42 Search Results for "Miller, Gary L."

Document
DOI: 10.4230/LIPIcs.SWAT.2026.30
Parallel Algorithms for Group Isomorphism via Code Equivalence

Authors: Michael Levet

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

Abstract
In this paper, we exhibit AC³ isomorphism tests for coprime extensions H ⋉ N where H is elementary Abelian and N is Abelian; and groups where Rad(G) = Z(G) is elementary Abelian and G = Soc^{*}(G). The fact that isomorphism testing for these families is in P was established respectively by Qiao, Sarma, and Tang (STACS 2011), and Grochow and Qiao (CCC 2014, SIAM J. Comput. 2017). The polynomial-time isomorphism tests for both of these families crucially leveraged small (size O(log |G|)) instances of Linear Code Equivalence (Babai, SODA 2011). Here, we combine Luks' group-theoretic method for Graph Isomorphism (FOCS 1980, J. Comput. Syst. Sci. 1982) with the fact that G is given by its multiplication table, to implement the corresponding instances of Linear Code Equivalence in AC³. As a byproduct of our work, we show that isomorphism testing of arbitrary central-radical groups is decidable using AC circuits of depth O(log³ n) and size n^{O(log log n)}. This improves upon the previous bound of n^{O(log log n)}-time due to Grochow and Qiao (ibid.).
Cite as

Michael Levet. Parallel Algorithms for Group Isomorphism via Code Equivalence. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{levet:LIPIcs.SWAT.2026.30,
  author =	{Levet, Michael},
  title =	{{Parallel Algorithms for Group Isomorphism via Code Equivalence}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{30:1--30:19},
  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.2026.30},
  URN =		{urn:nbn:de:0030-drops-260660},
  doi =		{10.4230/LIPIcs.SWAT.2026.30},
  annote =	{Keywords: Group Isomorphism, Circuit Complexity, Code Equivalence}
}
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.2026.30
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.2026.50
Separators for Intersection Graphs of Spheres

Authors: Jacob Fox and Jonathan Tidor

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

Abstract
We prove the existence of optimal separators for intersection graphs of balls and spheres in any dimension d. One of our results is that if an intersection graph of n spheres in ℝ^d has m edges, then it contains a balanced separator of size O_d(m^{1/d}n^{1-2/d}). This bound is best possible in terms of the parameters involved. The same result holds if the balls and spheres are replaced by fat convex bodies and their boundaries.
Cite as

Jacob Fox and Jonathan Tidor. Separators for Intersection Graphs of Spheres. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 50:1-50:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fox_et_al:LIPIcs.SoCG.2026.50,
  author =	{Fox, Jacob and Tidor, Jonathan},
  title =	{{Separators for Intersection Graphs of Spheres}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{50:1--50:16},
  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.2026.50},
  URN =		{urn:nbn:de:0030-drops-258566},
  doi =		{10.4230/LIPIcs.SoCG.2026.50},
  annote =	{Keywords: graph separators, intersection graphs}
}
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.
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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.FUN.2026.11
An Almost-Optimal Upper Bound on the Push Number of the Torus Puzzle

Authors: Matteo Caporrella and Stefano Leucci

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
We study the Torus Puzzle, a solitaire game in which the elements of an input m × n matrix need to be rearranged into a target configuration via a sequence of unit rotations (i.e., circular shifts) of rows and/or columns. Amano et al. proposed a more permissive variant of the above puzzle, where each row and column rotation can shift the involved elements by any amount of positions. The number of rotations needed to solve the original and the permissive variants of the puzzle are respectively known as the push number and the drag number, where the latter is always smaller than or equal to the former and admits an existential lower bound of Ω(mn). While this lower bound is matched by an O(mn) upper bound, the push number is not so well understood. Indeed, to the best of our knowledge, only an O(mn ⋅ max{m, n}) upper bound is currently known. In this paper, we provide an algorithm that solves the Torus Puzzle using O(mn ⋅ log max {m, n}) unit rotations in a model that is more restricted than that of the original puzzle. This implies a corresponding upper bound on the push number and reduces the gap between the known upper and lower bounds from Θ(max{m,n}) to Θ(log max{m, n}).
Cite as

