Kernel and fast algorithm for dense triplet inconsistency

Authors:
Sylvain Guillemot;Matthias Mnich
Affiliations:
Lehrstuhl für Bioinformatik, Friedrich-Schiller Universität Jena, Jena, Germany;Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Eindhoven, MB, The Netherlands
Venue:
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Year:
2010

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Abstract

We study the parameterized complexity of inferring supertrees from sets of rooted triplets, an important problem in phylogenetics For a set L of labels and a dense set $\mathcal R$ of triplets distinctly leaf-labeled by 3-subsets of L we seek a tree distinctly leaf-labeled by L and containing all but at most p triplets from $\mathcal R$ as homeomorphic subtree Our results are the first polynomial kernel for this problem, with O(p2) labels, and a subexponential fixed-parameter algorithm running in time $2^{O(p^{1/3} \log p)} + O(n^4)$.