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DOI: 10.4230/LIPIcs.FSTTCS.2008.1760
URN: urn:nbn:de:0030-drops-17600
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1760/
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Komusiewicz, Christian ; Uhlmann, Johannes

A Cubic-Vertex Kernel for Flip Consensus Tree

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08004.KomusiebiczChristian.1760.pdf (0.4 MB)

Abstract

Given a bipartite graph G=(V_c,V_t,E) and a non-negative integer k, the NP-complete Minimum-Flip Consensus Tree problem asks whether G can be transformed, using up to k edge insertions and deletions, into a graph that does not contain an induced P_5 with its first vertex in V_t (a so-called M-graph or Sigma-graph). This problem plays an important role in computational phylogenetics, V_c standing for the characters and V_t standing for taxa. Chen et al. [IEEE/ACM TCBB 2006] showed that Minimum-Flip Consensus Tree is NP-complete and presented a parameterized algorithm with running time O(6^k\cdot |V_t|\cdot |V_c|).
Recently, Boecker et al. [IWPEC'08] presented a refined search tree algorithm
with running time O(4.83^k(|V_t|+|V_c|) + |V_t|\cdot |V_c|).
We complement these results by polynomial-time executable data reduction rules yielding a problem kernel with O(k^3) vertices.

BibTeX - Entry

@InProceedings{komusiewicz_et_al:LIPIcs:2008:1760,
  author =	{Christian Komusiewicz and Johannes Uhlmann},
  title =	{{A Cubic-Vertex Kernel for Flip Consensus Tree}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{280--291},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Ramesh Hariharan and Madhavan Mukund and V Vinay},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1760},
  URN =		{urn:nbn:de:0030-drops-17600},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1760},
  annote =	{Keywords: Fixed-parameter algorithm, problem kernel, NP-hard problem, graph modification problem, computational phylogenetics}
}

Keywords: Fixed-parameter algorithm, problem kernel, NP-hard problem, graph modification problem, computational phylogenetics
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Issue Date: 2008
Date of publication: 05.12.2008

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