26 Search Results for "Liu, Chih-Hung"

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DOI: 10.4230/TGDK.4.1.2
Temporal Modelling in Cultural Heritage Knowledge Graphs: Use Cases, Requirements, Evaluation, and Decision Support

Authors: Oleksandra Bruns, Jörg Waitelonis, Jeff Z. Pan, and Harald Sack

Published in: TGDK, Volume 4, Issue 1 (2026). Transactions on Graph Data and Knowledge, Volume 4, Issue 1

Abstract
Our culture, history and world are in constant motion, continuously shaped by the flow of time, evolving narratives, and shifting relationships. Capturing this temporal complexity within cultural heritage (CH) knowledge graphs is essential for preserving the dynamic nature of human heritage. However, standard RDF predicates fail to effectively model the temporal aspects of cultural data, such as changing facts, evolving relationships, and temporal concepts. Over the past two decades, a variety of RDF-based approaches have been proposed to address this limitation, yet guidance is missing on which method best suits specific CH contexts. This paper presents a systematic evaluation of temporal RDF modelling approaches from a CH perspective. Based on an analysis of real-world CH use cases, core temporal requirements are identified that reflect both modelling expressivity and practical concerns. Six prominent approaches - RDF*, tRDF, Named Graphs, Singleton Property, N-ary Relations, and 4D Fluents - are assessed across these requirements. Our findings reveal that no single solution fits all scenarios, but suitable approaches can be selected based on project-specific priorities. To support practitioners, a decision-support tool is introduced to guide them in selecting the most suitable extension for their specific needs. This work provides practical guidance for CH modelling and contributes to the broader development of temporally aware Linked Data.
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Oleksandra Bruns, Jörg Waitelonis, Jeff Z. Pan, and Harald Sack. Temporal Modelling in Cultural Heritage Knowledge Graphs: Use Cases, Requirements, Evaluation, and Decision Support. In Transactions on Graph Data and Knowledge (TGDK), Volume 4, Issue 1, pp. 2:1-2:46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{bruns_et_al:TGDK.4.1.2,
  author =	{Bruns, Oleksandra and Waitelonis, J\"{o}rg and Pan, Jeff Z. and Sack, Harald},
  title =	{{Temporal Modelling in Cultural Heritage Knowledge Graphs: Use Cases, Requirements, Evaluation, and Decision Support}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:46},
  ISSN =	{2942-7517},
  year =	{2026},
  volume =	{4},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.4.1.2},
  URN =		{urn:nbn:de:0030-drops-256871},
  doi =		{10.4230/TGDK.4.1.2},
  annote =	{Keywords: Temporal Data Representation, RDF Extensions, Cultural Heritage, Knowledge Graphs}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.16
Structural Parameterizations of k-Planarity

Authors: Tatsuya Gima, Yasuaki Kobayashi, and Yuto Okada

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

Abstract
The concept of k-planarity is extensively studied in the context of Beyond Planarity. A graph is k-planar if it admits a drawing in the plane in which each edge is crossed at most k times. The local crossing number of a graph is the minimum integer k such that it is k-planar. The problem of determining whether an input graph is 1-planar is known to be NP-complete even for near-planar graphs [Cabello and Mohar, SIAM J. Comput. 2013], that is, the graphs obtained from planar graphs by adding a single edge. Moreover, the local crossing number is hard to approximate within a factor 2 - ε for any ε > 0 [Urschel and Wellens, IPL 2021]. To address this computational intractability, Bannister, Cabello, and Eppstein [JGAA 2018] investigated the parameterized complexity of the case of k = 1, particularly focusing on structural parameterizations on input graphs, such as treedepth, vertex cover number, and feedback edge number. In this paper, we extend their approach by considering the general case k ≥ 1 and give (tight) parameterized upper and lower bound results. In particular, we strengthen the aforementioned lower bound results to subclasses of constant-treewidth graphs: we show that testing 1-planarity is NP-complete even for near-planar graphs with feedback vertex set number at most 3 and pathwidth at most 4, and the local crossing number is hard to approximate within any constant factor for graphs with feedback vertex set number at most 2.
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Tatsuya Gima, Yasuaki Kobayashi, and Yuto Okada. Structural Parameterizations of k-Planarity. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gima_et_al:LIPIcs.GD.2025.16,
  author =	{Gima, Tatsuya and Kobayashi, Yasuaki and Okada, Yuto},
  title =	{{Structural Parameterizations of k-Planarity}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{16:1--16:17},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-250021},
  doi =		{10.4230/LIPIcs.GD.2025.16},
  annote =	{Keywords: 1-planar graphs, local crossing number, beyond planarity, parameterized complexity, kernelization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.31
An Optimal Algorithm for Shortest Paths in Unweighted Disk Graphs

