Compatibility of unrooted phylogenetic trees is FPT

Authors:
David Bryant;Jens Lagergren
Affiliations:
McGill Centre for Bioinformatics, Montreal, Que., Canada;Stockholm Bioinformatics Center and Department of Numerical Analysis and Computer Science, KTH, Stockholm, Sweden
Venue:
Theoretical Computer Science - Parameterized and exact computation
Year:
2006

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Abstract

A collection of T1, T2,...,Tk of unrooted, leaf labelled (phylogenetic) trees, all with different leaf sets, is said to be compatible if there exists a tree T such that each tree Ti can be obtained from T by deleting leaves and contracting edges. Determining compatibility is NP-hard, and the fastest algorithm to date has worst case complexity of around Ω(nk) time, n being the number of leaves. Here, we present an O(nf(k)) algorithm, proving that compatibility of unrooted phylogenetic trees is fixed parameter tractable (FPT) with respect to the number k of trees.