina and Kindermann, Philipp and Lenhart, William and Liotta, Giuseppe},
  title =	{{Separability of Witness Gabriel Drawings}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{13:1--13:18},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-249998},
  doi =		{10.4230/LIPIcs.GD.2025.13},
  annote =	{Keywords: Proximity Drawings, Witness Gabriel Graphs, Geometric Graph Theory}
}
Document
DOI: 10.4230/LIPIcs.TIME.2025.12
On the Complexity of the Realisability Problem for Visit Events in Trajectory Sample Databases

Authors: Arthur Jansen and Bart Kuijpers

Published in: LIPIcs, Volume 355, 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)

Abstract
Trajectory sample databases store finite sequences of measured space-time locations of moving objects, along with a speed bound for each object. These databases can be seen as uncertain databases. We propose a language that allows the formulation of queries about the uncertainty in trajectory sample databases. As part of that language, we introduce the notion of visit events, which are used to describe certain constraints on the movement of an object. In our language, an atomic query asks whether a moving object can, given its limitations, realise such an event. We give complexity results for this realisability problem, in various settings.
Cite as

Arthur Jansen and Bart Kuijpers. On the Complexity of the Realisability Problem for Visit Events in Trajectory Sample Databases. In 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 355, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.TIME.2025.12,
  author =	{Jansen, Arthur and Kuijpers, Bart},
  title =	{{On the Complexity of the Realisability Problem for Visit Events in Trajectory Sample Databases}},
  booktitle =	{32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-401-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{355},
  editor =	{Vidal, Thierry and Wa{\l}\k{e}ga, Przemys{\l}aw Andrzej},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2025.12},
  URN =		{urn:nbn:de:0030-drops-244586},
  doi =		{10.4230/LIPIcs.TIME.2025.12},
  annote =	{Keywords: Trajectory sample databases, uncertain databases, query languages, complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.102
A Combinatorial Proof of Universal Optimality for Computing a Planar Convex Hull

Authors: Ivor van der Hoog, Eva Rotenberg, and Daniel Rutschmann

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

Abstract
For a planar point set P, its convex hull is the smallest convex polygon that encloses all points in P. The construction of the convex hull from an array I_P containing P is a fundamental problem in computational geometry. By sorting I_P in lexicographical order, one can construct the convex hull of P in O(n log n) time which is worst-case optimal. Standard worst-case analysis, however, has been criticized as overly coarse or pessimistic, and researchers search for more refined analyses. For an algorithm A, worst-case analysis fixes n, and considers the maximum running time of A across all size-n point sets P and permutations I_P of P. Output-sensitive analysis fixes n and k, and considers the maximum running time across all size-n points sets P with k hull points and permutations I_P of P. Universal analysis provides an even stronger guarantee. It fixes a point set P and considers the maximum running time across all permutations I_P of P. Kirkpatrick, McQueen, and Seidel [SICOMP'86] consider output-sensitive analysis. If the convex hull of P contains k points, then their algorithm runs in O(n log k) time. Afshani, Barbay, Chan [FOCS'07] prove that the algorithm by Kirkpatrick, McQueen, and Seidel is also universally optimal. Their proof restricts the model of computation to any algebraic decision tree model where the test functions have at most constant degree and at most a constant number of arguments. They rely upon involved algebraic arguments to construct a lower bound for each point set P that matches the universal running time of [SICOMP'86]. We provide a different proof of universal optimality. Instead of restricting the computational model, we further specify the output. We require as output (1) the convex hull, and (2) for each internal point of P a witness for it being internal. Our argument is shorter, perhaps simpler, and applicable in more general models of computation.
Cite as

Ivor van der Hoog, Eva Rotenberg, and Daniel Rutschmann. A Combinatorial Proof of Universal Optimality for Computing a Planar Convex Hull. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 102:1-102:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanderhoog_et_al:LIPIcs.ESA.2025.102,
  author =	{van der Hoog, Ivor and Rotenberg, Eva and Rutschmann, Daniel},
  title =	{{A Combinatorial Proof of Universal Optimality for Computing a Planar Convex Hull}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{102:1--102:13},
  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.2025.102},
  URN =		{urn:nbn:de:0030-drops-245715},
  doi =		{10.4230/LIPIcs.ESA.2025.102},
  annote =	{Keywords: Convex hull, Combinatorial proofs, Universal optimality}
}
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)

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@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.2025.104
Optimal Antimatroid Sorting