Authors: Bruce W. Brewer and Haitao Wang

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

Abstract
Given in the plane a set S of n points and a set of disks centered at these points, the disk graph G(S) induced by these disks has vertex set S and an edge between two vertices if their disks intersect. Note that the disks may have different radii. We consider the problem of computing shortest paths from a source point s ∈ S to all vertices in G(S) where the length of a path in G(S) is defined as the number of edges in the path. The previously best algorithm solves the problem in O(nlog² n) time. A lower bound of Ω(nlog n) is also known for this problem under the algebraic decision tree model. In this paper, we present an O(nlog n) time algorithm, which matches the lower bound and thus is optimal. Another virtue of our algorithm is that it is quite simple.
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Bruce W. Brewer and Haitao Wang. An Optimal Algorithm for Shortest Paths in Unweighted Disk Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 31:1-31:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brewer_et_al:LIPIcs.ESA.2025.31,
  author =	{Brewer, Bruce W. and Wang, Haitao},
  title =	{{An Optimal Algorithm for Shortest Paths in Unweighted Disk Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{31:1--31:8},
  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.2025.31},
  URN =		{urn:nbn:de:0030-drops-244997},
  doi =		{10.4230/LIPIcs.ESA.2025.31},
  annote =	{Keywords: disk graphs, weighted Voronoi diagrams, shortest paths}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.81
An O(nlog n) Algorithm for Single-Source Shortest Paths in Disk Graphs

Authors: Mark de Berg and Sergio Cabello

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

Abstract
We prove that the single-source shortest-path problem on disk graphs can be solved in O(n log n) expected time, and that it can be solved on intersection graphs of fat triangles in O(n log³ n) time.
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Mark de Berg and Sergio Cabello. An O(nlog n) Algorithm for Single-Source Shortest Paths in Disk Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 81:1-81:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deberg_et_al:LIPIcs.ESA.2025.81,
  author =	{de Berg, Mark and Cabello, Sergio},
  title =	{{An O(nlog n) Algorithm for Single-Source Shortest Paths in Disk Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{81:1--81:15},
  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.2025.81},
  URN =		{urn:nbn:de:0030-drops-245494},
  doi =		{10.4230/LIPIcs.ESA.2025.81},
  annote =	{Keywords: shortest path, geometric intersection graph, disk graph, fat triangles}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.10
On Geodesic Disks Enclosing Many Points

Authors: Prosenjit Bose, Guillermo Esteban, David Orden, Rodrigo I. Silveira, and Tyler Tuttle

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

Abstract
Let Π(n) be the largest number such that for every set S of n points in a polygon P, there always exist two points x, y ∈ S, where every geodesic disk containing x and y contains Π(n) points of S. We establish upper and lower bounds for Π(n), and show that ⌈n/5⌉ +1 ≤ Π(n) ≤ ⌈n/4⌉ +1. We also show that there always exist two points x, y ∈ S such that every geodesic disk with x and y on its boundary contains at least 16/665(n-2) ≈ ⌈(n-2)/41.6⌉ points both inside and outside the disk. For the special case where the points of S are restricted to be the vertices of a geodesically convex polygon we give a tight bound of ⌈n/3⌉ + 1. We provide the same tight bound when we only consider geodesic disks having x and y as diametral endpoints. Finally, we give a lower bound of ⌈(n-2)/36⌉+2 for the two-colored version of the problem.
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Prosenjit Bose, Guillermo Esteban, David Orden, Rodrigo I. Silveira, and Tyler Tuttle. On Geodesic Disks Enclosing Many Points. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bose_et_al:LIPIcs.WADS.2025.10,
  author =	{Bose, Prosenjit and Esteban, Guillermo and Orden, David and Silveira, Rodrigo I. and Tuttle, Tyler},
  title =	{{On Geodesic Disks Enclosing Many Points}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{10:1--10:20},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-242414},
  doi =		{10.4230/LIPIcs.WADS.2025.10},
  annote =	{Keywords: Enclosing disks, Geodesic disks, Bichromatic}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.24
Computational Geometry with Probabilistically Noisy Primitive Operations