Matteo Caporrella and Stefano Leucci. An Almost-Optimal Upper Bound on the Push Number of the Torus Puzzle. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{caporrella_et_al:LIPIcs.FUN.2026.11,
  author =	{Caporrella, Matteo and Leucci, Stefano},
  title =	{{An Almost-Optimal Upper Bound on the Push Number of the Torus Puzzle}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.11},
  URN =		{urn:nbn:de:0030-drops-257307},
  doi =		{10.4230/LIPIcs.FUN.2026.11},
  annote =	{Keywords: Torus puzzle, Push number, Permutation puzzles}
}
Document
DOI: 10.4230/OASIcs.NINeS.2026.4
Understanding Partial Reachability in the Internet Core

Authors: Guillermo Baltra, Tarang Saluja, Yuri Pradkin, and John Heidemann

Published in: OASIcs, Volume 139, 1st New Ideas in Networked Systems (NINeS 2026)

Abstract
Routing strives to connect all the Internet, but compete: political pressure threatens routing fragmentation; architectural changes such as private clouds, carrier-grade NAT, and firewalls make connectivity conditional; and commercial disputes create partial reachability for days or years. This paper suggests persistent, partial reachability is fundamental to the Internet and an underexplored problem. We first derive a conceptual definition of the Internet core based on connectivity, not authority. We identify peninsulas: persistent, partial connectivity; and islands: when computers are partitioned from the Internet core. Second, we develop algorithms to observe each across the Internet, and apply them to two existing measurement systems: Trinocular, where 6 locations observe 5M networks frequently, and RIPE Atlas, where 13k locations scan the DNS roots frequently. Cross-validation shows our findings are stable over three years of data, and consistent with as few as 3 geographically-distributed observers. We validate peninsulas and islands against CAIDA Ark, showing good recall (0.94) and bounding precision between 0.42 and 0.82. Finally, our work has broad practical impact: we show that peninsulas are more common than Internet outages. Factoring out peninsulas and islands as noise can improve existing measurement systems; their "noise" is 5× to 9.7× larger than the operational events in RIPE’s DNSmon. We show that most peninsula events are routing transients (45%), but most peninsula-time (90%) is due to a few (7%) long-lived events. Our work helps inform Internet policy and governance, with our neutral definition showing no single country or organization can unilaterally control the Internet core.
Cite as

Guillermo Baltra, Tarang Saluja, Yuri Pradkin, and John Heidemann. Understanding Partial Reachability in the Internet Core. In 1st New Ideas in Networked Systems (NINeS 2026). Open Access Series in Informatics (OASIcs), Volume 139, pp. 4:1-4:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{baltra_et_al:OASIcs.NINeS.2026.4,
  author =	{Baltra, Guillermo and Saluja, Tarang and Pradkin, Yuri and Heidemann, John},
  title =	{{Understanding Partial Reachability in the Internet Core}},
  booktitle =	{1st New Ideas in Networked Systems (NINeS 2026)},
  pages =	{4:1--4:32},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-414-7},
  ISSN =	{2190-6807},
  year =	{2026},
  volume =	{139},
  editor =	{Argyraki, Katerina and Panda, Aurojit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.NINeS.2026.4},
  URN =		{urn:nbn:de:0030-drops-255892},
  doi =		{10.4230/OASIcs.NINeS.2026.4},
  annote =	{Keywords: Internet, Internet reliability, Network outages, Active measurements}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.38
Fully Dynamic Spectral Sparsification for Directed Hypergraphs

