5 Search Results for "Bacsó, Gábor"

Document
DOI: 10.4230/LIPIcs.ISAAC.2025.12
Star-Based Separators for Intersection Graphs of c-Colored Pseudo-Segments

Authors: Mark de Berg, Bart M. P. Jansen, and Jeroen S. K. Lamme

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

Abstract
The Planar Separator Theorem, which states that any planar graph 𝒢 has a separator consisting of O(√n) nodes whose removal partitions 𝒢 into components of size at most 2n/3, is a widely used tool to obtain fast algorithms on planar graphs. Intersection graphs of disks, which generalize planar graphs, do not admit such separators. It has recently been shown that disk graphs do admit so-called clique-based separators that consist of O(√n) cliques. This result has been generalized to intersection graphs of various other types of disk-like objects. Unfortunately, segment intersection graphs do not admit small clique-based separators, because they can contain arbitrarily large bicliques. This is true even in the simple case of axis-aligned segments. In this paper we therefore introduce biclique-based separators (and, in particular, star-based separators), which are separators consisting of a small number of bicliques (or stars). We prove that any c-oriented set of n segments in the plane, where c is a constant, admits a star-based separator consisting of O(√n) stars. In fact, our result is more general, as it applies to any set of n pseudo-segments that is partitioned into c subsets such that the pseudo-segments in the same subset are pairwise disjoint. We extend our result to intersection graphs of c-oriented polygons. These results immediately lead to an almost-exact distance oracle for such intersection graphs, which has O(n√n) storage and O(√n) query time, and that can report the hop-distance between any two query nodes in the intersection graph with an additive error of at most 2. This is the first distance oracle for such types of intersection graphs that has subquadratic storage and sublinear query time and that only has an additive error.
Cite as

Mark de Berg, Bart M. P. Jansen, and Jeroen S. K. Lamme. Star-Based Separators for Intersection Graphs of c-Colored Pseudo-Segments. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{deberg_et_al:LIPIcs.ISAAC.2025.12,
  author =	{de Berg, Mark and Jansen, Bart M. P. and Lamme, Jeroen S. K.},
  title =	{{Star-Based Separators for Intersection Graphs of c-Colored Pseudo-Segments}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{12:1--12:16},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-249207},
  doi =		{10.4230/LIPIcs.ISAAC.2025.12},
  annote =	{Keywords: Computational geometry, intersection graphs, biclique-based separators, distance oracles}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.40
Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs

Authors: Esther Galby, Paloma T. Lima, Andrea Munaro, and Amir Nikabadi

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

Abstract
We show that, for every fixed positive integers r and k, Max-Weight List r-Colorable Induced Subgraph admits a polynomial-time algorithm on kP₃-free graphs. This problem is a common generalization of Max-Weight Independent Set, Odd Cycle Transversal and List r-Coloring, among others. Our result has several consequences. First, it implies that, for every fixed r ≥ 5, assuming 𝖯 ≠ NP, Max-Weight List r-Colorable Induced Subgraph is polynomial-time solvable on H-free graphs if and only if H is an induced subgraph of either kP₃ or P₅+kP₁, for some k ≥ 1. Second, it makes considerable progress toward a complexity dichotomy for Odd Cycle Transversal on H-free graphs, allowing to answer a question of Agrawal, Lima, Lokshtanov, Rzążewski, Saurabh, and Sharma [ACM Trans. Algorithms 2025]. Third, it gives a short and self-contained proof of the known result of Chudnovsky, Hajebi, and Spirkl [Combinatorica 2024] that List r-Coloring on kP₃-free graphs is polynomial-time solvable for every fixed r and k. We also consider two natural distance-d generalizations of Max-Weight Independent Set and List r-Coloring and provide polynomial-time algorithms on kP₃-free graphs for every fixed integers r, k, and d ≥ 6.
Cite as

Esther Galby, Paloma T. Lima, Andrea Munaro, and Amir Nikabadi. Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 40:1-40:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{galby_et_al:LIPIcs.ESA.2025.40,
  author =	{Galby, Esther and Lima, Paloma T. and Munaro, Andrea and Nikabadi, Amir},
  title =	{{Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{40:1--40:13},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-245086},
  doi =		{10.4230/LIPIcs.ESA.2025.40},
  annote =	{Keywords: Hereditary classes, list coloring, odd cycle transversal, independent set}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.28
Graphs with No Long Claws: An Improved Bound for the Analog of the Gyárfás' Path Argument

