74 Search Results for "Le, Hung"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.40
Fast Shortest Path in Graphs with Sparse Signed Tree Models and Applications

Authors: Édouard Bonnet, Colin Geniet, Eun Jung Kim, and Sungmin Moon

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

Abstract
A signed tree model of a graph G is a compact binary structure consisting of a rooted binary tree whose leaves are bijectively mapped to the vertices of G, together with 2-colored edges xy, called transversal pairs, interpreted as bicliques or anti-bicliques whose sides are the leaves of the subtrees rooted at x and at y. We design an algorithm that, given such a representation of an unweighted n-vertex graph G with p transversal pairs, and given a source v ∈ V(G), computes a shortest-path tree rooted at v in G in time O(p log n). A wide variety of graph classes are such that for all n, their n-vertex graphs admit signed tree models with O(n) transversal pairs: for instance, those of bounded symmetric difference (hence, in particular, those of bounded flip-width, merge-width, twin-width, and degeneracy), more generally of bounded sd-degeneracy, as well as interval graphs. As applications of our Single-Source Shortest Path algorithm and new techniques, we - improve the runtime of the fixed-parameter algorithm for first-order model checking on graphs given with a witness of low merge-width from cubic [Dreier & Toruńczyk, STOC '25] to quadratic; - give an O(n² log n)-time algorithm for All-Pairs Shortest Path on graphs given with a witness of low merge-width, generalizing a result known for twin-width [Twin-Width III, SICOMP '24]; - significantly extend and simplify an O(n² log n)-time algorithm for multiplying two n × n matrices A, B of bounded twin-width in [Twin-Width V, STACS '23]: now A solely has to be an adjacency matrix of a graph of bounded twin-width and B can be arbitrary; - give an O(n² log² n)-time algorithm for All-Pairs Shortest Path on graphs of bounded twin-width, bypassing the need for contraction sequences in [Twin-Width III, SICOMP '24; Bannach et al. STACS '24]; - give an O(n^{7/3} log² n)-time algorithm for All-Pairs Shortest Path on graphs of symmetric difference O(n^{1/3}). The second and the last two items imply the same for Diameter, Radius, Eccentricity, Wiener Index, etc. The last three items do not assume any witness to be given as part of the input.
Cite as

Édouard Bonnet, Colin Geniet, Eun Jung Kim, and Sungmin Moon. Fast Shortest Path in Graphs with Sparse Signed Tree Models and Applications. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 40:1-40:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bonnet_et_al:LIPIcs.ICALP.2026.40,
  author =	{Bonnet, \'{E}douard and Geniet, Colin and Kim, Eun Jung and Moon, Sungmin},
  title =	{{Fast Shortest Path in Graphs with Sparse Signed Tree Models and Applications}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{40:1--40:23},
  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.2026.40},
  URN =		{urn:nbn:de:0030-drops-264297},
  doi =		{10.4230/LIPIcs.ICALP.2026.40},
  annote =	{Keywords: Shortest path, tree model, twin-width, merge-width, symmetric difference}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.54
Charting the Landscape of Diameter Computation on Geometric Intersection Graphs in the Plane

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

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

Abstract
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in 2D, the problem is solvable in truly subquadratic time [Chan et al., 2025], while for other objects, including unit segments and equilateral triangles in 2D or unit balls and axis-parallel unit cubes in 3D, there is no truly subquadratic time algorithm under the Orthogonal Vector (OV) hypothesis [Bringmann et al., 2022]. We undertake a comprehensive study of computing the diameter of geometric intersection graphs for various types of objects. We discover many new irregularities, showing that the landscape is extremely nuanced: the source of hardness is a combination of the object type, the true diameter value, and how the objects intersect with each other. Our highlighted results for the 2D case include: 1) The diameter of non-degenerate, axis-aligned line segments can be computed in truly subquadratic time. Previous hardness result [Bringmann et al., 2022] for line segments applies only to degenerate instances. On the other hand, for the degenerate case, we show that a truly subquadratic time algorithm exists when the true diameter is constant. 2) An almost-linear-time algorithm for unit-square graphs of constant diameter. Previous algorithms [Duraj et al., 2024; Chan et al., 2025] rely on succinct representation assuming bounded VC-dimension; for such a strategy Ω(n^{7/4}) time is an inherent barrier. 3) An Õ(n^{4/3})-time algorithm to decide if the diameter of a unit-disk graph is at most 2. This improves upon the recent algorithm with running time Õ(n^{2-1/9}) [Chan et al., 2025]. 4) Deciding if the diameter of intersection graphs of fat triangles or line segments is at most 2 is truly subquadratic-hard under fine-grained complexity assumptions. Previous lower bounds [Bringmann et al., 2022] only hold when deciding if diameter is at most 3. Our findings are presented in a pair of papers. This paper focuses solely on the 2D case, while the companion paper is devoted to higher-dimensional cases.
Cite as

