18 Search Results for "Spinrad, Jeremy P."

Document
DOI: 10.4230/LIPIcs.IPEC.2025.4
On the Complexity of Secluded Path Problems

Authors: Tesshu Hanaka and Daisuke Tsuru

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

Abstract
This paper investigates the complexity of finding secluded paths in graphs. We focus on the Short Secluded Path problem and a natural new variant we introduce, Shortest Secluded Path. Formally, given an undirected graph G = (V, E), two vertices s,t ∈ V, and two integers k,l, the Short Secluded Path problem asks whether there exists an s-t path of length at most k with at most l neighbors. This problem is known to be computationally hard: it is W[1]-hard when parameterized by the path length k or by cliquewidth, and para-NP-complete when parameterized by the number l of neighbors. The fixed-parameter tractability is known for k+l or treewidth. In this paper, we expand the parameterized complexity landscape by designing (1) an XP algorithm parameterized by cliquewidth and (2) fixed-parameter algorithms parameterized by neighborhood diversity and twin cover number, respectively. As a byproduct, our results also provide parameterized algorithms for the classic s-t k-Path problem. Furthermore, we introduce the Shortest Secluded Path problem, which seeks a shortest s-t path with the minimum number of neighbors. In contrast to the hardness of the original problem, we reveal that this variant is solvable in polynomial time on unweighted graphs. We complete this by showing that for edge-weighted graphs, the problem becomes W[1]-hard yet remains in XP when parameterized by the shortest path distance between s and t.
Cite as

Tesshu Hanaka and Daisuke Tsuru. On the Complexity of Secluded Path Problems. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hanaka_et_al:LIPIcs.IPEC.2025.4,
  author =	{Hanaka, Tesshu and Tsuru, Daisuke},
  title =	{{On the Complexity of Secluded Path Problems}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.4},
  URN =		{urn:nbn:de:0030-drops-251361},
  doi =		{10.4230/LIPIcs.IPEC.2025.4},
  annote =	{Keywords: Secluded path, Parameterized complexity, Polynomial-time algorithm}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.29
Hitting Geodesic Intervals in Structurally Restricted Graphs

Authors: Tatsuya Gima, Yasuaki Kobayashi, Yuto Okada, Yota Otachi, and Hayato Takaike

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

Abstract
Given a graph G = (V,E), a set T of vertex pairs, and an integer k, Hitting Geodesic Intervals asks whether there is a set S ⊆ V of size at most k such that for each terminal pair {u,v} ∈ T, the set S intersects at least one shortest u-v path. Aravind and Saxena [WALCOM 2024] introduced this problem and showed several parameterized complexity results. In this paper, we extend the known results in both negative and positive directions and present sharp complexity contrasts with respect to structural graph parameters. We first show that the problem is NP-complete even on graphs with highly restricted shortest-path structures. More precisely, we show the NP-completeness on graphs obtained by adding a single vertex to a disjoint union of 5-vertex paths. By modifying the proof of this result, we also show the NP-completeness on graphs obtained from a path by adding one vertex and on graphs obtained from a disjoint union of triangles by adding one universal vertex. Furthermore, we show the NP-completeness on graphs of bandwidth 4 and maximum degree 5 by replacing the universal vertex in the last case with a long path. Under standard complexity assumptions, these negative results rule out fixed-parameter algorithms for most of the structural parameters studied in the literature (if the solution size k is not part of the parameter). We next present fixed-parameter algorithms parameterized by k plus modular-width and by k plus vertex integrity. The algorithm for the latter case does indeed solve a more general setting that includes the parameterization by the minimum vertex multiway-cut size of the terminal vertices. We show that this is tight in the sense that the problem parameterized by the minimum vertex multicut size of the terminal pairs is W[2]-complete. We then modify the proof of this intractability result and show that the problem is W[2]-complete parameterized by k even in the setting where T = binom(Q,2) for some Q ⊆ V.
Cite as

