Kernel and fast algorithm for dense triplet inconsistency

Authors:
Sylvain Guillemot;Matthias Mnich
Affiliations:
Lehrstuhl für Bioinformatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe Platz 2, 07743 Jena, Germany;Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Theoretical Computer Science
Year:
2013

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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 T 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 k triplets from T as homeomorphic subtree. Our results are the first polynomial kernel for this problem, with O(k^2) labels, and a subexponential fixed-parameter algorithm running in time O(|L|^4)+2^O^(^k^^^1^^^/^^^3^l^o^g^k^).