When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2008.1760
URN: urn:nbn:de:0030-drops-17600
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1760/
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### A Cubic-Vertex Kernel for Flip Consensus Tree

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### 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},