Tatsuya Gima, Yasuaki Kobayashi, Yuto Okada, Yota Otachi, and Hayato Takaike. Hitting Geodesic Intervals in Structurally Restricted Graphs. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gima_et_al:LIPIcs.IPEC.2025.29,
  author =	{Gima, Tatsuya and Kobayashi, Yasuaki and Okada, Yuto and Otachi, Yota and Takaike, Hayato},
  title =	{{Hitting Geodesic Intervals in Structurally Restricted Graphs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.29},
  URN =		{urn:nbn:de:0030-drops-251618},
  doi =		{10.4230/LIPIcs.IPEC.2025.29},
  annote =	{Keywords: Terminal monitoring set, Structural graph parameter, Geodesic interval}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.38
Structural Parameters for Steiner Orientation

Authors: Tesshu Hanaka, Michael Lampis, Nikolaos Melissinos, Edouard Nemery, Hirotaka Ono, and Manolis Vasilakis

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

Abstract
We consider the Steiner Orientation problem, where we are given as input a mixed graph G = (V,E,A) and a set of k demand pairs (s_i,t_i), i ∈ [k]. The goal is to orient the undirected edges of G in a way that the resulting directed graph has a directed path from s_i to t_i for all i ∈ [k]. We adopt the point of view of structural parameterized complexity and investigate the complexity of Steiner Orientation for standard measures, such as treewidth. Our results indicate that Steiner Orientation is a surprisingly hard problem from this point of view. In particular, our main contributions are the following: 1) We show that Steiner Orientation is NP-complete on instances where the underlying graph has feedback vertex number 2, treewidth 2, pathwidth 3, and vertex integrity 6. 2) We present an XP algorithm parameterized by vertex cover number vc of complexity n^O(vc²). Furthermore, we show that this running time is essentially optimal by proving that a running time of n^o(vc²) would refute the ETH. 3) We consider parameterizations by the number of undirected or directed edges (|E| or |A|) and we observe that the trivial 2^|E| n^O(1)-time algorithm for the former parameter is optimal under the SETH. Complementing this, we show that the problem admits a 2^O(|A|) n^O(1)-time algorithm. In addition to the above, we consider the complexity of Steiner Orientation parameterized by tw+k (FPT), distance to clique (FPT), and vc+k (FPT with a polynomial kernel).
Cite as

Tesshu Hanaka, Michael Lampis, Nikolaos Melissinos, Edouard Nemery, Hirotaka Ono, and Manolis Vasilakis. Structural Parameters for Steiner Orientation. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hanaka_et_al:LIPIcs.ISAAC.2025.38,
  author =	{Hanaka, Tesshu and Lampis, Michael and Melissinos, Nikolaos and Nemery, Edouard and Ono, Hirotaka and Vasilakis, Manolis},
  title =	{{Structural Parameters for Steiner Orientation}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{38:1--38:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.38},
  URN =		{urn:nbn:de:0030-drops-249461},
  doi =		{10.4230/LIPIcs.ISAAC.2025.38},
  annote =	{Keywords: ETH, Steiner Orientation, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.17
Visualizing Treewidth

Authors: Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, and Martin Nöllenburg

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

Abstract
A witness drawing of a graph is a visualization that clearly shows a given property of a graph. We study and implement various drawing paradigms for witness drawings to clearly show that graphs have bounded pathwidth or treewidth. Our approach draws the tree decomposition or path decomposition as a tree of bags, with induced subgraphs shown in each bag, and with "tracks" for each graph vertex connecting its copies in multiple bags. Within bags, we optimize the vertex layout to avoid crossings of edges and tracks. We implement a visualization prototype for crossing minimization using dynamic programming for graphs of small width and heuristic approaches for graphs of larger width. We introduce a taxonomy of drawing styles, which render the subgraph for each bag as an arc diagram with one or two pages or as a circular layout with straight-line edges, and we render tracks either with straight lines or with orbital-radial paths.
Cite as

Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, and Martin Nöllenburg. Visualizing Treewidth. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chiu_et_al:LIPIcs.GD.2025.17,
  author =	{Chiu, Alvin and Depian, Thomas and Eppstein, David and Goodrich, Michael T. and N\"{o}llenburg, Martin},
  title =	{{Visualizing Treewidth}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{17:1--17:20},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-250034},
  doi =		{10.4230/LIPIcs.GD.2025.17},
  annote =	{Keywords: Graph drawing, witness drawings, pathwidth, treewidth}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.3
On the Structure of Normalized Models of Circular-Arc Graphs I. Hsu’s Approach

Authors: Tomasz Krawczyk

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

Abstract
In the work [𝒪(m⋅ n) algorithms for the recognition and isomorphism problems on circular-arc graphs, SIAM J. Comput. 24(3), 411-439, (1995)], Wen-Lian Hsu claims three results concerning the class of circular-arc graphs: - the design of so-called decomposition trees that represent the structure of all normalized intersection models of circular-arc graphs, - an 𝒪(nm)-time recognition algorithm for circular-arc graphs, - an 𝒪(nm)-time isomorphism algorithm for circular-arc graphs. In [Discrete Math. Theor. Comput. Sci., 15(1), 157-182, 2013] Curtis, Lin, McConnell, Nussbaum, Soulignac, Spinrad, and Szwarcfiter showed that Hsu’s isomorphism algorithm is incorrect. In this note, we show that the other two results - namely, the construction of decomposition trees and the recognition algorithm - are also flawed. We also present the main ideas that made it possible to construct a data structure that maintains normalized models of circular-arc graphs.
Cite as

Tomasz Krawczyk. On the Structure of Normalized Models of Circular-Arc Graphs I. Hsu’s Approach. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{krawczyk:LIPIcs.GD.2025.3,
  author =	{Krawczyk, Tomasz},
  title =	{{On the Structure of Normalized Models of Circular-Arc Graphs I. Hsu’s Approach}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{3:1--3:15},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-249892},
  doi =		{10.4230/LIPIcs.GD.2025.3},
  annote =	{Keywords: intersection graphs and models, circular-arc graphs and circular-arc intersection models}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.10
Connected Partitions via Connected Dominating Sets

Authors: Aikaterini Niklanovits, Kirill Simonov, Shaily Verma, and Ziena Zeif

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

Abstract
The classical theorem due to Győri and Lovász states that any k-connected graph G admits a partition into k connected subgraphs, where each subgraph has a prescribed size and contains a prescribed vertex, as long as the total size of target subgraphs is equal to the size of G. However, this result is notoriously evasive in terms of efficient constructions, and it is still unknown whether such a partition can be computed in polynomial time, even for k = 5. We make progress towards an efficient constructive version of the Győri-Lovász theorem by considering a natural strengthening of the k-connectivity requirement. Specifically, we show that the desired connected partition can be found in polynomial time, if G contains k disjoint connected dominating sets. As a consequence of this result, we give several efficient approximate and exact constructive versions of the original Győri-Lovász theorem: - On general graphs, a Győri-Lovász partition with k parts can be computed in polynomial time when the input graph has connectivity Ω(k ⋅ log² n); - On convex bipartite graphs, connectivity of 4k is sufficient; - On biconvex graphs and interval graphs, connectivity of k is sufficient, meaning that our algorithm gives a "true" constructive version of the theorem on these graph classes.
Cite as

