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Open Access Research

Constructing perfect phylogenies and proper triangulations for three-state characters

Rob Gysel*, Fumei Lam* and Dan Gusfield

Author Affiliations

Department of Computer Science, University of California, Davis, 1 Shields Avenue, Davis CA 95616, USA

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Algorithms for Molecular Biology 2012, 7:26  doi:10.1186/1748-7188-7-26

Published: 24 September 2012

Abstract

In this paper, we study the problem of constructing perfect phylogenies for three-state characters. Our work builds on two recent results. The first result states that for three-state characters, the local condition of examining all subsets of three characters is sufficient to determine the global property of admitting a perfect phylogeny. The second result applies tools from minimal triangulation theory to the partition intersection graph to determine if a perfect phylogeny exists. Despite the wealth of combinatorial tools and algorithms stemming from the chordal graph and minimal triangulation literature, it is unclear how to use such approaches to efficiently construct a perfect phylogeny for three-state characters when the data admits one. We utilize structural properties of both the partition intersection graph and the original data in order to achieve a competitive time bound.

Keywords:
Perfect phylogeny; Chordal graph; Minimal triangulation; Minimal separator