62 Search Results for "Roditty, Liam"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.121
Faster Algorithms for (2k-1)-Stretch Distance Oracles

Authors: Avi Kadria and Liam Roditty

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
The seminal distance oracles of Thorup and Zwick [STOC 2001, JACM 2005] provide optimal stretch/space tradeoffs. However, their O(mn^{1/k}) construction time is not optimal, and they posed the question of whether a faster construction time is possible (especially for small k). In this paper, we present the first improvement upon their construction algorithm in graphs that are not super sparse, i.e., when m = Ω(n^{1+1/k+ε}), for any ε > 0. Moreover, our construction improves upon the O(n²)-time construction of Baswana and Kavitha [FOCS 2006, SICOMP 2010], for every k > 2. By achieving the first subquadratic construction for 2 < k < 6, we resolve the open problem posed by Wulff-Nilsen [SODA 2012] of whether such subquadratic-time constructions exist. Wulff-Nilsen [SODA 2012] targeted nearly linear construction times and presented algorithms running in Õ(m + n^{1+f(k)}) time, which is near-linear whenever the graph density m exceeds the threshold n^{1+f(k)}. We obtain improved bounds on f(k) for all k > 3, and thus expand the regime of graph densities for which nearly linear construction times are achievable. In addition, for unweighted graphs, we present several new algorithms for constructing (2k - 1,β)-oracles that improve upon the results of Baswana, Gaur, Sen, and Upadhyay [ICALP 2008]. Our results are achieved through the development of several new algorithmic tools, which may be of independent interest. One of our main technical contributions is a hierarchy of parameterized distance oracles, which plays a central role in our fast construction algorithms.
Cite as

Avi Kadria and Liam Roditty. Faster Algorithms for (2k-1)-Stretch Distance Oracles. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 121:1-121:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kadria_et_al:LIPIcs.ICALP.2026.121,
  author =	{Kadria, Avi and Roditty, Liam},
  title =	{{Faster Algorithms for (2k-1)-Stretch Distance Oracles}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{121:1--121:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.121},
  URN =		{urn:nbn:de:0030-drops-265105},
  doi =		{10.4230/LIPIcs.ICALP.2026.121},
  annote =	{Keywords: Fine-grained complexity, Graph algorithms, shortest cycle, girth approximations}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.127
New Diameter Approximations via Distance Oracle Techniques

Authors: Yael Kirkpatrick, Liam Roditty, Richard Qi, and Virginia Vassilevska Williams

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
Computing the diameter of a graph is a problem of great interest both in general algorithms research and specifically within fine-grained complexity, where it is a cornerstone hard problem. As computing the exact diameter in m-edge graphs requires m^{2-o(1)} time under the Strong Exponential Time Hypothesis, much work has gone into approximating this parameter. Recent work has achieved a full conditional lower bound tradeoff curve for both directed and undirected graphs [Dalirrooyfard, Li and Vassilevska W., FOCS'21]. However, the best known upper bounds do not match the lower bounds. In particular, the best known approximation scheme for undirected graph diameter [Cairo-Grossi-Rizzi, SODA 2016] has not been improved. Moreover, this scheme is randomized and no similar deterministic scheme is known. Another fundamental field of research in shortest paths computation is the construction of approximate distance oracles. Thorup and Zwick [JACM'05] provided the first such distance oracle with constant query time and (conditionally) optimal space, and in the years since many advances have led to a vast toolbox of techniques and data structures. These two areas of research seem natural to combine since they both concern approximating shortest paths. However, the known diameter approximation algorithms only use a small subset of the techniques used in distance oracles research. In this work we show that in fact approximate diameter and distance oracles are intricately connected. We first demonstrate a strong connection between the current best known diameter approximation scheme of Cairo, Grossi and Rizzi ("CGR") and the (2k-1)-approximate distance oracle of Thorup and Zwick. This allows us to derandomize the CGR algorithm and obtain the first deterministic diameter approximation tradeoff. We further derandomize other central techniques in the field of distance oracles and use them to achieve new deterministic diameter approximation algorithms, including a simpler 3/2-approximation with no additive error and a new 5/3-approximation, the first new step in the diameter approximation tradeoff in almost a decade. Finally, we show how these new techniques can be used to derandomize many current best known results in various fields of shortest paths approximations.
Cite as