Aikaterini Niklanovits, Kirill Simonov, Shaily Verma, and Ziena Zeif. Connected Partitions via Connected Dominating Sets. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{niklanovits_et_al:LIPIcs.ESA.2025.10,
  author =	{Niklanovits, Aikaterini and Simonov, Kirill and Verma, Shaily and Zeif, Ziena},
  title =	{{Connected Partitions via Connected Dominating Sets}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.10},
  URN =		{urn:nbn:de:0030-drops-244785},
  doi =		{10.4230/LIPIcs.ESA.2025.10},
  annote =	{Keywords: Gy\H{o}ri-Lov\'{a}sz theorem, connected dominating sets, graph classes}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.67
Compact Representation of Semilinear and Terrain-Like Graphs

Authors: Jean Cardinal and Yelena Yuditsky

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

Abstract
We consider the existence and construction of biclique covers of graphs, consisting of coverings of their edge sets by complete bipartite graphs. The size of such a cover is the sum of the sizes of the bicliques. Small-size biclique covers of graphs are ubiquitous in computational geometry, and have been shown to be useful compact representations of graphs. We give a brief survey of classical and recent results on biclique covers and their applications, and give new families of graphs having biclique covers of near-linear size. In particular, we show that semilinear graphs, whose edges are defined by linear relations in bounded dimensional space, always have biclique covers of size O(npolylog n). This generalizes many previously known results on special classes of graphs including interval graphs, permutation graphs, and graphs of bounded boxicity, but also new classes such as intersection graphs of L-shapes in the plane. It also directly implies the bounds for Zarankiewicz’s problem derived by Basit, Chernikov, Starchenko, Tao, and Tran (Forum Math. Sigma, 2021). We also consider capped graphs, also known as terrain-like graphs, defined as ordered graphs forbidding a certain ordered pattern on four vertices. Terrain-like graphs contain the induced subgraphs of terrain visibility graphs. We give an elementary proof that these graphs admit biclique partitions of size O(nlog³ n). This provides a simple combinatorial analogue of a classical result from Agarwal, Alon, Aronov, and Suri on polygon visibility graphs (Discrete Comput. Geom. 1994). Finally, we prove that there exists families of unit disk graphs on n vertices that do not admit biclique coverings of size o(n^{4/3}), showing that we are unlikely to improve on Szemerédi-Trotter type incidence bounds for higher-degree semialgebraic graphs.
Cite as

Jean Cardinal and Yelena Yuditsky. Compact Representation of Semilinear and Terrain-Like Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 67:1-67:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cardinal_et_al:LIPIcs.ESA.2025.67,
  author =	{Cardinal, Jean and Yuditsky, Yelena},
  title =	{{Compact Representation of Semilinear and Terrain-Like Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{67:1--67:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.67},
  URN =		{urn:nbn:de:0030-drops-245359},
  doi =		{10.4230/LIPIcs.ESA.2025.67},
  annote =	{Keywords: Biclique covers, intersection graphs, visibility graphs, Zarankiewicz’s problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.20
Kernelization in Almost Linear Time for Clustering into Bounded Vertex Cover Components

Authors: Sriram Bhyravarapu, Pritesh Kumar, Madhumita Kundu, Shivesh K. Roy, Sahiba, and Saket Saurabh