Timothy M. Chan, Hsien-Chih Chang, Jie Gao, Sándor Kisfaludi-Bak, Hung Le, and Da Wei Zheng. Charting the Landscape of Diameter Computation on Geometric Intersection Graphs in the Plane. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 54:1-54:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chan_et_al:LIPIcs.ICALP.2026.54,
  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 Landscape of Diameter Computation on Geometric Intersection Graphs in the Plane}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{54:1--54:22},
  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.2026.54},
  URN =		{urn:nbn:de:0030-drops-264432},
  doi =		{10.4230/LIPIcs.ICALP.2026.54},
  annote =	{Keywords: String graphs, Fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.9
QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes

Authors: Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski

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

Abstract
We present a quasipolynomial-time approximation scheme (QPTAS) for the Maximum Independent Set (MWIS) in graphs with a bounded number of pairwise vertex-disjoint and non-adjacent long induced cycles. More formally, for every fixed s and t, we show a QPTAS for MWIS in graphs that exclude sC_t as an induced minor. Combining this with known results, we obtain a QPTAS for the problem of finding a largest induced subgraph of bounded treewidth with given hereditary property definable in Counting Monadic Second Order Logic, in the same classes of graphs. This is a step towards a conjecture of Gartland and Lokshtanov which asserts that for any planar graph H, graphs that exclude H as an induced minor admit a polynomial-time algorithm for the latter problem. This conjecture is notoriously open and even its weaker variants are confirmed only for very restricted graphs H.
Cite as

Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski. QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bonnet_et_al:LIPIcs.SWAT.2026.9,
  author =	{Bonnet, \'{E}douard and Czy\.{z}ewska, Jadwiga and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{9:1--9:14},
  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.2026.9},
  URN =		{urn:nbn:de:0030-drops-260454},
  doi =		{10.4230/LIPIcs.SWAT.2026.9},
  annote =	{Keywords: independent set, long holes, QPTAS, induced subgraphs}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.7
On the Doubling Dimension and the Perimeter of Geodesically Convex Sets in Fat Polygons

Authors: Mark de Berg, Prosenjit Bose, and Leonidas Theocharous

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

Abstract
Many algorithmic problems can be solved (almost) as efficiently in metric spaces of bounded doubling dimension as in Euclidean space. Unfortunately, the metric space defined by points in a simple polygon equipped with the geodesic distance does not necessarily have bounded doubling dimension. We therefore study the doubling dimension of fat polygons, for two well-known fatness definitions. We prove that locally-fat simple polygons do not always have bounded doubling dimension, while any (α,β)-covered polygon does have bounded doubling dimension (even if it has holes). We also study the perimeter of geodesically convex sets in (α,β)-covered polygons (possibly with holes), and show that this perimeter is at most a constant times the Euclidean diameter of the set. Using these two results, we obtain new results for several problems on (α,β)-covered polygons, including an algorithm that computes the closest pair of a set of m points in an (α,β)-covered polygon with n vertices that runs in O(n + mlog n) expected time.
Cite as

Mark de Berg, Prosenjit Bose, and Leonidas Theocharous. On the Doubling Dimension and the Perimeter of Geodesically Convex Sets in Fat Polygons. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{deberg_et_al:LIPIcs.SWAT.2026.7,
  author =	{de Berg, Mark and Bose, Prosenjit and Theocharous, Leonidas},
  title =	{{On the Doubling Dimension and the Perimeter of Geodesically Convex Sets in Fat Polygons}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{7:1--7:16},
  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.2026.7},
  URN =		{urn:nbn:de:0030-drops-260439},
  doi =		{10.4230/LIPIcs.SWAT.2026.7},
  annote =	{Keywords: Fat polygons, doubling dimension}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.21
Dynamic MIS Revisited: Incremental, Fault Tolerant and Fully Dynamic