Yael Kirkpatrick, Liam Roditty, Richard Qi, and Virginia Vassilevska Williams. New Diameter Approximations via Distance Oracle Techniques. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 127:1-127:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kirkpatrick_et_al:LIPIcs.ICALP.2026.127,
  author =	{Kirkpatrick, Yael and Roditty, Liam and Qi, Richard and Vassilevska Williams, Virginia},
  title =	{{New Diameter Approximations via Distance Oracle Techniques}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{127:1--127:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.127},
  URN =		{urn:nbn:de:0030-drops-265169},
  doi =		{10.4230/LIPIcs.ICALP.2026.127},
  annote =	{Keywords: Graph Algorithms, Diameter, Distance Oracle, Approximation Algorithm}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.8
General Multiplicative Spanners in Practice

Authors: Fritz Bökler, Markus Chimani, and Henning Jasper

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

Abstract
Given an undirected graph G with edge weights and lengths, a minimum α-spanner is a least-weight subgraph H ⊆ G that preserves distances w.r.t. the lengths between all node pairs up to a factor of α. Literature often takes the simplifying assumption of a single (coupled) edge function for weights and lengths. For such instances, several exact and non-exact algorithms are known and have been thoroughly evaluated in practice. However, many practical instances have decoupled form, as their weights and lengths are generally independent. Due to the increased complexity, only few (and even fewer practical) algorithms are able to guarantee low-weight solutions. This prompts practitioners to force their naturally decoupled instances into a coupled format, forsaking any quality guarantee. We implement several exact, approximative and heuristic algorithms for decoupled α-spanners, and use algorithm engineering to speed them up in practice. Our hypothesis-driven experiments evaluate their performance w.r.t. solution quality and speed. Generally, many practical instances can indeed be solved exactly within reasonable time, while LP-based approximation algorithms are not worthwhile. We find that standard greedy algorithms often yield acceptable results, but there are also practical instances for which they yield arbitrarily poor solutions. Here, augmented greedy variations offer a good compromise between solution quality and speed.
Cite as

Fritz Bökler, Markus Chimani, and Henning Jasper. General Multiplicative Spanners in Practice. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bokler_et_al:LIPIcs.SEA.2026.8,
  author =	{B\"{o}kler, Fritz and Chimani, Markus and Jasper, Henning},
  title =	{{General Multiplicative Spanners in Practice}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{8:1--8:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.8},
  URN =		{urn:nbn:de:0030-drops-260120},
  doi =		{10.4230/LIPIcs.SEA.2026.8},
  annote =	{Keywords: Graph spanners, ILP, experimental study, algorithm engineering}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.38
New Algorithms for Girth and Cycle Detection

Authors: Liam Roditty and Plia Trabelsi

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
Let G = (V,E) be an unweighted undirected graph with n vertices and m edges. Let g be the girth of G, that is, the length of a shortest cycle in G. We present a randomized algorithm with a running time of Õ(𝓁 ⋅ n^{1 + 1/(𝓁-ε)}) that returns a cycle of length at most 2𝓁 ⌈g/2⌉ - 2 ⌊ε⌈g/2⌉⌋, where 𝓁 ≥ 2 is an integer and ε ∈ [0,1], for every graph with g = polylog(n). Our algorithm generalizes an algorithm of Kadria et al. [SODA'22] that computes a cycle of length at most 4 ⌈g/2⌉ - 2 ⌊ε⌈g/2⌉⌋ in Õ(n^{1 + 1/(2 - ε)}) time. Kadria et al. presented also an algorithm that finds a cycle of length at most 2𝓁 ⌈g/2⌉ in Õ(n^{1 + 1/(𝓁)}) time, where 𝓁 must be an integer. Our algorithm generalizes this algorithm, as well, by replacing the integer parameter 𝓁 in the running time exponent with a real-valued parameter 𝓁 - ε, thereby offering greater flexibility in parameter selection and enabling a broader spectrum of combinations between running times and cycle lengths. We also show that for sparse graphs a better tradeoff is possible, by presenting an Õ(𝓁⋅ m^{1+ 1/(𝓁-ε)}) time randomized algorithm that returns a cycle of length at most 2𝓁(⌊(g-1)/2⌋) - 2(⌊ε⌊(g-1)/2⌋⌋+1), where 𝓁 ≥ 3 is an integer and ε ∈ [0,1), for every graph with g = polylog(n). To obtain our algorithms we develop several techniques and introduce a formal definition of hybrid cycle detection algorithms. Both may prove useful in broader contexts, including other cycle detection and approximation problems. Among our techniques is a new cycle searching technique, in which we search for a cycle from a given vertex and possibly all its neighbors in linear time. Using this technique together with more ideas we develop two hybrid algorithms. The first allows us to obtain an Õ(m^{2-2/(⌈g/2⌉+1))-time, (+1)-approximation of g. The second is used to obtain our Õ(𝓁⋅ n^{1+ 1/(𝓁-ε)})-time and Õ(𝓁⋅ m^{1+ 1/(𝓁-ε)})-time approximation algorithms.
Cite as