Authors: Romain Bourneuf, Jana Masaříková, Wojciech Nadara, and Marcin Pilipczuk

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

Abstract
For a fixed integer t ⩾ 1, a (t-)long claw, denoted S_{t,t,t}, is the unique tree with three leaves, each at distance exactly t from the vertex of degree three. Majewski et al. [ICALP 2022, ACM ToCT 2024] proved an analog of the Gyárfás' path argument for S_{t,t,t}-free graphs: given an n-vertex S_{t,t,t}-free graph, one can delete neighborhoods of 𝒪(log n) vertices so that the remainder admits an extended strip decomposition (an appropriate generalization of partition into connected components) into particles of multiplicatively smaller size. In this work, we refine the argument of Majewski et al. to its arguably final form: we show that a constant number of neighborhoods suffice. The statement of Majewski et al. is one of the two pillars of a recent quasi-polynomial time algorithm for Maximum Weight Independent Set in S_{t,t,t}-free graphs [Gartland et al., STOC 2024]; our work immediately improves the quasi-polynomial function in the running time bound. Furthermore, our result significantly simplifies known polynomial-time algorithms for Maximum Weight Independent Set in S_{t,t,t}-free graphs with an additional sparsity assumption such as bounded degree or excluding a fixed biclique as a subgraph.
Cite as

Romain Bourneuf, Jana Masaříková, Wojciech Nadara, and Marcin Pilipczuk. Graphs with No Long Claws: An Improved Bound for the Analog of the Gyárfás' Path Argument. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bourneuf_et_al:LIPIcs.MFCS.2025.28,
  author =	{Bourneuf, Romain and Masa\v{r}{\'\i}kov\'{a}, Jana and Nadara, Wojciech and Pilipczuk, Marcin},
  title =	{{Graphs with No Long Claws: An Improved Bound for the Analog of the Gy\'{a}rf\'{a}s' Path Argument}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{28:1--28:16},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-241350},
  doi =		{10.4230/LIPIcs.MFCS.2025.28},
  annote =	{Keywords: long-claw-free graphs, extended strip decomposition, maximum weight independent set, Gy\'{a}rf\'{a}s' path, three in a tree}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.44
Independence and Domination on Bounded-Treewidth Graphs: Integer, Rational, and Irrational Distances

Authors: Tim A. Hartmann and Dániel Marx

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

Abstract
The distance-d variants of Independent Set and Dominating Set problems have been extensively studied from different algorithmic viewpoints. In particular, the complexity of these problems are well understood on bounded-treewidth graphs [Katsikarelis, Lampis, and Paschos, Discret. Appl. Math 2022][Borradaile and Le, IPEC 2016]: given a tree decomposition of width t, the two problems can be solved in time d^t⋅ n^O(1) and (2d+1)^t⋅ n^O(1), respectively. Furthermore, assuming the Strong Exponential-Time Hypothesis (SETH), the base constants are best possible in these running times: they cannot be improved to d-ε and 2d+1-ε, respectively, for any ε > 0. We investigate continuous versions of these problems in a setting introduced by Megiddo and Tamir [SICOMP 1983], where every edge is modeled by a unit-length interval of points. In the δ-Dispersion problem, the task is to find a maximum number of points (possibly inside edges) that are pairwise at distance at least δ from each other. Similarly, in the δ-Covering problem, the task is to find a minimum number of points (possibly inside edges) such that every point of the graph (including those inside edges) is at distance at most δ from the selected point set. We provide a comprehensive understanding of these two problems on bounded-treewidth graphs. 1) Let δ = a/b with a and b being coprime. If a ≤ 2, then δ-Dispersion is polynomial-time solvable. For a ≥ 3, given a tree decomposition of width t, the problem can be solved in time (2a)^t⋅ n^O(1), and, assuming SETH, there is no (2a-ε)^t⋅n^{O(1)} time algorithm for any ε > 0. 2) Let δ = a/b with a and b being coprime. If a = 1, then δ-Covering is polynomial-time solvable. For a ≥ 2, given a tree decomposition of width t, the problem can be solved in time ((2+2(bod 2)) a)^t⋅ n^O(1), and, assuming SETH, there is no ((2+2(bod 2))a -ε)^t⋅n^O(1) time algorithm for any ε > 0. 3) For every fixed irrational number δ > 0 satisfying some mild computability condition, both δ-Dispersion and δ-Covering can be solved in time n^O(t) on graphs of treewidth t. We show a very explicitly defined irrational number δ = (4∑_{j=1}^∞ 2^{-2^j})^{-1} ≈ 0.790085 such that δ-Dispersion and δ/2-Covering are W[1]-hard parameterized by the treewidth t of the input graph, and, assuming ETH, cannot be solved in time f(t)⋅n^o(t). As a key step in obtaining these results, we extend earlier results on distance-d versions of Independent Set and Dominating Set: We determine the exact complexity of these problems in the special case when the input graph arises from some graph G' by subdividing every edge exactly b times.
Cite as