Authors: Manoj Gupta, Shahbaz Khan, and Madhu Surendra

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

Abstract
Given a dynamic graph G, we aim to maintain a maximal independent set (MIS). This problem admits a deterministic solution in O(m^{2/3}) time [SOSA21], while randomized algorithms for oblivious adversary take O(polylog n) [FOCS19] time. Recently, Bernstein et al. [SODA26] proved a conditional lower bound of Ω(n^{1-o(1)}) amortized update time even for incremental MIS with adaptive adversary. In this paper, we establish similar deterministic bounds through the lens of incremental and fault tolerant algorithms for MIS, and show the following: 1) Incremental: MIS can be maintained under edge insertions in O(√m) amortized update time. 2) Fault Tolerant: Using O(m) preprocessing time, the MIS can be reported after k edge deletions in O(k+ ̅{n}²) time, where ̅{n} is the number of vertices on which deleted edges are incident. 3) Fully Dynamic: MIS can be maintained under fully dynamic edge updates (insertions and deletions) in O(m^{2/3}) amortized update time. Our incremental result is thus polynomially optimal even on allowing randomization with an adaptive adversary. Our fully dynamic result matches the state-of-the-art [SOSA21], and uses our incremental and fault tolerant algorithms as a black box. Although our fully dynamic algorithm does not improve the existing bounds, it provides additional insights into the harder edge-insertion case. We believe these insights may potentially be useful for improving the bounds for fully dynamic MIS in the future to match the incremental MIS bounds.
Cite as

Manoj Gupta, Shahbaz Khan, and Madhu Surendra. Dynamic MIS Revisited: Incremental, Fault Tolerant and Fully Dynamic. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 21:1-21:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gupta_et_al:LIPIcs.SWAT.2026.21,
  author =	{Gupta, Manoj and Khan, Shahbaz and Surendra, Madhu},
  title =	{{Dynamic MIS Revisited: Incremental, Fault Tolerant and Fully Dynamic}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{21:1--21:11},
  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.2026.21},
  URN =		{urn:nbn:de:0030-drops-260577},
  doi =		{10.4230/LIPIcs.SWAT.2026.21},
  annote =	{Keywords: Maximal Independent Set, MIS, Incremental, Fault Tolerant, Fully dynamic}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.35
Path-Reporting Distance Oracles for Vertex-Labeled Graphs

Authors: Ofer Neiman and Alon Spector

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

Abstract
Let G = (V,E) be a weighted undirected graph, with n vertices. A distance oracle is a data structure that can quickly answer distance queries, with some stretch factor. A seminal work of [Thorup and Zwick, 2005], given an integer k ≥ 1, provides such an oracle with stretch 2k-1, query time O(k), and size O(k⋅ n^{1+1/k}). Furthermore, this oracle can also report a path in G corresponding to the returned distance. In this paper we focus on vertex-labeled graphs, in which each vertex is given a label from a set L of size 𝓁. A vertex-label distance oracle answers queries of the form (v,λ), where v ∈ V and λ ∈ L, by reporting (an approximation to) the distance from v to the closest vertex of label λ. Following [Danny Hermelin et al., 2011], it was shown in [Chechik, 2012] that for any integer k > 1, there exists a vertex-label distance oracle with stretch 4k-5, query time O(k), and size O(k⋅ n⋅ 𝓁^{1/k}). This state-of-the-art result suffers from two main drawbacks: The stretch is roughly a factor of 2 larger than in [Thorup and Zwick, 2005], and it is not path-reporting. We address these concerns in this work, and provide the following results. - First, we devise a path-reporting vertex-label distance oracle, at the cost of a slight increase in stretch and size. For any constant 0 < ε < 1, our oracle has stretch (4k-5)⋅(1+ε), query time O(k), and size O(n^{1+o(1)}⋅ 𝓁^{1/k}). - Second, we show how to improve the stretch to the optimal 2k-1, at the cost of mildly increasing the query time. Specifically, we devise a vertex-label distance oracle with stretch 2k-1, query time O(𝓁^{1/k}⋅log n), and size O(k⋅ n⋅ 𝓁^{1/k}).
Cite as