Liam Roditty and Plia Trabelsi. New Algorithms for Girth and Cycle Detection. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{roditty_et_al:LIPIcs.SWAT.2026.38,
  author =	{Roditty, Liam and Trabelsi, Plia},
  title =	{{New Algorithms for Girth and Cycle Detection}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.38},
  URN =		{urn:nbn:de:0030-drops-260742},
  doi =		{10.4230/LIPIcs.SWAT.2026.38},
  annote =	{Keywords: Graph algorithms, All pairs shortest path, Girth, Cycle approximation}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.17
Incremental Strongly Connected Components with Predictions

Authors: Ronald Deng, Samuel McCauley, Aidin Niaparast, Helia Niaparast, Bennett Ptak, Shirel Quintanilla, Shikha Singh, and Nathan Vosburg

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
Algorithms with predictions is a growing area that aims to leverage machine-learned predictions to design faster beyond-worst-case algorithms. In this paper, we use this framework to design a learned data structure for the incremental strongly connected components (SCC) problem. In this problem, the n vertices of a graph are known a priori and the m directed edges arrive over time. The goal is to efficiently maintain the strongly connected components of the graph after each insert. Our algorithm receives a possibly erroneous prediction of the edge sequence and uses it to precompute partial solutions to support fast inserts. We show that our algorithm achieves nearly optimal bounds with good predictions and its performance smoothly degrades with the prediction error. We also implement our data structure and perform experiments on real datasets. Our empirical results show that the theory is predictive of practical runtime improvements.
Cite as

Ronald Deng, Samuel McCauley, Aidin Niaparast, Helia Niaparast, Bennett Ptak, Shirel Quintanilla, Shikha Singh, and Nathan Vosburg. Incremental Strongly Connected Components with Predictions. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{deng_et_al:LIPIcs.SWAT.2026.17,
  author =	{Deng, Ronald and McCauley, Samuel and Niaparast, Aidin and Niaparast, Helia and Ptak, Bennett and Quintanilla, Shirel and Singh, Shikha and Vosburg, Nathan},
  title =	{{Incremental Strongly Connected Components with Predictions}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.17},
  URN =		{urn:nbn:de:0030-drops-260530},
  doi =		{10.4230/LIPIcs.SWAT.2026.17},
  annote =	{Keywords: algorithms with predictions, learning augmented algorithms, incremental graph algorithms, strongly connected components, data structures}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.20
Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs

Authors: Jie Gao, Paweł Gawrychowski, Panos Giannopoulos, Wolfgang Mulzer, Satyam Singh, Frank Staals, and Meirav Zehavi

