Uniqueness, intractability and exact algorithms : reflections on level-k phylogenetic networks

L.J.J. Iersel, van, S.M. Kelk, M. Mnich

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)597-623
Number of pages7
JournalJournal of Bioinformatics and Computational Biology
Volume7
Issue number4
DOIs
Publication statusPublished - 2009

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