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.2016.8
URN: urn:nbn:de:0030-drops-69199
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/6919/
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Borradaile, Glencora ; Le, Hung

Optimal Dynamic Program for r-Domination Problems over Tree Decompositions

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LIPIcs-IPEC-2016-8.pdf (0.6 MB)

Abstract

There has been recent progress in showing that the exponential dependence on treewidth in dynamic programming algorithms for solving NP-hard problems is optimal under the Strong Exponential Time Hypothesis (SETH). We extend this work to r-domination problems. In r-dominating set, one wishes to find a minimum subset S of vertices such that every vertex of G is within r hops of some vertex in S. In connected r-dominating set, one additionally requires that the set induces a connected subgraph of G. We give a O((2r+1)^tw n) time algorithm for r-dominating set and a randomized O((2r+2)^tw n^{O(1)}) time algorithm for connected r-dominating set in n-vertex graphs of treewidth tw. We show that the running time dependence on r and tw is the best possible under SETH. This adds to earlier observations that a "+1" in the denominator is required for connectivity constraints.

BibTeX - Entry

@InProceedings{borradaile_et_al:LIPIcs:2017:6919,
  author =	{Glencora Borradaile and Hung Le},
  title =	{{Optimal Dynamic Program for r-Domination Problems over Tree Decompositions}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{8:1--8:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Jiong Guo and Danny Hermelin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/6919},
  URN =		{urn:nbn:de:0030-drops-69199},
  doi =		{10.4230/LIPIcs.IPEC.2016.8},
  annote =	{Keywords: r-dominating set, Exponential Time Hypothesis, Dynamic Programming}
}

Keywords: r-dominating set, Exponential Time Hypothesis, Dynamic Programming
Collection: 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)
Issue Date: 2017
Date of publication: 09.02.2017

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