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.FSTTCS.2014.73
URN: urn:nbn:de:0030-drops-48340
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4834/
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Basavaraju, Manu ; Fomin, Fedor V. ; Golovach, Petr A. ; Saurabh, Saket

Connecting Vertices by Independent Trees

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Abstract

We study the paramereteized complexity of the following connectivity problem. For a vertex subset U of a graph G, trees T_1,...,T_s of G are completely independent spanning trees of U if each of them contains U, and for every two distinct vertices u,v in U, the paths from u to v in T_1,...,T_s are pairwise vertex disjoint except for end-vertices u and v. Then for a given s >= 2 and a parameter k, the task is to decide if a given n-vertex graph G contains a set U of size at least k such that there are s completely independent spanning trees of U. The problem is known to be NP-complete already for s=2. We prove the following results: (*) For s=2 the problem is solvable in time 2^{O(k)}*n^{O(1)}. (*) For s=2 the problem does not admit a polynomial kernel unless NP subseteq coNP/poly. (*) For arbitrary s, we show that the problem is solvable in time f(s,k)n^{O(1)} for some function f of s and k only.

BibTeX - Entry

@InProceedings{basavaraju_et_al:LIPIcs:2014:4834,
  author =	{Manu Basavaraju and Fedor V. Fomin and Petr A. Golovach and Saket Saurabh},
  title =	{{Connecting Vertices by Independent Trees}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{73--84},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Venkatesh Raman and S. P. Suresh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4834},
  URN =		{urn:nbn:de:0030-drops-48340},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.73},
  annote =	{Keywords: Parameterized complexity, FPT-algorithms, completely independent spanning trees}
}

Keywords: Parameterized complexity, FPT-algorithms, completely independent spanning trees
Collection: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
Issue Date: 2014
Date of publication: 12.12.2014

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