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Motivated by the growing interest in graph clustering and the framework proposed during the Dagstuhl Seminar 23331, we consider a natural specialization of this general approach (as also suggested during the seminar). The seminar introduced a broad perspective on clustering, where the goal is to partition a graph into connected components (or "clusters") that satisfy simple structural integrity constraints - not necessarily limited to cliques. In our work, we focus on the case where each cluster is required to have bounded vertex cover number. Specifically, a connected component C satisfies this condition if there exists a set S ⊆ V(C) with |S| ≤ d such that C - S is an independent set. We study this within the framework of the {Vertex Deletion to d-Vertex Cover Components} ({Vertex Deletion to d-VCC}) problem: given a graph G and an integer k, the task is to determine whether there exists a vertex set S ⊆ V(G) of size at most k such that every connected component of G - S has vertex cover number at most d. We also examine the edge-deletion variant, {Edge Deletion to d-Vertex Cover Components} ({Edge Deletion to d-VCC}), where the goal is to delete at most k edges so that each connected component of the resulting graph has vertex cover number at most d. We obtain following results. 1) {Vertex Deletion to d-VCC} admits a kernel with {𝒪}(d⁶k³) vertices and {𝒪}(d⁹k⁴) edges. 2) {Edge Deletion to d-VCC}, admits a kernel with {𝒪}(d⁴k) vertices and {𝒪}(d⁵k) edges. Both of our kernelization algorithms run in time 𝒪(1.253^d ⋅ (kd)^{𝒪(1)} ⋅ n log n). It is important to note that, unless the Exponential Time Hypothesis (ETH) fails, the dependence on d cannot be improved to 2^{o(d)}, as the case k = 0 reduces to solving the classical Vertex Cover problem, which is known to require 2^{Ω(d)} time under ETH. A key ingredient in our kernelization algorithms is a structural result about the hereditary graph class 𝒢_d, consisting of graphs in which every connected component has vertex cover number at most d. We show that 𝒢_d admits a finite obstruction set (with respect to the induced subgraph relation) of size 2^{𝒪(d²)}, where each obstruction graph has at most 3d + 2 vertices. This combinatorial result may be of independent interest.
Cite as

Sriram Bhyravarapu, Pritesh Kumar, Madhumita Kundu, Shivesh K. Roy, Sahiba, and Saket Saurabh. Kernelization in Almost Linear Time for Clustering into Bounded Vertex Cover Components. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhyravarapu_et_al:LIPIcs.MFCS.2025.20,
  author =	{Bhyravarapu, Sriram and Kumar, Pritesh and Kundu, Madhumita and Roy, Shivesh K. and Sahiba and Saurabh, Saket},
  title =	{{Kernelization in Almost Linear Time for Clustering into Bounded Vertex Cover Components}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.20},
  URN =		{urn:nbn:de:0030-drops-241276},
  doi =		{10.4230/LIPIcs.MFCS.2025.20},
  annote =	{Keywords: Parameterized complexity, Polynomial Kernels, Vertex Cover, Finite Forbidden Characterization}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.86
Optimal Distance Labeling for Permutation Graphs

Authors: Paweł Gawrychowski and Wojciech Janczewski

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

Abstract
A permutation graph is the intersection graph of a set of segments between two parallel lines. In other words, they are defined by a permutation π on n elements, such that u and v are adjacent if an only if u < v but π(u) > π(v). We consider the problem of computing the distances in such a graph in the setting of informative labeling schemes. The goal of such a scheme is to assign a short bitstring 𝓁(u) to every vertex u, such that the distance between u and v can be computed using only 𝓁(u) and 𝓁(v), and no further knowledge about the whole graph (other than that it is a permutation graph). This elegantly captures the intuition that we would like our data structure to be distributed, and often leads to interesting combinatorial challenges while trying to obtain lower and upper bounds that match up to the lower-order terms. For distance labeling of permutation graphs on n vertices, Katz, Katz, and Peleg [STACS 2000] showed how to construct labels consisting of 𝒪(log² n) bits. Later, Bazzaro and Gavoille [Discret. Math. 309(11)] obtained an asymptotically optimal bound by showing how to construct labels consisting of 9log{n}+𝒪(1) bits, and proving that 3log{n}-𝒪(log{log{n}}) bits are necessary. This however leaves a quite large gap between the known lower and upper bounds. We close this gap by showing how to construct labels consisting of 3log{n}+𝒪(1) bits.
Cite as

Paweł Gawrychowski and Wojciech Janczewski. Optimal Distance Labeling for Permutation Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 86:1-86:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gawrychowski_et_al:LIPIcs.ICALP.2025.86,
  author =	{Gawrychowski, Pawe{\l} and Janczewski, Wojciech},
  title =	{{Optimal Distance Labeling for Permutation Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{86:1--86:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.86},
  URN =		{urn:nbn:de:0030-drops-234632},
  doi =		{10.4230/LIPIcs.ICALP.2025.86},
  annote =	{Keywords: informative labeling, permutation graph, distance labeling}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.63
The Maximum Clique Problem in a Disk Graph Made Easy

