License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2020.65
URN: urn:nbn:de:0030-drops-129316
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12931/
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Koana, Tomohiro ; Komusiewicz, Christian ; Sommer, Frank

Exploiting c-Closure in Kernelization Algorithms for Graph Problems

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Abstract

A graph is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of a graph G is the smallest number c such that G is c-closed. Fox et al. [SIAM J. Comput. '20] defined c-closure and investigated it in the context of clique enumeration. We show that c-closure can be applied in kernelization algorithms for several classic graph problems. We show that Dominating Set admits a kernel of size k^?(c), that Induced Matching admits a kernel with ?(c⁷ k⁸) vertices, and that Irredundant Set admits a kernel with ?(c^{5/2} k³) vertices. Our kernelization exploits the fact that c-closed graphs have polynomially-bounded Ramsey numbers, as we show.

BibTeX - Entry

@InProceedings{koana_et_al:LIPIcs:2020:12931,
  author =	{Tomohiro Koana and Christian Komusiewicz and Frank Sommer},
  title =	{{Exploiting c-Closure in Kernelization Algorithms for Graph Problems}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{65:1--65:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12931},
  URN =		{urn:nbn:de:0030-drops-129316},
  doi =		{10.4230/LIPIcs.ESA.2020.65},
  annote =	{Keywords: Fixed-parameter tractability, kernelization, c-closure, Dominating Set, Induced Matching, Irredundant Set, Ramsey numbers}
}

Keywords: Fixed-parameter tractability, kernelization, c-closure, Dominating Set, Induced Matching, Irredundant Set, Ramsey numbers
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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