Authors: David Eppstein, Michael T. Goodrich, and Vinesh Sridhar

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

Abstract
Much prior work has been done on designing computational geometry algorithms that handle input degeneracies, data imprecision, and arithmetic round-off errors. We take a new approach, inspired by the noisy sorting literature, and study computational geometry algorithms subject to noisy Boolean primitive operations in which, e.g., the comparison "is point q above line 𝓁?" returns the wrong answer with some fixed probability. We propose a novel technique called path-guided pushdown random walks that generalizes the results of noisy sorting. We apply this technique to solve point-location, plane-sweep, convex hulls in 2D and 3D, and Delaunay triangulations for noisy primitives in optimal time with high probability.
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David Eppstein, Michael T. Goodrich, and Vinesh Sridhar. Computational Geometry with Probabilistically Noisy Primitive Operations. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eppstein_et_al:LIPIcs.WADS.2025.24,
  author =	{Eppstein, David and Goodrich, Michael T. and Sridhar, Vinesh},
  title =	{{Computational Geometry with Probabilistically Noisy Primitive Operations}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{24:1--24:20},
  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.2025.24},
  URN =		{urn:nbn:de:0030-drops-242552},
  doi =		{10.4230/LIPIcs.WADS.2025.24},
  annote =	{Keywords: Computational geometry, noisy comparisons, random walks}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.22
Enumerating All Boolean Matches

Authors: Alexander Nadel and Yogev Shalmon

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

Abstract
Boolean matching, a fundamental problem in circuit design, determines whether two Boolean circuits are equivalent under input/output permutations and negations. While most works focus on finding a single match or proving its absence, the problem of enumerating all matches remains largely unexplored, with BooM being a notable exception. Motivated by timing challenges in Intel’s library mapping flow, we introduce EBat - an open-source tool for enumerating all matches between single-output circuits. Built from scratch, EBat reuses BooM’s SAT encoding and introduces novel high-level algorithms and performance-critical subroutines to efficiently identify and block multiple mismatches and matches simultaneously. Experiments demonstrate that EBat substantially outperforms BooM’s baseline algorithm, solving 3 to 4 times more benchmarks within a given time limit. EBat has been productized as part of Intel’s library mapping flow, effectively addressing the timing challenges.
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Alexander Nadel and Yogev Shalmon. Enumerating All Boolean Matches. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 22:1-22:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nadel_et_al:LIPIcs.SAT.2025.22,
  author =	{Nadel, Alexander and Shalmon, Yogev},
  title =	{{Enumerating All Boolean Matches}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{22:1--22:21},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-237568},
  doi =		{10.4230/LIPIcs.SAT.2025.22},
  annote =	{Keywords: Boolean Matching, All-Boolean-Matching, Enumeration, SAT, Generalization}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.28
Faster & Deterministic FPT Algorithm for Worst-Case Tensor Decomposition

Authors: Vishwas Bhargava and Devansh Shringi

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

Abstract
We present a deterministic 2^{k^{𝒪(1)}} poly(n,d) time algorithm for decomposing d-dimensional, width-n tensors of rank at most k over ℝ and ℂ. This improves upon the previous randomized algorithm of Peleg, Shpilka, and Volk (ITCS '24) that takes 2^{k^{k^{𝒪(k)}}} poly(n,d) time and the deterministic n^k^k time algorithms of Bhargava, Saraf, and Volkovich (STOC '21). Our work resolves an open question asked by Peleg, Shpilka, and Volk (ITCS '24) on whether a deterministic Fixed Parameter Tractable (FPT) algorithm exists for worst-case tensor decomposition. We also make substantial progress on the fundamental problem of how the tractability of tensor decomposition varies as the tensor rank increases. Our result implies that we can achieve deterministic polynomial-time decomposition as long as the rank of the tensor is at most (log n)^{1/C}, where C is some fixed constant independent of n and d. Further, we note that there cannot exist a polynomial-time algorithm for k = ω(log n) unless ETH fails. Our algorithm works for all fields; however, the time complexity worsens to 2^{k^{k^{𝒪(1)}}} and requires randomization for finite fields of large characteristics. Both conditions are provably necessary unless there are improvements in the state of the art for system solving over the corresponding fields. Our approach achieves this by designing a proper learning (reconstruction) algorithm for set-multilinear depth-3 arithmetic circuits. On a technical note, we design a "partial" clustering algorithm for set-multilinear depth-3 arithmetic circuits that lets us isolate a cluster from any set-multilinear depth-3 circuit while preserving the structure of the circuit.
Cite as