Authors: Benjamin Aram Berendsohn

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

Abstract
The classical comparison-based sorting problem asks us to find the underlying total ordering of a given set of elements, where we can only access the elements via comparisons. In this paper, we study a restricted version, where, as a hint, a set T of possible total orderings is given, usually in some compressed form. Recently, an algorithm called topological heapsort with optimal running time was found for case where T is the set of topological orderings of a given directed acyclic graph, or, equivalently, T is the set of linear extensions of a partial ordering [Haeupler et al. 2024]. We show that a simple generalization of topological heapsort is applicable to a much broader class of restricted sorting problems, where T corresponds to a given antimatroid. As a consequence, we obtain optimal algorithms for the following restricted sorting problems, where the allowed total orders are … - … restricted by a given set of monotone precedence formulas; - … the perfect elimination orders of a given chordal graph; or - … the possible vertex search orders of a given connected rooted graph.
Cite as

Benjamin Aram Berendsohn. Optimal Antimatroid Sorting. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 104:1-104:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berendsohn:LIPIcs.ESA.2025.104,
  author =	{Berendsohn, Benjamin Aram},
  title =	{{Optimal Antimatroid Sorting}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{104:1--104:14},
  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.2025.104},
  URN =		{urn:nbn:de:0030-drops-245735},
  doi =		{10.4230/LIPIcs.ESA.2025.104},
  annote =	{Keywords: sorting, working-set heap, greedy, antimatroid}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.42
(Multivariate) k-SUM as Barrier to Succinct Computation

Authors: Geri Gokaj, Marvin Künnemann, Sabine Storandt, and Carina Truschel

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

Abstract
How does the time complexity of a problem change when the input is given succinctly rather than explicitly? We study this question for several geometric problems defined on a set X of N points in ℤ^d. As succinct representation, we choose a sumset (or Minkowski sum) representation: Instead of receiving X explicitly, we are given sets A,B of n points that define X as A+B = {a+b∣ a ∈ A,b ∈ B}. We investigate the fine-grained complexity of this succinct version for several Õ(N)-time computable geometric primitives. Remarkably, we can tie their complexity tightly to the complexity of corresponding k-SUM problems. Specifically, we introduce as All-ints 3-SUM(n,n,k) the following multivariate, multi-output variant of 3-SUM: given sets A,B of size n and set C of size k, determine for all c ∈ C whether there are a ∈ A and b ∈ B with a+b = c. We obtain the following results: 1) Succinct closest L_∞-pair requires time N^{1-o(1)} under the 3-SUM hypothesis, while succinct furthest L_∞-pair can be solved in time Õ(n). 2) Succinct bichromatic closest L_∞-Pair requires time N^{1-o(1)} iff the 4-SUM hypothesis holds. 3) The following problems are fine-grained equivalent to All-ints 3-SUM(n,n,k): succinct skyline computation in 2D with output size k and succinct batched orthogonal range search with k given ranges. This establishes conditionally tight Õ(min{nk, N})-time algorithms for these problems. We obtain further connections with All-ints 3-SUM(n,n,k) for succinctly computing independent sets in unit interval graphs. Thus, (Multivariate) k-SUM problems precisely capture the barrier for enabling sumset-succinct computation for various geometric primitives.
Cite as

Geri Gokaj, Marvin Künnemann, Sabine Storandt, and Carina Truschel. (Multivariate) k-SUM as Barrier to Succinct Computation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 42:1-42:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gokaj_et_al:LIPIcs.ESA.2025.42,
  author =	{Gokaj, Geri and K\"{u}nnemann, Marvin and Storandt, Sabine and Truschel, Carina},
  title =	{{(Multivariate) k-SUM as Barrier to Succinct Computation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{42:1--42:19},
  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.2025.42},
  URN =		{urn:nbn:de:0030-drops-245101},
  doi =		{10.4230/LIPIcs.ESA.2025.42},
  annote =	{Keywords: Fine-grained complexity theory, sumsets, additive combinatorics, succinct inputs, computational geometry}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.36
Verifying Datalog Reasoning with Lean