Authors: Sebastian Forster, Gramoz Goranci, and Ali Momeni

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
There has been a surge of interest in spectral hypergraph sparsification, a natural generalization of spectral sparsification for graphs. In this paper, we present a simple fully dynamic algorithm for maintaining spectral hypergraph sparsifiers of directed hypergraphs. Our algorithm achieves a near-optimal size of O(n² / ε ² log ⁷ m) and amortized update time of O(r² log ³ m), where n is the number of vertices, and m and r respectively upper bound the number of hyperedges and the rank of the hypergraph at any time. We also extend our approach to the parallel batch-dynamic setting, where a batch of any k hyperedge insertions or deletions can be processed with O(kr² log ³ m) amortized work and O(log ² m) depth. This constitutes the first spectral-based sparsification algorithm in this setting.
Cite as

Sebastian Forster, Gramoz Goranci, and Ali Momeni. Fully Dynamic Spectral Sparsification for Directed Hypergraphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 38:1-38:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{forster_et_al:LIPIcs.STACS.2026.38,
  author =	{Forster, Sebastian and Goranci, Gramoz and Momeni, Ali},
  title =	{{Fully Dynamic Spectral Sparsification for Directed Hypergraphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{38:1--38:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.38},
  URN =		{urn:nbn:de:0030-drops-255272},
  doi =		{10.4230/LIPIcs.STACS.2026.38},
  annote =	{Keywords: Spectral sparsification, Dynamic algorithms, (Directed) hypergraphs, Data structures}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.80
FPT Approximations for Connected Maximum Coverage

Authors: Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We revisit connectivity-constrained coverage through a unifying model, Partial Connected Red-Blue Dominating Set (PartialConRBDS). Given a bipartite graph G = (R∪ B,E) with red vertices R and blue vertices B, an auxiliary connectivity graph G_{conn} on R, and integers k,t, the task is to find a set S ⊆ R with |S| ≤ k such that G_{conn}[S] is connected and S dominates at least t blue vertices. This formulation captures connected variants of Maximum Coverage [Hochbaum-Rao, Inf. Proc. Lett., 2020; D'Angelo-Delfaraz, AAMAS 2025], Partial Vertex Cover, and Partial Dominating Set [Khuller et al., SODA 2014; Lamprou et al., TCS 2021] via standard encodings. Limits to parameterized tractability. PartialConRBDS is W[1]-hard parameterized by k even under strong restrictions: it remains hard when G_{conn} is a clique or a star and the incidence graph G is 3-degenerate, or when G is K_{2,2}-free. Inapproximability. For every ε > 0, there is no polynomial-time (1, 1-1/e+ε)-approximation unless 𝖯 = NP. Moreover, under ETH, no algorithm running in f(k)⋅ n^{o(k)} time achieves an g(k)-approximation for k for any computable function g(⋅), or for any ε > 0, a (1-1/e+ε)-approximation for t. Graphical special cases. Partial Connected Dominating Set is W[2]-hard parameterized by k and inherits the same ETH-based f(k)⋅ n^{o(k)} inapproximability bound as above; Partial Connected Vertex Cover is W[1]-hard parameterized by k. These hardness boundaries delineate a natural "sweet spot" for study: within appropriate structural restrictions on the incidence graph, one can still aim for fine-grained (FPT) approximations. Our algorithms. We solve PartialConRBDS exactly by reducing it to Relaxed Directed Steiner Out-Tree in time (2e)^t ⋅ n^{𝒪(1)}. For biclique-free incidences (i.e., when G excludes K_{d,d} as an induced subgraph), we obtain two complementary parameterized schemes: - An Efficient Parameterized Approximation Scheme (EPAS) running in time 2^{𝒪(k² d/ε)}⋅ n^{𝒪(1)} that either returns a connected solution of size at most k covering at least (1-ε)t blue vertices, or correctly reports that no connected size-k solution covers t; and - A Parameterized Approximation Scheme (PAS) running in time 2^{𝒪(kd(k²+log d))}⋅ n^{𝒪(1/ε)} that either returns a connected solution of size at most (1+ε)k covering at least t blue vertices, or correctly reports that no connected size-k solution covers t. Together, these results chart the boundary between hardness and FPT-approximability for connectivity-constrained coverage.
Cite as

Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi. FPT Approximations for Connected Maximum Coverage. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 80:1-80:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{inamdar_et_al:LIPIcs.ITCS.2026.80,
  author =	{Inamdar, Tanmay and Jana, Satyabrata and Kundu, Madhumita and Lokshtanov, Daniel and Saurabh, Saket and Zehavi, Meirav},
  title =	{{FPT Approximations for Connected Maximum Coverage}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{80:1--80:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.80},
  URN =		{urn:nbn:de:0030-drops-253674},
  doi =		{10.4230/LIPIcs.ITCS.2026.80},
  annote =	{Keywords: Partial Dominating Set, Connectivity, Maximum Coverage, FPT Approximation, Fixed-parameter Tractability}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.3
Linear Matroid Intersection Is in Catalytic Logspace

Authors: Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Linear matroid intersection is an important problem in combinatorial optimization. Given two linear matroids over the same ground set, the linear matroid intersection problem asks you to find a common independent set of maximum size. The deep interest in linear matroid intersection is due to the fact that it generalises many classical problems in theoretical computer science, such as bipartite matching, edge disjoint spanning trees, rainbow spanning tree, and many more. We study this problem in the model of catalytic computation: space-bounded machines are granted access to catalytic space, which is additional working memory that is full with arbitrary data that must be preserved at the end of its computation. Although linear matroid intersection has had a polynomial time algorithm for over 50 years, it remains an important open problem to show that linear matroid intersection belongs to any well studied subclass of {P}. We address this problem for the class catalytic logspace (CL) with a polynomial time bound (CLP). Recently, Agarwala and Mertz (2025) showed that bipartite maximum matching can be computed in the class CLP ⊆ {P}. This was the first subclass of {P} shown to contain bipartite matching, and additionally the first problem outside TC¹ shown to be contained in CL. We significantly improve the result of Agarwala and Mertz by showing that linear matroid intersection can be computed in CLP.
Cite as

Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra. Linear Matroid Intersection Is in Catalytic Logspace. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.3,
  author =	{Agarwala, Aryan and Alekseev, Yaroslav and Vinciguerra, Antoine},
  title =	{{Linear Matroid Intersection Is in Catalytic Logspace}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.3},
  URN =		{urn:nbn:de:0030-drops-252908},
  doi =		{10.4230/LIPIcs.ITCS.2026.3},
  annote =	{Keywords: Catalytic Computing, Computational Complexity, Matroid Theory, Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.36
Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election

Authors: Yi-Jun Chang, Lyuting Chen, and Haoran Zhou

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
The content-oblivious model, introduced by Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022; Distributed Computing 2023), captures an extremely weak form of communication where nodes can only send asynchronous, content-less pulses. They showed that in 2-edge-connected networks, any distributed algorithm can be simulated in the content-oblivious model, provided that a unique leader is designated a priori. Subsequent works of Frei, Gelles, Ghazy, and Nolin (DISC 2024) and Chalopin et al. (DISC 2025) developed content-oblivious leader election algorithms, first for unoriented rings and then for general 2-edge-connected graphs. These results establish that all graph problems are solvable in content-oblivious, 2-edge-connected networks. Much less is known about networks that are not 2-edge-connected. Censor-Hillel, Cohen, Gelles, and Sela showed that no non-constant function f(x,y) can be computed correctly by two parties using content-oblivious communication over a single edge, where one party holds x and the other holds y. This seemingly ruled out many natural graph problems on non-2-edge-connected graphs. In this work, we show that, with the knowledge of network topology G, leader election is possible in a wide range of graphs. Our main contributions are as follows: Impossibility: Graphs symmetric about an edge admit no randomized terminating leader election algorithm, even when nodes have unique identifiers and full knowledge of G. Leader election algorithms: Trees that are not symmetric about any edge admit a quiescently terminating leader election algorithm with topology knowledge, even in anonymous networks, using O(n²) messages, where n is the number of nodes. Moreover, even-diameter trees admit a terminating leader election given only the knowledge of the network diameter D = 2r, with message complexity O(nr). Necessity of topology knowledge: In the family of graphs 𝒢 = {P₃, P₅}, both the 3-path P₃ and the 5-path P₅ admit a quiescently terminating leader election if nodes know the topology exactly. However, if nodes only know that the underlying topology belongs to 𝒢, then terminating leader election is impossible.
Cite as