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
A disk graph is the intersection graph of (closed) disks in the plane. We consider the classic problem of finding a maximum clique in a disk graph. For general disk graphs, the complexity of this problem is still open, but for unit disk graphs, it is well known to be in P. The currently fastest algorithm runs in time O(n^{7/3+ o(1)}), where n denotes the number of disks [Jared Espenant et al., 2023; J. Mark Keil and Debajyoti Mondal, 2025]. Moreover, for the case of disk graphs with t distinct radii, the problem has also recently been shown to be in XP. More specifically, it is solvable in time O^*(n^{2t}) [J. Mark Keil and Debajyoti Mondal, 2025]. In this paper, we present algorithms with improved running times by allowing for approximate solutions and by using randomization: [(i)] 1) for unit disk graphs, we give an algorithm that, with constant success probability, computes a (1-ε)-approximate maximum clique in expected time Õ(n/ε²); and 2) for disk graphs with t distinct radii, we give a parameterized approximation scheme that, with a constant success probability, computes a (1-ε)-approximate maximum clique in expected time Õ(f(t)⋅ (1/ε)^{O(t)} ⋅ n), for some (exponential) function f(t).
Cite as

Jie Gao, Paweł Gawrychowski, Panos Giannopoulos, Wolfgang Mulzer, Satyam Singh, Frank Staals, and Meirav Zehavi. Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gao_et_al:LIPIcs.SWAT.2026.20,
  author =	{Gao, Jie and Gawrychowski, Pawe{\l} and Giannopoulos, Panos and Mulzer, Wolfgang and Singh, Satyam and Staals, Frank and Zehavi, Meirav},
  title =	{{Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.20},
  URN =		{urn:nbn:de:0030-drops-260563},
  doi =		{10.4230/LIPIcs.SWAT.2026.20},
  annote =	{Keywords: Maximum Clique, Disk Graphs, Unit Disk Graphs, FPT Approximation}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.36
Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates

Authors: Seongbin Park and Eunjin Oh

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
In this paper, we study the many-to-many matching problem on planar point sets with integer coordinates: Given two disjoint sets R,B ⊂ [Δ]² with |R|+|B| = n, the goal is to select a set of edges between R and B so that every point is incident to at least one edge and the total Euclidean length is minimized. In the general case that R and B are point sets in the plane, the best-known algorithm for the many-to-many matching problem takes Õ(n²) time. We present an exact Õ(n^{1.5} log Δ) time algorithm for point sets in [Δ]². To the best of our knowledge, this is the first subquadratic exact algorithm for planar many-to-many matching under bounded integer coordinates.
Cite as

Seongbin Park and Eunjin Oh. Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{park_et_al:LIPIcs.SWAT.2026.36,
  author =	{Park, Seongbin and Oh, Eunjin},
  title =	{{Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{36:1--36:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.36},
  URN =		{urn:nbn:de:0030-drops-260728},
  doi =		{10.4230/LIPIcs.SWAT.2026.36},
  annote =	{Keywords: Edge cover, many-to-many matching, similarity, geometric matching}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.23
Shortest Paths in Geodesic Unit-Disk Graphs

Authors: Bruce W. Brewer and Haitao Wang

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

Abstract
Let S be a set of n points in a polygon P with m vertices. The geodesic unit-disk graph G(S) induced by S has vertex set S and contains an edge between two vertices whenever their geodesic distance in P is at most one. In the weighted version, each edge is assigned weight equal to the geodesic distance between its endpoints; in the unweighted version, every edge has weight 1. Given a source point s ∈ S, we study the problem of computing shortest paths from s to all vertices of G(S). To the best of our knowledge, this problem has not been investigated previously. A naive approach constructs G(S) explicitly and then applies a standard shortest path algorithm for general graphs, but this requires quadratic time in the worst case, since G(S) may contain Ω(n²) edges. In this paper, we give the first subquadratic-time algorithms for this problem. For the weighted case, when P is a simple polygon, we obtain an O(m + n log³ n log² m)-time algorithm. For the unweighted case, we provide an O(m + n log n log² m)-time algorithm for simple polygons, and an O(√n (n+m)log(n+m))-time algorithm for polygons with holes.
Cite as

Bruce W. Brewer and Haitao Wang. Shortest Paths in Geodesic Unit-Disk Graphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{brewer_et_al:LIPIcs.SoCG.2026.23,
  author =	{Brewer, Bruce W. and Wang, Haitao},
  title =	{{Shortest Paths in Geodesic Unit-Disk Graphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.23},
  URN =		{urn:nbn:de:0030-drops-258297},
  doi =		{10.4230/LIPIcs.SoCG.2026.23},
  annote =	{Keywords: unit-disk graph, geodesic distance, shortest paths, geodesic Voronoi diagrams, range emptiness queries, dynamic data structures}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.29
Charting the Diameter Computation Landscape of Intersection Graphs in 3D and Above