Vishwas Bhargava and Devansh Shringi. Faster & Deterministic FPT Algorithm for Worst-Case Tensor Decomposition. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhargava_et_al:LIPIcs.ICALP.2025.28,
  author =	{Bhargava, Vishwas and Shringi, Devansh},
  title =	{{Faster \& Deterministic FPT Algorithm for Worst-Case Tensor Decomposition}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{28:1--28:20},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-234052},
  doi =		{10.4230/LIPIcs.ICALP.2025.28},
  annote =	{Keywords: Algebraic circuits, Deterministic algorithms, FPT algorithm, Learning circuits, Reconstruction, Tensor Decomposition, Tensor Rank}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.100
Robust-Sorting and Applications to Ulam-Median

Authors: Ragesh Jaiswal, Amit Kumar, and Jatin Yadav

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

Abstract
Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However, many real-world sorting applications operate in scenarios where the outcome of each comparison can be noisy. In this work, we explore settings where a bounded number of comparisons are potentially corrupted by erroneous agents, resulting in arbitrary, adversarial outcomes. We model the sorting problem as a query-limited tournament graph where edges involving erroneous nodes may yield arbitrary results. Our primary contribution is a randomized algorithm inspired by quick-sort that, in expectation, produces an ordering close to the true total order while only querying Õ(n) edges. We achieve a distance from the target order π within (3 + ε)|B|, where B is the set of erroneous nodes, balancing the competing objectives of minimizing both query complexity and misalignment with π. Our algorithm needs to carefully balance two aspects - identify a pivot that partitions the vertex set evenly and ensure that this partition is "truthful" and yet query as few "triangles" in the graph G as possible. Since the nodes in B can potentially hide in an intricate manner, our algorithm requires several technical steps that ensure that progress is made in each recursive step. Additionally, we demonstrate significant implications for the Ulam-k-Median problem. This is a classical clustering problem where the metric is defined on the set of permutations on a set of d elements. Chakraborty, Das, and Krauthgamer gave a (2-ε) FPT approximation algorithm for this problem, where the running time is super-linear in both n and d. We give the first (2-ε) FPT linear time approximation algorithm for this problem. Our main technical result gives a strengthening of the results in Chakraborty et al. by showing that a good 1-median solution can be obtained from a constant-size random sample of the input. We use our robust sorting framework to find a good solution from such a random sample. We feel that the notion of robust sorting should have applications in several such settings.
Cite as

Ragesh Jaiswal, Amit Kumar, and Jatin Yadav. Robust-Sorting and Applications to Ulam-Median. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 100:1-100:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jaiswal_et_al:LIPIcs.ICALP.2025.100,
  author =	{Jaiswal, Ragesh and Kumar, Amit and Yadav, Jatin},
  title =	{{Robust-Sorting and Applications to Ulam-Median}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{100:1--100:19},
  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.2025.100},
  URN =		{urn:nbn:de:0030-drops-234774},
  doi =		{10.4230/LIPIcs.ICALP.2025.100},
  annote =	{Keywords: Sorting, clustering, query complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.12
Higher-Order Color Voronoi Diagrams and the Colorful Clarkson-Shor Framework