Authors: Johannes Tantow, Lukas Gerlach, Stephan Mennicke, and Markus Krötzsch

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Datalog is an essential logical rule language with many applications, and modern rule engines compute logical consequences for Datalog with high performance and scalability. While Datalog is rather simple and, in principle, explainable by design, such sophisticated implementations and optimizations are hard to verify. We therefore propose a certificate-based approach to validate results of Datalog reasoners in a formally verified checker for Datalog proofs. Using the proof assistant Lean, we implement such a checker and verify its correctness against direct formalizations of the Datalog semantics. We propose two JSON encodings for Datalog proofs: one using the widely supported Datalog proof trees, and one using directed acyclic graphs for succinctness. To evaluate the practical feasibility and performance of our approach, we validate proofs that we obtain by converting derivation traces of an existing Datalog reasoner into our tool-independent format.
Cite as

Johannes Tantow, Lukas Gerlach, Stephan Mennicke, and Markus Krötzsch. Verifying Datalog Reasoning with Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tantow_et_al:LIPIcs.ITP.2025.36,
  author =	{Tantow, Johannes and Gerlach, Lukas and Mennicke, Stephan and Kr\"{o}tzsch, Markus},
  title =	{{Verifying Datalog Reasoning with Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{36:1--36:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.36},
  URN =		{urn:nbn:de:0030-drops-246342},
  doi =		{10.4230/LIPIcs.ITP.2025.36},
  annote =	{Keywords: Certifying Algorithms, Datalog, Formal Verification}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.12
Testing Whether a Subgraph Is Convex or Isometric

Authors: Sergio Cabello

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We consider the following two algorithmic problems: given a graph G and a subgraph H ⊆ G, decide whether H is an isometric or a geodesically convex subgraph of G. It is relatively easy to see that the problems can be solved by computing the distances between all pairs of vertices. We provide a conditional lower bound showing that, for sparse graphs with n vertices and Θ(n) edges, we cannot expect to solve the problem in O(n^{2-ε}) time for any constant ε > 0. We also show that the problem can be solved in subquadratic time for planar graphs and in near-linear time for graphs of bounded treewidth. Finally, we provide a near-linear time algorithm for the setting where G is a plane graph and H is defined by a few cycles in G.
Cite as

Sergio Cabello. Testing Whether a Subgraph Is Convex or Isometric. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cabello:LIPIcs.WADS.2025.12,
  author =	{Cabello, Sergio},
  title =	{{Testing Whether a Subgraph Is Convex or Isometric}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.12},
  URN =		{urn:nbn:de:0030-drops-242439},
  doi =		{10.4230/LIPIcs.WADS.2025.12},
  annote =	{Keywords: convex subgraph, isometric subgraph, plane graph}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.14
Quantum Speedups for Polynomial-Time Dynamic Programming Algorithms

Authors: Susanna Caroppo, Giordano Da Lozzo, Giuseppe Di Battista, Michael T. Goodrich, and Martin Nöllenburg

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We introduce a quantum dynamic programming framework that allows us to directly extend to the quantum realm a large body of classical dynamic programming algorithms. The corresponding quantum dynamic programming algorithms retain the same space complexity as their classical counterpart, while achieving a computational speedup. For a combinatorial (search or optimization) problem P and an instance I of P, such a speedup can be expressed in terms of the average degree δ of the {dependency digraph} G_𝒫(I) of I, determined by a recursive formulation of P. The nodes of this graph are the subproblems of P induced by I and its arcs are directed from each subproblem to those on whose solution it relies. In particular, our framework allows us to solve the considered problems in Õ(|V(G_𝒫(I))| √δ) time. As an example, we obtain a quantum version of the Bellman-Ford algorithm for computing shortest paths from a single source vertex to all the other vertices in a weighted n-vertex digraph with m edges that runs in Õ(n√{nm}) time, which improves the best known classical upper bound when m ∈ Ω(n^{1.4}).
Cite as

Susanna Caroppo, Giordano Da Lozzo, Giuseppe Di Battista, Michael T. Goodrich, and Martin Nöllenburg. Quantum Speedups for Polynomial-Time Dynamic Programming Algorithms. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{caroppo_et_al:LIPIcs.WADS.2025.14,
  author =	{Caroppo, Susanna and Da Lozzo, Giordano and Di Battista, Giuseppe and Goodrich, Michael T. and N\"{o}llenburg, Martin},
  title =	{{Quantum Speedups for Polynomial-Time Dynamic Programming Algorithms}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{14:1--14:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.14},
  URN =		{urn:nbn:de:0030-drops-242454},
  doi =		{10.4230/LIPIcs.WADS.2025.14},
  annote =	{Keywords: Dynamic Programming, Quantum Algorithms, Quantum Random Access Memory}
}
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