Authors: Timothy M. Chan, Hsien-Chih Chang, Jie Gao, Sándor Kisfaludi-Bak, Hung Le, and Da Wei Zheng

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

Abstract
Recent research on computing the diameter of geometric intersection graphs has made significant strides, primarily focusing on the 2D case [Duraj et al., 2024; Hsien-Chih Chang et al., 2024; Chan et al., 2025] where truly subquadratic-time algorithms were given for simple objects such as unit-disks and (axis-aligned) squares. However, in three or higher dimensions, there is no known truly subquadratic-time algorithm for any intersection graph of non-trivial objects, even basic ones such as unit balls or (axis-aligned) unit cubes. This was partially explained by the pioneering work of Bringmann et al. [Karl Bringmann et al., 2022] which gave several truly subquadratic lower bounds, notably for unit balls or unit cubes in 3D when the graph diameter Δ is at least Ω(log n), hinting at a pessimistic outlook for the complexity of the diameter problem in higher dimensions. In this paper, we substantially extend the landscape of diameter computation for objects in three and higher dimensions, giving a few positive results. Our highlighted findings include: 1) A truly subquadratic-time algorithm for deciding if the diameter of unit cubes in 3D is at most 3 (Diameter-3 hereafter), the first algorithm of its kind for objects in 3D or higher dimensions. Our algorithm is based on a novel connection to pseudolines, which is of independent interest. 2) A truly subquadratic time lower bound for Diameter-3 of unit balls in 3D under the Orthogonal Vector (OV) hypothesis, giving the first separation between unit balls and unit cubes in the small diameter regime. Previously, computing the diameter for both objects was known to be quadratic hard when the diameter is Ω(log n) [Karl Bringmann et al., 2022]. 3) A near-linear-time algorithm for Diameter-2 of unit cubes in 3D, generalizing the previous result for unit squares in 2D [Karl Bringmann et al., 2022]. 4) A truly subquadratic-time algorithm and lower bound for Diameter-2 and Diameter-3 of rectangular boxes (of arbitrary dimension and sizes), respectively.
Cite as

Timothy M. Chan, Hsien-Chih Chang, Jie Gao, Sándor Kisfaludi-Bak, Hung Le, and Da Wei Zheng. Charting the Diameter Computation Landscape of Intersection Graphs in 3D and Above. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chan_et_al:LIPIcs.SoCG.2026.29,
  author =	{Chan, Timothy M. and Chang, Hsien-Chih and Gao, Jie and Kisfaludi-Bak, S\'{a}ndor and Le, Hung and Zheng, Da Wei},
  title =	{{Charting the Diameter Computation Landscape of Intersection Graphs in 3D and Above}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.29},
  URN =		{urn:nbn:de:0030-drops-258357},
  doi =		{10.4230/LIPIcs.SoCG.2026.29},
  annote =	{Keywords: Graph Diameter, Geometric Intersection Graphs, Unit Ball Graphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.30
Computing the Girth of a Segment Intersection Graph

Authors: Timothy M. Chan and Yuancheng Yu

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

Abstract
We present an algorithm that computes the girth of the intersection graph of n given line segments in the plane in O(n^1.483) expected time. This is the first such algorithm with O(n^{3/2-ε}) running time for a positive constant ε, and makes progress towards an open question posed by Chan (SODA 2023). The main techniques include (i) the usage of recent subcubic algorithms for bounded-difference min-plus matrix multiplication, and (ii) an interesting variant of the planar graph separator theorem. The result extends to intersection graphs of connected algebraic curves or semialgebraic sets of constant description complexity.
Cite as

Timothy M. Chan and Yuancheng Yu. Computing the Girth of a Segment Intersection Graph. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chan_et_al:LIPIcs.SoCG.2026.30,
  author =	{Chan, Timothy M. and Yu, Yuancheng},
  title =	{{Computing the Girth of a Segment Intersection Graph}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{30:1--30:16},
  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.2026.30},
  URN =		{urn:nbn:de:0030-drops-258364},
  doi =		{10.4230/LIPIcs.SoCG.2026.30},
  annote =	{Keywords: Geometric intersection graphs, girth, shortest paths, graph separators, matrix multiplication}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.65
Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces

Authors: Sándor Kisfaludi-Bak and Geert van Wordragen

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

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

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

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@InProceedings{kisfaludibak_et_al:LIPIcs.SoCG.2026.65,
  author =	{Kisfaludi-Bak, S\'{a}ndor and van Wordragen, Geert},
  title =	{{Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{65:1--65:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.65},
  URN =		{urn:nbn:de:0030-drops-258728},
  doi =		{10.4230/LIPIcs.SoCG.2026.65},
  annote =	{Keywords: hyperbolic geometry, Steiner spanner, dynamic approximate nearest neighbours}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.69
Approximate Dynamic Nearest Neighbor Searching in a Polygonal Domain

Authors: Joost van der Laan, Frank Staals, and Lorenzo Theunissen

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

Abstract
We present efficient data structures for approximate nearest neighbor searching and approximate 2-point shortest path queries in a two-dimensional polygonal domain P with n vertices. Our goal is to store a dynamic set of m point sites S in P so that we can efficiently find a site s ∈ S closest to an arbitrary query point q. We will allow both insertions and deletions in the set of sites S. However, as even just computing the distance between an arbitrary pair of points q,s ∈ P requires a substantial amount of space, we allow for approximating the distances. Given a parameter ε > 0, we build an O(n/(ε)log n) space data structure that can compute a 1+ε-approximation of the distance between q and s in O((1/ε²)log n) time. Building on this, we then obtain an O((n+m)/ε log n + m/ε log m) space data structure that allows us to report a site s ∈ S so that the distance between query point q and s is at most (1+ε)-times the distance between q and its true nearest neighbor in O((1/ε²)log n + 1/(ε)log n log m + (1/ε)log² m) time. Our data structure supports updates in O((1/ε²)log n + (1/ε)log n log m + (1/ε)log² m) amortized time.
Cite as

Joost van der Laan, Frank Staals, and Lorenzo Theunissen. Approximate Dynamic Nearest Neighbor Searching in a Polygonal Domain. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 69:1-69:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{vanderlaan_et_al:LIPIcs.SoCG.2026.69,
  author =	{van der Laan, Joost and Staals, Frank and Theunissen, Lorenzo},
  title =	{{Approximate Dynamic Nearest Neighbor Searching in a Polygonal Domain}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{69:1--69:16},
  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.2026.69},
  URN =		{urn:nbn:de:0030-drops-258769},
  doi =		{10.4230/LIPIcs.SoCG.2026.69},
  annote =	{Keywords: dynamic data structure, nearest neighbor search, polygonal domain}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.12
Dynamic and Streaming Algorithms for Union Volume Estimation

Authors: Sujoy Bhore, Karl Bringmann, Timothy M. Chan, and Yanheng Wang

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

Abstract
The union volume estimation problem asks to (1±ε)-approximate the volume of the union of n given objects X₁,…,X_n ⊂ ℝ^d. In their seminal work in 1989, Karp, Luby, and Madras solved this problem in time O(n/ε²) in an oracle model where each object X_i can be accessed via three types of queries: obtain the volume of X_i, sample a random point from X_i, and test whether X_i contains a given point x. This running time was recently shown to be optimal [Bringmann, Larsen, Nusser, Rotenberg, and Wang, SoCG'25]. In another line of work, Meel, Vinodchandran, and Chakraborty [PODS'21] designed algorithms that read the objects in one pass using polylogarithmic time per object and polylogarithmic space; this can be phrased as a dynamic algorithm supporting insertions of objects for union volume estimation in the oracle model. In this paper, we study algorithms for union volume estimation in the oracle model that support both insertions and deletions of objects. We obtain the following results: 1) an algorithm supporting insertions and deletions in polylogarithmic update and query time and linear space (this is the first such dynamic algorithm, even for 2D triangles); 2) an algorithm supporting insertions and suffix queries (which generalizes the sliding window setting) in polylogarithmic update and query time and space; 3) an algorithm supporting insertions and deletions of convex bodies of constant dimension in polylogarithmic update and query time and space.
Cite as