Ofer Neiman and Alon Spector. Path-Reporting Distance Oracles for Vertex-Labeled Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{neiman_et_al:LIPIcs.SWAT.2026.35,
  author =	{Neiman, Ofer and Spector, Alon},
  title =	{{Path-Reporting Distance Oracles for Vertex-Labeled Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{35:1--35:16},
  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.2026.35},
  URN =		{urn:nbn:de:0030-drops-260719},
  doi =		{10.4230/LIPIcs.SWAT.2026.35},
  annote =	{Keywords: Graph Algorithms, Shortest Paths, Distance Oracles}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.24
Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support

Authors: Reilly Browne and Hsien-Chih Chang

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

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

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

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@InProceedings{browne_et_al:LIPIcs.SoCG.2026.24,
  author =	{Browne, Reilly and Chang, Hsien-Chih},
  title =	{{Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.24},
  URN =		{urn:nbn:de:0030-drops-258300},
  doi =		{10.4230/LIPIcs.SoCG.2026.24},
  annote =	{Keywords: Minimum dominating set, planar graphs, shallow cell complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.29
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.2026.53
Constructing Doppelgängers of Greedy Geometric Spanners in Practice

Authors: Anirban Ghosh

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

Abstract
Greedy geometric spanners are considered to be the gold standard for their near-optimal guarantees in terms of sparsity and total weight. However, their inefficient construction poses significant challenges for large-scale geometric networks, especially for low values of stretch factors (< 2). We present Θ-Greedy, a simple and practical parallel algorithm engineered for constructing doppelgängers of greedy geometric spanners that empirically resemble the greedy spanners in key structural and performance metrics, including average degree, degree, and lightness. Unlike approximate greedy spanners, doppelgängers of greedy spanners are almost indistinguishable from the actual greedy spanners in practice. In our experiments, Θ-Greedy consistently produced greedy spanner doppelgängers across a broad range of synthetic and real-world datasets, offering the first practical alternative to the computationally intensive greedy spanners. Θ-Greedy can construct a 1.1-spanner on a 128K-element uniformly distributed point set in well under 5 minutes. In contrast, Bucketing, the most practical greedy spanner algorithm, takes around 3 hours. For million-sized point sets, Θ-Greedy can run to completion in a few hours, making it much faster than Bucketing, which takes days to finish. In extensive experiments on synthetic and real-world datasets, Θ-Greedy delivered speedups of up to 147x over Bucketing while preserving greedy-like sparsity and weight. For broader uses of the algorithm and reproducibility, we share our engineered C++ code.
Cite as

Anirban Ghosh. Constructing Doppelgängers of Greedy Geometric Spanners in Practice. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 53:1-53:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ghosh:LIPIcs.SoCG.2026.53,
  author =	{Ghosh, Anirban},
  title =	{{Constructing Doppelg\"{a}ngers of Greedy Geometric Spanners in Practice}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{53:1--53:21},
  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.2026.53},
  URN =		{urn:nbn:de:0030-drops-258599},
  doi =		{10.4230/LIPIcs.SoCG.2026.53},
  annote =	{Keywords: geometric graph, geometric spanners, greedy spanners, algorithm engineering}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.55
Linear Time Single-Source Shortest Path Algorithms in Euclidean Graph Classes

Authors: Joachim Gudmundsson, Yuan Sha, and Sampson Wong

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

Abstract
In the celebrated paper of Henzinger, Klein, Rao and Subramanian (1997), it was shown that planar graphs admit a linear time single-source shortest path algorithm. Their algorithm unfortunately does not extend to Euclidean graph classes. We give criteria and prove that any Euclidean graph class satisfying the criteria admits a linear time single-source shortest path algorithm. As a main ingredient, we show that the contracted graphs of these Euclidean graph classes admit sublinear separators.
Cite as

Joachim Gudmundsson, Yuan Sha, and Sampson Wong. Linear Time Single-Source Shortest Path Algorithms in Euclidean Graph Classes. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 55:1-55:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gudmundsson_et_al:LIPIcs.SoCG.2026.55,
  author =	{Gudmundsson, Joachim and Sha, Yuan and Wong, Sampson},
  title =	{{Linear Time Single-Source Shortest Path Algorithms in Euclidean Graph Classes}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{55:1--55:14},
  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.2026.55},
  URN =		{urn:nbn:de:0030-drops-258618},
  doi =		{10.4230/LIPIcs.SoCG.2026.55},
  annote =	{Keywords: Graph algorithms, Single-Source Shortest Path, Euclidean Graphs, Recursive Division}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.64
Gap-ETH-Tight Algorithms for Hyperbolic TSP and Steiner Tree