Yi-Jun Chang, Lyuting Chen, and Haoran Zhou. Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 36:1-36:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chang_et_al:LIPIcs.ITCS.2026.36,
  author =	{Chang, Yi-Jun and Chen, Lyuting and Zhou, Haoran},
  title =	{{Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{36:1--36:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.36},
  URN =		{urn:nbn:de:0030-drops-253239},
  doi =		{10.4230/LIPIcs.ITCS.2026.36},
  annote =	{Keywords: Asynchronous model, fault tolerance, quiescent termination}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.23
Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes

Authors: Archit Chauhan, Samir Datta, and M. Praveen

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Constructing a Depth First Search (DFS) tree is a fundamental graph problem, whose parallel complexity is still not settled. Reif showed parallel intractability of lex-first DFS. In contrast, randomized parallel algorithms (and more recently, deterministic quasipolynomial parallel algorithms) are known for constructing a DFS tree in general (di)graphs. However a deterministic parallel algorithm for DFS in general graphs remains an elusive goal. Working towards this, a series of works gave deterministic NC algorithms for DFS in planar graphs and digraphs. We further extend these results to more general graph classes, by providing NC algorithms for (di)graphs of bounded genus, and for undirected H-minor-free graphs where H is a fixed graph with at most one crossing. For the case of (di)graphs of bounded treewidth, we further improve the complexity to a Logspace bound. Constructing a maximal path is a simpler problem (that reduces to DFS) for which no deterministic parallel bounds are known for general graphs. For planar graphs a bound of O(log n) parallel time on a CRCW PRAM (thus in NC²) is known. We improve this bound to Logspace.
Cite as

Archit Chauhan, Samir Datta, and M. Praveen. Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chauhan_et_al:LIPIcs.FSTTCS.2025.23,
  author =	{Chauhan, Archit and Datta, Samir and Praveen, M.},
  title =	{{Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{23:1--23:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.23},
  URN =		{urn:nbn:de:0030-drops-251041},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.23},
  annote =	{Keywords: Parallel Complexity, Graph Algorithms, Depth First Search, Maximal Path, Planar Graphs, Minor-Free, Treewidth, Logspace}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.37
Show Me Your Best Side: Characteristics of User-Preferred Perspectives for 3D Graph Drawings

Authors: Lucas Joos, Gavin J. Mooney, Maximilian T. Fischer, Daniel A. Keim, Falk Schreiber, Helen C. Purchase, and Karsten Klein

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

Abstract
The visual analysis of graphs in 3D has become increasingly popular, accelerated by the rise of immersive technology, such as augmented and virtual reality. Unlike 2D drawings, 3D graph layouts are highly viewpoint-dependent, making perspective selection critical for revealing structural and relational patterns. Despite its importance, there is limited empirical evidence guiding what constitutes an effective or preferred viewpoint from the user’s perspective. In this paper, we present a systematic investigation into user-preferred viewpoints in 3D graph visualisations. We conducted a controlled study with 23 participants in a virtual reality environment, where users selected their most and least preferred viewpoints for 36 different graphs varying in size and layout. From this data, enriched by qualitative feedback, we distil common strategies underlying viewpoint choice. We further analyse the alignment of user preferences with classical 2D aesthetic criteria (e.g., Crossings), 3D-specific measures (e.g., Node-Node Occlusion), and introduce a novel measure capturing the perceivability of a graph’s principal axes (Isometric Viewpoint Deviation). Our data-driven analysis indicates that Stress, Crossings, Gabriel Ratio, Edge-Node Overlap, and Isometric Viewpoint Deviation are key indicators of viewpoint preference. Beyond our findings, we contribute a publicly available dataset consisting of the graphs and computed aesthetic measures, supporting further research and the development of viewpoint evaluation measures for 3D graph drawing.
Cite as