Authors: J. Mark Keil and Debajyoti Mondal

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

Abstract
A disk graph is an intersection graph of disks in ℝ². Determining the computational complexity of finding a maximum clique in a disk graph is a long-standing open problem. In 1990, Clark, Colbourn, and Johnson gave a polynomial-time algorithm for computing a maximum clique in a unit disk graph. However, finding a maximum clique when disks are of arbitrary size is widely believed to be a challenging open problem. In this paper, we provide a new perspective to examine adjacencies in a disk graph that helps obtain the following results. - We design an 𝒪^*(n^{2k})-time algorithm, where 𝒪^* hides a polynomial factor, to find a maximum clique in a n-vertex disk graph with k different sizes of radii. This is polynomial for every fixed k, and thus settles the open question for the case when k = 2. - Given a set of n unit disks, we show how to compute a maximum clique inside each possible axis-aligned rectangle determined by the disk centers in O(n⁵log n)-time. This is at least a factor of n^{4/3} faster than applying the fastest known algorithm for finding a maximum clique in a unit disk graph for each rectangle independently. - We give an 𝒪^*(n^{2rk})-time algorithm to find a maximum clique in a n-vertex ball graph with k different sizes of radii where the ball centers lie on r parallel planes. This is polynomial for every fixed k and r, and thus contrasts the previously known NP-hardness result for finding a maximum clique in an arbitrary ball graph. - We design an 𝒪^*(n^{2k})-time algorithm to find a maximum clique in the intersection graph of a set S of n L-visible convex polygons, where k is the number of distinct shapes in S. This contrasts the known hardness result on finding a maximum clique in the intersection graph of unit disks and axis-aligned rectangles.
Cite as

J. Mark Keil and Debajyoti Mondal. The Maximum Clique Problem in a Disk Graph Made Easy. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 63:1-63:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{keil_et_al:LIPIcs.SoCG.2025.63,
  author =	{Keil, J. Mark and Mondal, Debajyoti},
  title =	{{The Maximum Clique Problem in a Disk Graph Made Easy}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{63:1--63:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.63},
  URN =		{urn:nbn:de:0030-drops-232155},
  doi =		{10.4230/LIPIcs.SoCG.2025.63},
  annote =	{Keywords: Geometric Intersection Graphs, Disk Graphs, Ball Graphs, Maximum Clique}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.6
Twin-Width One

Authors: Jungho Ahn, Hugo Jacob, Noleen Köhler, Christophe Paul, Amadeus Reinald, and Sebastian Wiederrecht

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

Abstract
We investigate the structure of graphs of twin-width at most 1, and obtain the following results: - Graphs of twin-width at most 1 are permutation graphs. In particular they have an intersection model and a linear structure. - There is always a 1-contraction sequence closely following a given permutation diagram. - Based on a recursive decomposition theorem, we obtain a simple algorithm running in linear time that produces a 1-contraction sequence of a graph, or guarantees that it has twin-width more than 1. - We characterise distance-hereditary graphs based on their twin-width and deduce a linear time algorithm to compute optimal sequences on this class of graphs.
Cite as

Jungho Ahn, Hugo Jacob, Noleen Köhler, Christophe Paul, Amadeus Reinald, and Sebastian Wiederrecht. Twin-Width One. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ahn_et_al:LIPIcs.STACS.2025.6,
  author =	{Ahn, Jungho and Jacob, Hugo and K\"{o}hler, Noleen and Paul, Christophe and Reinald, Amadeus and Wiederrecht, Sebastian},
  title =	{{Twin-Width One}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.6},
  URN =		{urn:nbn:de:0030-drops-228319},
  doi =		{10.4230/LIPIcs.STACS.2025.6},
  annote =	{Keywords: Twin-width, Hereditary graph classes, Intersection model}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.21
Adjacency Labeling Schemes for Small Classes

Authors: Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev

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

Abstract
A graph class admits an implicit representation if, for every positive integer n, its n-vertex graphs have a O(log n)-bit (adjacency) labeling scheme, i.e., their vertices can be labeled by binary strings of length O(log n) such that the presence of an edge between any pair of vertices can be deduced solely from their labels. The famous Implicit Graph Conjecture posited that every hereditary (i.e., closed under taking induced subgraphs) factorial (i.e., containing 2^O(n log n) n-vertex graphs) class admits an implicit representation. The conjecture was recently refuted [Hatami and Hatami, FOCS '22], and does not even hold among monotone (i.e., closed under taking subgraphs) factorial classes [Bonnet et al., ICALP '24]. However, monotone small (i.e., containing at most n! cⁿ many n-vertex graphs for some constant c) classes do admit implicit representations. This motivates the Small Implicit Graph Conjecture: Every hereditary small class admits an O(log n)-bit labeling scheme. We provide evidence supporting the Small Implicit Graph Conjecture. First, we show that every small weakly sparse (i.e., excluding some fixed bipartite complete graph as a subgraph) class has an implicit representation. This is a consequence of the following fact of independent interest proved in the paper: Every weakly sparse small class has bounded expansion (hence, in particular, bounded degeneracy). Second, we show that every hereditary small class admits an O(log³ n)-bit labeling scheme, which provides a substantial improvement of the best-known polynomial upper bound of n^(1-ε) on the size of adjacency labeling schemes for such classes. This is a consequence of another fact of independent interest proved in the paper: Every small class has neighborhood complexity O(n log n).
Cite as

Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev. Adjacency Labeling Schemes for Small Classes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonnet_et_al:LIPIcs.ITCS.2025.21,
  author =	{Bonnet, \'{E}douard and Duron, Julien and Sylvester, John and Zamaraev, Viktor},
  title =	{{Adjacency Labeling Schemes for Small Classes}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.21},
  URN =		{urn:nbn:de:0030-drops-226493},
  doi =		{10.4230/LIPIcs.ITCS.2025.21},
  annote =	{Keywords: Adjacency labeling, degeneracy, weakly sparse classes, small classes, implicit graph conjecture}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.69
Double Threshold Digraphs

Authors: Peter Hamburger, Ross M. McConnell, Attila Pór, Jeremy P. Spinrad, and Zhisheng Xu

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
A semiorder is a model of preference relations where each element x is associated with a utility value alpha(x), and there is a threshold t such that y is preferred to x iff alpha(y) - alpha(x) > t. These are motivated by the notion that there is some uncertainty in the utility values we assign an object or that a subject may be unable to distinguish a preference between objects whose values are close. However, they fail to model the well-known phenomenon that preferences are not always transitive. Also, if we are uncertain of the utility values, it is not logical that preference is determined absolutely by a comparison of them with an exact threshold. We propose a new model in which there are two thresholds, t_1 and t_2; if the difference alpha(y) - alpha(x) is less than t_1, then y is not preferred to x; if the difference is greater than t_2 then y is preferred to x; if it is between t_1 and t_2, then y may or may not be preferred to x. We call such a relation a (t_1,t_2) double-threshold semiorder, and the corresponding directed graph G = (V,E) a (t_1,t_2) double-threshold digraph. Every directed acyclic graph is a double-threshold digraph; increasing bounds on t_2/t_1 give a nested hierarchy of subclasses of the directed acyclic graphs. In this paper we characterize the subclasses in terms of forbidden subgraphs, and give algorithms for finding an assignment of utility values that explains the relation in terms of a given (t_1,t_2) or else produces a forbidden subgraph, and finding the minimum value lambda of t_2/t_1 that is satisfiable for a given directed acyclic graph. We show that lambda gives a useful measure of the complexity of a directed acyclic graph with respect to several optimization problems that are NP-hard on arbitrary directed acyclic graphs.
Cite as