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

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

Abstract
We give an approximation scheme for the TSP in d-dimensional hyperbolic space that has optimal dependence on ε under Gap-ETH. For any fixed dimension d ≥ 2 and for any ε > 0 our randomized algorithm gives a (1+ε)-approximation in time 2^O(1/ε^{d-1}) n^{1+o(1)}. We also provide an algorithm for the hyperbolic Steiner tree problem with the same running time. Our algorithm is an Arora-style dynamic program based on a randomly shifted hierarchical decomposition. However, we introduce a new hierarchical decomposition called the hybrid hyperbolic quadtree to achieve the desired large-scale structure, which deviates significantly from the recently proposed hyperbolic quadtree of Kisfaludi-Bak and Van Wordragen (JoCG'25). Moreover, we have a new non-uniform portal placement, and our structure theorem employs a new weighted crossing analysis. We believe that these techniques could form the basis for further developments in geometric optimization in curved spaces.
Cite as

Sándor Kisfaludi-Bak, Saeed Odak, Satyam Singh, and Geert van Wordragen. Gap-ETH-Tight Algorithms for Hyperbolic TSP and Steiner Tree. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 64:1-64:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kisfaludibak_et_al:LIPIcs.SoCG.2026.64,
  author =	{Kisfaludi-Bak, S\'{a}ndor and Odak, Saeed and Singh, Satyam and van Wordragen, Geert},
  title =	{{Gap-ETH-Tight Algorithms for Hyperbolic TSP and Steiner Tree}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{64:1--64:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.64},
  URN =		{urn:nbn:de:0030-drops-258710},
  doi =		{10.4230/LIPIcs.SoCG.2026.64},
  annote =	{Keywords: Hyperbolic traveling salesman problem, TSP, Hyperbolic Steiner tree problem, Approximation scheme, Banyan, Hyperbolic geometry}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.65
Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces

Authors: Sándor Kisfaludi-Bak and Geert van Wordragen

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

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

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

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@InProceedings{kisfaludibak_et_al:LIPIcs.SoCG.2026.65,
  author =	{Kisfaludi-Bak, S\'{a}ndor and van Wordragen, Geert},
  title =	{{Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{65:1--65:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.65},
  URN =		{urn:nbn:de:0030-drops-258728},
  doi =		{10.4230/LIPIcs.SoCG.2026.65},
  annote =	{Keywords: hyperbolic geometry, Steiner spanner, dynamic approximate nearest neighbours}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.68
Optimal Bounds for Spanners and Tree Covers in Doubling Metrics

Authors: An La, Hung Le, Shay Solomon, Cuong Than, Vinayak, Shuang Yang, and Tianyi Zhang

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

Abstract
It is known that any n-point set in the d-dimensional Euclidean space ℝ^d, for d = O(1), admits: 1) A (1+ε)-spanner with maximum degree Õ(ε^{-d+1}) and with lightness Õ(ε^{-d}), for any ε > 0. 2) A (1+ε)-tree cover with Õ(n ⋅ ε^{-d+1}) trees and maximum degree of O(1) in each tree. Moreover, all the parameters in these constructions are optimal: For any 2 ≤ d = O(1), there exists an n-point set in ℝ^d, for which any (1+ε)-spanner has Ω̃(n⋅ε^{-d+1}) edges and lightness Ω̃(ε^{-d}). The upper bounds for Euclidean spanners rely heavily on the spatial property of cone partitioning in ℝ^d, which does not seem to extend to the wider family of doubling metrics, i.e., metric spaces of constant doubling dimension. In doubling metrics, a simple spanner construction from two decades ago, the net-tree spanner, has Õ(n⋅ε^{-d}) edges, and it could be transformed into a spanner of maximum degree Õ(ε^{-d}) and lightness Õ(n⋅ε^{-(d+1)}) by pruning redundant edges. Moreover, a careful refinement of the net-tree spanner yields a (1+ε)-tree cover with Õ(ε^{-d}) trees. Despite a large body of work, the problem of obtaining tight bounds for spanners and tree covers in the wider family of doubling metrics has remained elusive. We resolve this problem by presenting: 1) A surprisingly simple and tight lower bound, which shows that the net-tree spanner and its pruned version are optimal with respect to all the involved parameters. 2) A new construction of (1+ε)-tree covers with Õ(n⋅ε^{-d}) trees, with maximum degree O(1) in each tree. This construction is optimal with respect to the number of trees and maximum degree.
Cite as