Authors: Sang Won Bae, Nicolau Oliver, and Evanthia Papadopoulou

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

Abstract
Given a set S of n colored sites, each s ∈ S associated with a distance-to-site function δ_s : ℝ² → ℝ, we consider two distance-to-color functions for each color: one takes the minimum of δ_s for sites s ∈ S in that color and the other takes the maximum. These two sets of distance functions induce two families of higher-order Voronoi diagrams for colors in the plane, namely, the minimal and maximal order-k color Voronoi diagrams, which include various well-studied Voronoi diagrams as special cases. In this paper, we derive an exact upper bound 4k(n-k)-2n on the total number of vertices in both the minimal and maximal order-k color diagrams for a wide class of distance functions δ_s that satisfy certain conditions, including the case of point sites S under convex distance functions and the L_p metric for any 1 ≤ p ≤ ∞. For the L_1 (or, L_∞) metric, and other convex polygonal metrics, we show that the order-k minimal diagram of point sites has O(min{k(n-k), (n-k)²}) complexity, while its maximal counterpart has O(min{k(n-k), k²}) complexity. To obtain these combinatorial results, we extend the Clarkson-Shor framework to colored objects, and demonstrate its application to several fundamental geometric structures, including higher-order color Voronoi diagrams, colored j-facets, and levels in the arrangements of piecewise linear/algebraic curves/surfaces. We also present iterative algorithms to compute higher-order color Voronoi diagrams.
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Sang Won Bae, Nicolau Oliver, and Evanthia Papadopoulou. Higher-Order Color Voronoi Diagrams and the Colorful Clarkson-Shor Framework. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bae_et_al:LIPIcs.SoCG.2025.12,
  author =	{Bae, Sang Won and Oliver, Nicolau and Papadopoulou, Evanthia},
  title =	{{Higher-Order Color Voronoi Diagrams and the Colorful Clarkson-Shor Framework}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.12},
  URN =		{urn:nbn:de:0030-drops-231647},
  doi =		{10.4230/LIPIcs.SoCG.2025.12},
  annote =	{Keywords: higher-order Voronoi diagrams, color Voronoi diagrams, Hausdorff Voronoi diagrams, colored j-facets, arrangements, Clarkson-Shor technique}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.7
Single-Source Shortest Path Problem in Weighted Disk Graphs

Authors: Shinwoo An, Eunjin Oh, and Jie Xue

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

Abstract
In this paper, we present efficient algorithms for the single-source shortest path problem in weighted disk graphs. A disk graph is the intersection graph of a family of disks in the plane. Here, the weight of an edge is defined as the Euclidean distance between the centers of the disks corresponding to the endpoints of the edge. Given a family of n disks in the plane whose radii lie in [1,Ψ] and a source disk, we can compute a shortest path tree from a source vertex in the weighted disk graph in O(nlog² n log Ψ) time. Moreover, in the case that the radii of disks are arbitrarily large, we can compute a shortest path tree from a source vertex in the weighted disk graph in O(nlog⁴ n) time. This improves the best-known algorithm running in O(nlog⁶ n) time presented in ESA'23.
Cite as

Shinwoo An, Eunjin Oh, and Jie Xue. Single-Source Shortest Path Problem in Weighted Disk Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{an_et_al:LIPIcs.SoCG.2025.7,
  author =	{An, Shinwoo and Oh, Eunjin and Xue, Jie},
  title =	{{Single-Source Shortest Path Problem in Weighted Disk Graphs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.7},
  URN =		{urn:nbn:de:0030-drops-231594},
  doi =		{10.4230/LIPIcs.SoCG.2025.7},
  annote =	{Keywords: Disk graphs, shortest path problem, compressed quadtrees}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.78
Efficient Greedy Discrete Subtrajectory Clustering