Tim A. Hartmann and Dániel Marx. Independence and Domination on Bounded-Treewidth Graphs: Integer, Rational, and Irrational Distances. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{hartmann_et_al:LIPIcs.STACS.2025.44,
  author =	{Hartmann, Tim A. and Marx, D\'{a}niel},
  title =	{{Independence and Domination on Bounded-Treewidth Graphs: Integer, Rational, and Irrational Distances}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{44:1--44:19},
  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.2025.44},
  URN =		{urn:nbn:de:0030-drops-228700},
  doi =		{10.4230/LIPIcs.STACS.2025.44},
  annote =	{Keywords: Independence, Domination, Irrationals, Treewidth, SETH}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2016.3
H-Free Graphs, Independent Sets, and Subexponential-Time Algorithms

Authors: Gábor Bacsó, Dániel Marx, and Zsolt Tuza

Published in: LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

Abstract
It is an outstanding open question in algorithmic graph theory to determine the complexity of the MAXIMUM INDEPENDENT SET problem on P_t-free graphs, that is, on graphs not containing any induced path on t vertices. So far, polynomial-time algorithms are known only for t at most 5 [Lokshtanov et al., SODA 2014, 570-581, 2014]. Here we study the existence of subexponential-time algorithms for the problem: by generalizing an earlier result of Randerath and Schiermeyer for t=5 [Discrete App. Math., 158 (2010), 1041-1044], we show that for any t at least 5, there is an algorithm for MAXIMUM INDEPENDENT SET on P_t-free graphs whose running time is subexponential in the number of vertices. SCATTERED SET is the generalization of MAXIMUM INDEPENDENT SET where the vertices of the solution are required to be at distance at least $d$ from each other. We give a complete characterization of those graphs H for which SCATTERED SET on H-free graphs can be solved in time subexponential in the size of the input (that is, in the number of vertices plus the number of edges): * If every component of H is a path, then d-SCATTERED SET on H-free graphs with n vertices and m edges can be solved in time 2^{(n+m)^{1-O(1/|V(H)|)}}, even if d is part of the input. * Otherwise, assuming ETH, there is no 2^{o(n+m)} time algorithm for d-SCATTERED SET for any fixed d at least 3 on H-free graphs with n vertices and m edges.
Cite as

Gábor Bacsó, Dániel Marx, and Zsolt Tuza. H-Free Graphs, Independent Sets, and Subexponential-Time Algorithms. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 3:1-3:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{bacso_et_al:LIPIcs.IPEC.2016.3,
  author =	{Bacs\'{o}, G\'{a}bor and Marx, D\'{a}niel and Tuza, Zsolt},
  title =	{{H-Free Graphs, Independent Sets, and Subexponential-Time Algorithms}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{3:1--3:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Guo, Jiong and Hermelin, Danny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.3},
  URN =		{urn:nbn:de:0030-drops-69397},
  doi =		{10.4230/LIPIcs.IPEC.2016.3},
  annote =	{Keywords: independent set, scattered set, subexponential algorithms, H-free graphs}
}
  • Refine by Type
  • 5 Document/PDF
  • 4 Document/HTML

  • Refine by Publication Year
  • 4 2025
  • 1 2017

  • Refine by Author
  • 2 Marx, Dániel
  • 1 Bacsó, Gábor
  • 1 Bourneuf, Romain
  • 1 Galby, Esther
  • 1 Hartmann, Tim A.
  • Show More...

  • Refine by Series/Journal
  • 5 LIPIcs

  • Refine by Classification
  • 2 Mathematics of computing → Graph algorithms
  • 1 Mathematics of computing → Graph coloring
  • 1 Theory of computation → Design and analysis of algorithms
  • 1 Theory of computation → Discrete optimization
  • 1 Theory of computation → Graph algorithms analysis
  • Show More...

  • Refine by Keyword
  • 2 independent set
  • 1 Computational geometry
  • 1 Domination
  • 1 Gyárfás' path
  • 1 H-free graphs
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact