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A Cubic-Vertex Kernel for Flip Consensus Tree

Authors Christian Komusiewicz, Johannes Uhlmann

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LIPIcs.FSTTCS.2008.1760.pdf
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Keywords
  • Fixed-parameter algorithm
  • problem kernel
  • NP-hard problem
  • graph modification problem
  • computational phylogenetics

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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.

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Christian Komusiewicz and Johannes Uhlmann. A Cubic-Vertex Kernel for Flip Consensus Tree. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 280-291, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008) https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1760

Author Details

Christian Komusiewicz
Johannes Uhlmann
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