Lucas Joos, Gavin J. Mooney, Maximilian T. Fischer, Daniel A. Keim, Falk Schreiber, Helen C. Purchase, and Karsten Klein. Show Me Your Best Side: Characteristics of User-Preferred Perspectives for 3D Graph Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 37:1-37:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{joos_et_al:LIPIcs.GD.2025.37,
  author =	{Joos, Lucas and Mooney, Gavin J. and Fischer, Maximilian T. and Keim, Daniel A. and Schreiber, Falk and Purchase, Helen C. and Klein, Karsten},
  title =	{{Show Me Your Best Side: Characteristics of User-Preferred Perspectives for 3D Graph Drawings}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{37:1--37:19},
  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.2025.37},
  URN =		{urn:nbn:de:0030-drops-250236},
  doi =		{10.4230/LIPIcs.GD.2025.37},
  annote =	{Keywords: Graph Aesthetics, Immersive 3D, Node-Link Diagrams, Empirical Evaluation}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.34
Layered Polyline Drawings of Planar Graphs

Authors: Debajyoti Mondal

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

Abstract
A k-layer polyline drawing of a planar graph G is a planar drawing of G on a set L of k parallel lines such that each vertex is mapped to a point on L and each edge is mapped to a polygonal chain with the endpoints and bends lying on L. In the fixed embedding setting, the output drawing maintains the given planar embedding, whereas in the variable embedding setting, the embedding may change. Every n-vertex planar graph admits a polyline drawing on 2n/3 layers, which is the best known upper bound for both settings. We improve this bound in the variable embedding setting. We show that every planar graph can be drawn on 14n/27+O(√n) layers by choosing a proper planar embedding, breaking the long-standing 2n/3-layer barrier.
Cite as

Debajyoti Mondal. Layered Polyline Drawings of Planar Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 34:1-34:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mondal:LIPIcs.GD.2025.34,
  author =	{Mondal, Debajyoti},
  title =	{{Layered Polyline Drawings of Planar Graphs}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{34:1--34:10},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-250202},
  doi =		{10.4230/LIPIcs.GD.2025.34},
  annote =	{Keywords: Layered Drawing, Variable Embedding, Polyline Drawing, Cycle Separator}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.30
Team Formation and Applications

Authors: Yuval Emek, Shay Kutten, Ido Rafael, and Gadi Taubenfeld

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
A novel long-lived distributed problem, called Team Formation (TF), is introduced together with a message- and time-efficient randomized algorithm. The problem is defined over the asynchronous model with a complete communication graph, using bounded size messages, where a certain fraction of the nodes may experience a generalized, strictly stronger, version of initial failures. The goal of a TF algorithm is to assemble tokens injected by the environment, in a distributed manner, into teams of size σ, where σ is a parameter of the problem. The usefulness of TF is demonstrated by using it to derive efficient algorithms for many distributed problems. Specifically, we show that various (one-shot as well as long-lived) distributed problems reduce to TF. This includes well-known (and extensively studied) distributed problems such as several versions of leader election and threshold detection. For example, we are the first to break the linear message complexity bound for asynchronous implicit leader election. We also improve the time complexity of message-optimal algorithms for asynchronous explicit leader election. Other distributed problems that reduce to TF are new ones, including matching players in online gaming platforms, a generalization of gathering, constructing a perfect matching in an induced subgraph of the complete graph, and more. To complement our positive contribution, we establish a tight lower bound on the message complexity of TF algorithms.
Cite as

Yuval Emek, Shay Kutten, Ido Rafael, and Gadi Taubenfeld. Team Formation and Applications. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 30:1-30:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{emek_et_al:LIPIcs.DISC.2025.30,
  author =	{Emek, Yuval and Kutten, Shay and Rafael, Ido and Taubenfeld, Gadi},
  title =	{{Team Formation and Applications}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{30:1--30:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.30},
  URN =		{urn:nbn:de:0030-drops-248474},
  doi =		{10.4230/LIPIcs.DISC.2025.30},
  annote =	{Keywords: asynchronous message-passing, complete communication graph, initial failures, leader election, matching}
}
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