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

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

Abstract
We cluster a set of trajectories 𝒯 using subtrajectories of 𝒯. We require for a clustering C that any two subtrajectories (𝒯[a, b], 𝒯[c, d]) in a cluster have disjoint intervals [a,b] and [c, d]. Clustering quality may be measured by the number of clusters, the number of vertices of 𝒯 that are absent from the clustering, and by the Fréchet distance between subtrajectories in a cluster. A Δ-cluster of 𝒯 is a cluster 𝒫 of subtrajectories of 𝒯 with a centre P ∈ 𝒫, where all subtrajectories in 𝒫 have Fréchet distance at most Δ to P. Buchin, Buchin, Gudmundsson, Löffler and Luo present two O(n² + n m 𝓁)-time algorithms: SC(max, 𝓁, Δ, 𝒯) computes a single Δ-cluster where P has at least 𝓁 vertices and maximises the cardinality m of 𝒫. SC(m, max, Δ, 𝒯) computes a single Δ-cluster where 𝒫 has cardinality m and maximises the complexity 𝓁 of P. In this paper, which is a mixture of algorithms engineering and theoretical insights, we use such maximum-cardinality clusters in a greedy clustering algorithm. We first provide an efficient implementation of SC(max, 𝓁, Δ, 𝒯) and SC(m, max, Δ, 𝒯) that significantly outperforms previous implementations. Next, we use these functions as a subroutine in a greedy clustering algorithm, which performs well when compared to existing subtrajectory clustering algorithms on real-world data. Finally, we observe that, for fixed Δ and 𝒯, these two functions always output a point on the Pareto front of some bivariate function θ(𝓁, m). We design a new algorithm PSC(Δ, 𝒯) that in O(n² log⁴ n) time computes a 2-approximation of this Pareto front. This yields a broader set of candidate clusters, with comparable quality to the output of the previous functions. We show that using PSC(Δ, 𝒯) as a subroutine improves the clustering quality and performance even further.
Cite as

Ivor van der Hoog, Lara Ost, Eva Rotenberg, and Daniel Rutschmann. Efficient Greedy Discrete Subtrajectory Clustering. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanderhoog_et_al:LIPIcs.SoCG.2025.78,
  author =	{van der Hoog, Ivor and Ost, Lara and Rotenberg, Eva and Rutschmann, Daniel},
  title =	{{Efficient Greedy Discrete Subtrajectory Clustering}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{78:1--78:20},
  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.2025.78},
  URN =		{urn:nbn:de:0030-drops-232308},
  doi =		{10.4230/LIPIcs.SoCG.2025.78},
  annote =	{Keywords: Algorithms engineering, Fr\'{e}chet distance, subtrajectory clustering}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.37
Nearest Neighbor Searching in a Dynamic Simple Polygon

Authors: Sarita de Berg and Frank Staals

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

Abstract
In the nearest neighbor problem, we are given a set S of point sites that we want to store such that we can find the nearest neighbor of a (new) query point efficiently. In the dynamic version of the problem, the goal is to design a data structure that supports both efficient queries and updates, i.e. insertions and deletions in S. This problem has been widely studied in various settings, ranging from points in the plane to more general distance measures and even points within simple polygons. When the sites do not live in the plane but in some domain, another dynamic problem arises: what happens if not the sites, but the domain itself is subject to updates? Updating sites often results in local changes to the solution or data structure, while updating the domain may incur many global changes. For example, in the closest pair problem, inserting a point only requires us to check if this point is in the new closest pair, while updating the domain might change the distances between most pairs of points in our set. Presumably, this is the reason that this form of dynamization has received much less attention. Only some basic problems, such as shortest paths and ray shooting, have been studied in this setting. Here, we tackle the nearest neighbor problem in a dynamic simple polygon. We allow insertions into both the set of sites and the polygon. An insertion in the polygon is the addition of a line segment starting at the boundary of the polygon. We present a near-linear size -in both the number of sites and the complexity of the polygon- data structure with sublinear update and query time. This is the first nearest neighbor data structure that allows for updates to the domain.
Cite as

Sarita de Berg and Frank Staals. Nearest Neighbor Searching in a Dynamic Simple Polygon. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deberg_et_al:LIPIcs.SoCG.2025.37,
  author =	{de Berg, Sarita and Staals, Frank},
  title =	{{Nearest Neighbor Searching in a Dynamic Simple Polygon}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.37},
  URN =		{urn:nbn:de:0030-drops-231896},
  doi =		{10.4230/LIPIcs.SoCG.2025.37},
  annote =	{Keywords: dynamic data structure, simple polygon, geodesic distance, nearest neighbor}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.43
Approximating Densest Subgraph in Geometric Intersection Graphs

Authors: Sariel Har-Peled and Saladi Rahul

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
For an undirected graph 𝖦 = (𝖵, 𝖤), with n vertices and m edges, the densest subgraph problem, is to compute a subset S ⊆ 𝖵 which maximizes the ratio |𝖤_S|/|S|, where 𝖤_S ⊆ 𝖤 is the set of all edges of 𝖦 with endpoints in S. The densest subgraph problem is a well studied problem in computer science. Existing exact and approximation algorithms for computing the densest subgraph require Ω(m) time. We present near-linear time (in n) approximation algorithms for the densest subgraph problem on implicit geometric intersection graphs, where the vertices are explicitly given but not the edges. As a concrete example, we consider n disks in the plane with arbitrary radii and present two different approximation algorithms. As a by-product, we show a reduction from (shallow) range-reporting to approximate counting/sampling which seems to be new and is useful for other problems such as independent query sampling.
Cite as

Sariel Har-Peled and Saladi Rahul. Approximating Densest Subgraph in Geometric Intersection Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harpeled_et_al:LIPIcs.STACS.2025.43,
  author =	{Har-Peled, Sariel and Rahul, Saladi},
  title =	{{Approximating Densest Subgraph in Geometric Intersection Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{43:1--43:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.43},
  URN =		{urn:nbn:de:0030-drops-228697},
  doi =		{10.4230/LIPIcs.STACS.2025.43},
  annote =	{Keywords: Geometric intersection graphs, Densest subgraph, Range searching, Approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.96
Formulations and Constructions of Remote State Preparation with Verifiability, with Applications

Authors: Jiayu Zhang

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
Remote state preparation with verifiability (RSPV) is an important quantum cryptographic primitive [Alexandru Gheorghiu and Thomas Vidick, 2019; Jiayu Zhang, 2022]. In this primitive, a client would like to prepare a quantum state (sampled or chosen from a state family) on the server side, such that ideally the client knows its full description, while the server holds and only holds the state itself. In this work we make several contributions on its formulations, constructions and applications. In more detail: - We first work on the definitions and abstract properties of the RSPV problem. We select and compare different variants of definitions [Bennett et al., 2001; Alexandru Gheorghiu and Thomas Vidick, 2019; Jiayu Zhang, 2022; Alexandru Gheorghiu et al., 2022], and study their basic properties (like composability and amplification). - We also study a closely related question of how to certify the server’s operations (instead of solely the states). We introduce a new notion named remote operator application with verifiability (ROAV). We compare this notion with related existing definitions [Summers and Werner, 1987; Dominic Mayers and Andrew Chi-Chih Yao, 2004; Zhengfeng Ji et al., 2021; Tony Metger and Thomas Vidick, 2021; Anand Natarajan and Tina Zhang, 2023], study its abstract properties and leave its concrete constructions for further works. - Building on the abstract properties and existing results [Zvika Brakerski et al., 2023], we construct a series of new RSPV protocols. Our constructions not only simplify existing results [Alexandru Gheorghiu and Thomas Vidick, 2019] but also cover new state families, for example, states in the form of 1/√2 (|0⟩ + |x_0⟩ + |1⟩ |x_1⟩). All these constructions rely only on the existence of weak NTCF [Zvika Brakerski et al., 2020; Navid Alamati et al., 2022], without additional requirements like the adaptive hardcore bit property [Zvika Brakerski et al., 2018; Navid Alamati et al., 2022]. - As a further application, we show that the classical verification of quantum computations (CVQC) problem [Dorit Aharonov et al., 2010; Urmila Mahadev, 2018] could be constructed from assumptions on group actions [Navid Alamati et al., 2020]. This is achieved by combining our results on RSPV with group-action-based instantiation of weak NTCF [Navid Alamati et al., 2022], and then with the quantum-gadget-assisted quantum verification protocol [Ferracin et al., 2018].
Cite as

Jiayu Zhang. Formulations and Constructions of Remote State Preparation with Verifiability, with Applications. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 96:1-96:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang:LIPIcs.ITCS.2025.96,
  author =	{Zhang, Jiayu},
  title =	{{Formulations and Constructions of Remote State Preparation with Verifiability, with Applications}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{96:1--96:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.96},
  URN =		{urn:nbn:de:0030-drops-227245},
  doi =		{10.4230/LIPIcs.ITCS.2025.96},
  annote =	{Keywords: Quantum Cryptography, Remote State Preparation, Self-testing, Verification of Quantum Computations}
}
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