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.IPEC.2020.9
URN: urn:nbn:de:0030-drops-133127
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13312/
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Dublois, Louis ; Lampis, Michael ; Paschos, Vangelis Th.

New Algorithms for Mixed Dominating Set

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LIPIcs-IPEC-2020-9.pdf (0.5 MB)

Abstract

A mixed dominating set is a set of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for MDS, resolving some open questions. In particular, we settle the problem’s complexity parameterized by treewidth and pathwidth by giving an algorithm running in time O^*(5^{tw}) (improving the current best O^*(6^{tw})), and a lower bound showing that our algorithm cannot be improved under the SETH, even if parameterized by pathwidth (improving a lower bound of O^*((2-ε)^{pw})). Furthermore, by using a simple but so far overlooked observation on the structure of minimal solutions, we obtain branching algorithms which improve the best known FPT algorithm for this problem, from O^*(4.172^k) to O^*(3.510^k), and the best known exact algorithm, from O^*(2ⁿ) and exponential space, to O^*(1.912ⁿ) and polynomial space.

BibTeX - Entry

@InProceedings{dublois_et_al:LIPIcs:2020:13312,
  author =	{Louis Dublois and Michael Lampis and Vangelis Th. Paschos},
  title =	{{New Algorithms for Mixed Dominating Set}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Yixin Cao and Marcin Pilipczuk},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13312},
  URN =		{urn:nbn:de:0030-drops-133127},
  doi =		{10.4230/LIPIcs.IPEC.2020.9},
  annote =	{Keywords: FPT Algorithms, Exact Algorithms, Mixed Domination}
}

Keywords: FPT Algorithms, Exact Algorithms, Mixed Domination
Collection: 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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