Peter Hamburger, Ross M. McConnell, Attila Pór, Jeremy P. Spinrad, and Zhisheng Xu. Double Threshold Digraphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 69:1-69:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{hamburger_et_al:LIPIcs.MFCS.2018.69,
  author =	{Hamburger, Peter and McConnell, Ross M. and P\'{o}r, Attila and Spinrad, Jeremy P. and Xu, Zhisheng},
  title =	{{Double Threshold Digraphs}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{69:1--69:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.69},
  URN =		{urn:nbn:de:0030-drops-96519},
  doi =		{10.4230/LIPIcs.MFCS.2018.69},
  annote =	{Keywords: posets, preference relations, approximation algorithms}
}
Document
DOI: 10.4230/DagSemProc.07211.1
07211 Abstracts Collection – Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes

Authors: Andreas Brandstädt, Klaus Jansen, Dieter Kratsch, and Jeremy P. Spinrad

Published in: Dagstuhl Seminar Proceedings, Volume 7211, Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes (2007)

Abstract
From May 20 to May 25, 2007, the Dagstuhl Seminar 07211 ``Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Andreas Brandstädt, Klaus Jansen, Dieter Kratsch, and Jeremy P. Spinrad. 07211 Abstracts Collection – Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes. In Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes. Dagstuhl Seminar Proceedings, Volume 7211, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{brandstadt_et_al:DagSemProc.07211.1,
  author =	{Brandst\"{a}dt, Andreas and Jansen, Klaus and Kratsch, Dieter and Spinrad, Jeremy P.},
  title =	{{07211 Abstracts Collection – Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes}},
  booktitle =	{Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7211},
  editor =	{Andreas Brandst\"{a}dt and Klaus Jansen and Dieter Kratsch and Jeremy P. Spinrad},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07211.1},
  URN =		{urn:nbn:de:0030-drops-12697},
  doi =		{10.4230/DagSemProc.07211.1},
  annote =	{Keywords: Graph theory, approximation algorithms, certifying algorithms, exact algorithms}
}
Document
DOI: 10.4230/DagSemProc.07211.2
Linear-time certifying recognition for partitioned probe cographs

Authors: Van Bang Le and H.N. de Ridder

Published in: Dagstuhl Seminar Proceedings, Volume 7211, Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes (2007)

Abstract
Cographs are those graphs without induced path on four vetices. A graph $G=(V, E)$ with a partition $V=Pcup N$ where $N$ is an independent set is a partitioned probe cograph if one can add new edges between certain vertices in $N$ in such a way that the graph obtained is a cograph. We characterize partitioned probe cographs in terms of five forbidden induced subgraphs. Using this characterization, we give a linear-time recognition algorithm for partitioned probe cographs. Our algorithm produces a certificate for membership that can be checked in linear time and a certificate for non-membership that can be checked in sublinear time.
Cite as

Van Bang Le and H.N. de Ridder. Linear-time certifying recognition for partitioned probe cographs. In Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes. Dagstuhl Seminar Proceedings, Volume 7211, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{le_et_al:DagSemProc.07211.2,
  author =	{Le, Van Bang and de Ridder, H.N.},
  title =	{{Linear-time certifying recognition for partitioned probe cographs}},
  booktitle =	{Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7211},
  editor =	{Andreas Brandst\"{a}dt and Klaus Jansen and Dieter Kratsch and Jeremy P. Spinrad},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07211.2},
  URN =		{urn:nbn:de:0030-drops-12703},
  doi =		{10.4230/DagSemProc.07211.2},
  annote =	{Keywords: Cograph, probe cograph, certifying graph algorithm}
}
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