2 Search Results for "van Geffen, Bas A. M."

Document
DOI: 10.4230/LIPIcs.STACS.2023.14
Tight Bounds for Connectivity Problems Parameterized by Cutwidth

Authors: Narek Bojikian, Vera Chekan, Falko Hegerfeld, and Stefan Kratsch

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
In this work we start the investigation of tight complexity bounds for connectivity problems parameterized by cutwidth assuming the Strong Exponential-Time Hypothesis (SETH). Van Geffen et al. [Bas A. M. van Geffen et al., 2020] posed this question for Odd Cycle Transversal and Feedback Vertex Set. We answer it for these two and four further problems, namely Connected Vertex Cover, Connected Dominating Set, Steiner Tree, and Connected Odd Cycle Transversal. For the latter two problems it sufficed to prove lower bounds that match the running time inherited from parameterization by treewidth; for the others we provide faster algorithms than relative to treewidth and prove matching lower bounds. For upper bounds we first extend the idea of Groenland et al. [Carla Groenland et al., 2022] to solve what we call coloring-like problems. Such problems are defined by a symmetric matrix M over 𝔽₂ indexed by a set of colors. The goal is to count the number (modulo some prime p) of colorings of a graph such that M has a 1-entry if indexed by the colors of the end-points of any edge. We show that this problem can be solved faster if M has small rank over 𝔽_p. We apply this result to get our upper bounds for CVC and CDS. The upper bounds for OCT and FVS use a subdivision trick to get below the bounds that matrix rank would yield.
Cite as

Narek Bojikian, Vera Chekan, Falko Hegerfeld, and Stefan Kratsch. Tight Bounds for Connectivity Problems Parameterized by Cutwidth. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bojikian_et_al:LIPIcs.STACS.2023.14,
  author =	{Bojikian, Narek and Chekan, Vera and Hegerfeld, Falko and Kratsch, Stefan},
  title =	{{Tight Bounds for Connectivity Problems Parameterized by Cutwidth}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.14},
  URN =		{urn:nbn:de:0030-drops-176667},
  doi =		{10.4230/LIPIcs.STACS.2023.14},
  annote =	{Keywords: Parameterized complexity, connectivity problems, cutwidth}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2018.3
Lower Bounds for Dynamic Programming on Planar Graphs of Bounded Cutwidth

Authors: Bas A. M. van Geffen, Bart M. P. Jansen, Arnoud A. W. M. de Kroon, and Rolf Morel

Published in: LIPIcs, Volume 115, 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

Abstract
Many combinatorial problems can be solved in time O^*(c^{tw}) on graphs of treewidth tw, for a problem-specific constant c. In several cases, matching upper and lower bounds on c are known based on the Strong Exponential Time Hypothesis (SETH). In this paper we investigate the complexity of solving problems on graphs of bounded cutwidth, a graph parameter that takes larger values than treewidth. We strengthen earlier treewidth-based lower bounds to show that, assuming SETH, Independent Set cannot be solved in O^*((2-epsilon)^{ctw}) time, and Dominating Set cannot be solved in O^*((3-epsilon)^{ctw}) time. By designing a new crossover gadget, we extend these lower bounds even to planar graphs of bounded cutwidth or treewidth. Hence planarity does not help when solving Independent Set or Dominating Set on graphs of bounded width. This sharply contrasts the fact that in many settings, planarity allows problems to be solved much more efficiently.
Cite as

Bas A. M. van Geffen, Bart M. P. Jansen, Arnoud A. W. M. de Kroon, and Rolf Morel. Lower Bounds for Dynamic Programming on Planar Graphs of Bounded Cutwidth. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 3:1-3:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{vangeffen_et_al:LIPIcs.IPEC.2018.3,
  author =	{van Geffen, Bas A. M. and Jansen, Bart M. P. and de Kroon, Arnoud A. W. M. and Morel, Rolf},
  title =	{{Lower Bounds for Dynamic Programming on Planar Graphs of Bounded Cutwidth}},
  booktitle =	{13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-084-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{115},
  editor =	{Paul, Christophe and Pilipczuk, Michal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2018.3},
  URN =		{urn:nbn:de:0030-drops-102049},
  doi =		{10.4230/LIPIcs.IPEC.2018.3},
  annote =	{Keywords: planarization, dominating set, cutwidth, lower bounds, strong exponential time hypothesis}
}
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