Sujoy Bhore, Karl Bringmann, Timothy M. Chan, and Yanheng Wang. Dynamic and Streaming Algorithms for Union Volume Estimation. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhore_et_al:LIPIcs.SoCG.2026.12,
  author =	{Bhore, Sujoy and Bringmann, Karl and Chan, Timothy M. and Wang, Yanheng},
  title =	{{Dynamic and Streaming Algorithms for Union Volume Estimation}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.12},
  URN =		{urn:nbn:de:0030-drops-258180},
  doi =		{10.4230/LIPIcs.SoCG.2026.12},
  annote =	{Keywords: union volume estimation, dynamic algorithms, streaming algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.13
Dynamic Light Spanners in Doubling Metrics

Authors: Sujoy Bhore, Jonathan Conroy, and Arnold Filtser

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

Abstract
A t-spanner of a point set X in a metric space (𝒳, δ) is a graph G with vertex set P such that, for any pair of points u,v ∈ X, the distance between u and v in G is at most t times δ(u,v). We study the problem of maintaining a spanner for a dynamic point set X - that is, when X undergoes a sequence of insertions and deletions - in a metric space of constant doubling dimension. For any constant ε > 0, we maintain a (1+ε)-spanner of P whose total weight remains within a constant factor of the weight of the minimum spanning tree of X. Each update (insertion or deletion) can be performed in poly(log Φ) time, where Φ denotes the aspect ratio of X. Prior to our work, no efficient dynamic algorithm for maintaining a light-weight spanner was known even for point sets in low-dimensional Euclidean space.
Cite as

Sujoy Bhore, Jonathan Conroy, and Arnold Filtser. Dynamic Light Spanners in Doubling Metrics. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhore_et_al:LIPIcs.SoCG.2026.13,
  author =	{Bhore, Sujoy and Conroy, Jonathan and Filtser, Arnold},
  title =	{{Dynamic Light Spanners in Doubling Metrics}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{13:1--13:16},
  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.2026.13},
  URN =		{urn:nbn:de:0030-drops-258193},
  doi =		{10.4230/LIPIcs.SoCG.2026.13},
  annote =	{Keywords: Dynamic data structures, spanners, light-weight, Euclidean metrics, doubling metrics}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2026.9
Acyclic Join Sampling Under Selections: Dichotomy, Union Sampling, and Enumeration

Authors: Jinchao Huang, Yufei Tao, and Sibo Wang

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
Previous research on join sampling has focused on joins without selection conditions, even though such conditions are prevalent in everyday queries in database systems. Motivated by this, we undertake a systematic investigation on the complexity of sampling from the result of an acyclic join under equality conditions given only at runtime. When conditions are conjunctive, the goal is to understand when it is possible to precompute a feasible structure that uses Õ(IN) space and supports sampling in Õ(1) time, where IN is the input size. We present a dichotomy to characterize (subject to a widely-accepted conjecture) the existence of such structures based on the conditions supplied and, in every feasible scenario, give an optimal structure of O(IN) space and O(1) sample time. We then extend our investigation to conditions expressed in disjunctive normal form, where the core challenge reduces to the fundamental set union sampling problem. We overcome the challenge with an optimal algorithm and utilize it to develop optimal sampling structures. Our findings also lead to new results on the closely-related random enumeration problem.
Cite as

Jinchao Huang, Yufei Tao, and Sibo Wang. Acyclic Join Sampling Under Selections: Dichotomy, Union Sampling, and Enumeration. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{huang_et_al:LIPIcs.ICDT.2026.9,
  author =	{Huang, Jinchao and Tao, Yufei and Wang, Sibo},
  title =	{{Acyclic Join Sampling Under Selections: Dichotomy, Union Sampling, and Enumeration}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.9},
  URN =		{urn:nbn:de:0030-drops-256231},
  doi =		{10.4230/LIPIcs.ICDT.2026.9},
  annote =	{Keywords: Conjunctive Queries, Acyclic Joins, Sampling, Lower Bounds}
}
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