An La, Hung Le, Shay Solomon, Cuong Than, Vinayak, Shuang Yang, and Tianyi Zhang. Optimal Bounds for Spanners and Tree Covers in Doubling Metrics. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 68:1-68:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{la_et_al:LIPIcs.SoCG.2026.68,
  author =	{La, An and Le, Hung and Solomon, Shay and Than, Cuong and Vinayak and Yang, Shuang and Zhang, Tianyi},
  title =	{{Optimal Bounds for Spanners and Tree Covers in Doubling Metrics}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{68:1--68:16},
  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.2026.68},
  URN =		{urn:nbn:de:0030-drops-258756},
  doi =		{10.4230/LIPIcs.SoCG.2026.68},
  annote =	{Keywords: doubling metrics, doubling spanners, Euclidean spanners, tree cover}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.70
Tree-Like Shortcuttings of Trees

Authors: Hung Le, Lazar Milenković, Shay Solomon, and Cuong Than

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

Abstract
Sparse shortcuttings of trees - equivalently, sparse 1-spanners for tree metrics with bounded hop-diameter - have been studied extensively (under different names and settings), since the pioneering works of [Andrew Chi-Chih Yao, 1982; Chazelle, 1987; Noga Alon and Baruch Schieber, 1987; Hans L. Bodlaender et al., 1994], initially motivated by applications to range queries, online tree product, and MST verification, to name a few. These constructions were also lifted from trees to other graph families using known low-distortion embedding results. The works of [Andrew Chi-Chih Yao, 1982; Chazelle, 1987; Noga Alon and Baruch Schieber, 1987; Hans L. Bodlaender et al., 1994] establish a tight tradeoff between hop-diameter and sparsity (or average degree) for tree shortcuttings and imply constant-hop shortcuttings for n-node trees with sparsity O(log^* n). Despite their small sparsity, all known constant-hop shortcuttings contain dense subgraphs (of sparsity Ω(log n)), which is a significant drawback for many applications. We initiate a systematic study of constant-hop tree shortcuttings that are "tree-like". We focus on two well-studied graph parameters that measure how far a graph is from a tree: arboricity and treewidth. Our contribution is twofold. - New upper and lower bounds for tree-like shortcuttings of trees, including an optimal tradeoff between hop-diameter and treewidth for all hop-diameter up to O(log log n). We also provide a lower bound for larger values of k, which together yield hop-diameter× treewidth = Ω((log log n)²) for all values of hop-diameter, resolving an open question of [Arnold Filtser and Hung Le, 2022; H. Le, 2023]. - Applications of these bounds, focusing on low-dimensional Euclidean and doubling metrics. A seminal work of Arya et al. [S. Arya et al., 1995] presented a (1+ε)-spanner with constant hop-diameter and sparsity O(log^* n), but with large arboricity. We show that constant hop-diameter is sufficient to achieve arboricity O(log^*{n}). Furthermore, we present a (1+ε)-stretch routing scheme in the fixed-port model with 3 hops and a local memory of O(log²n / log log n) bits, resolving an open question of [Omri Kahalon et al., 2022].
Cite as

Hung Le, Lazar Milenković, Shay Solomon, and Cuong Than. Tree-Like Shortcuttings of Trees. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 70:1-70:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{le_et_al:LIPIcs.SoCG.2026.70,
  author =	{Le, Hung and Milenkovi\'{c}, Lazar and Solomon, Shay and Than, Cuong},
  title =	{{Tree-Like Shortcuttings of Trees}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{70:1--70:15},
  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.2026.70},
  URN =		{urn:nbn:de:0030-drops-258776},
  doi =		{10.4230/LIPIcs.SoCG.2026.70},
  annote =	{Keywords: spanner, tree shortcutting, arboricity, treewidth}
}
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