UNIQUENESS, INTRACTABILITY AND EXACT ALGORITHMS: REFLECTIONS ON LEVEL-K PHYLOGENETIC NETWORKS

Author:

VAN IERSEL LEO1,KELK STEVEN2,MNICH MATTHIAS1

Affiliation:

1. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P. O. Box 513, 5600 MB Eindhoven, The Netherlands

2. Centrum voor Wiskunde en Informatica (CWI), P. O. Box 94079, 1090 GB Amsterdam, The Netherlands

Abstract

Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network determines how non-treelike the evolution can be, with level-0 networks being trees. We study the problem of constructing level-k phylogenetic networks from triplets, i.e. phylogenetic trees for three leaves (taxa). We give, for each k, a level-k network that is uniquely defined by its triplets. We demonstrate the applicability of this result by using it to prove that (1) for all k ≥ 1 it is NP-hard to construct a level-k network consistent with all input triplets, and (2) for all k ≥ 0 it is NP-hard to construct a level-k network consistent with a maximum number of input triplets, even when the input is dense. As a response to this intractability, we give an exact algorithm for constructing level-1 networks consistent with a maximum number of input triplets.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computer Science Applications,Molecular Biology,Biochemistry

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