A Simple Characterization of the Minimal Obstruction Sets for Three-State Perfect Phylogenies

TL;DR

This paper provides a simplified characterization for identifying minimal obstruction sets in three-state perfect phylogenies, enabling detection of non-phylogenic sets through pairwise testing rather than exhaustive triple testing.

Contribution

It introduces a straightforward method to determine non-perfect phylogeny sets of three-state characters using pairwise tests, improving upon prior complex characterizations.

Findings

Characterization based on pairwise testing for three-state characters

Reduced computational complexity in detecting non-phylogenic sets

Enhanced understanding of minimal obstruction sets in phylogenetics

Abstract

Lam, Gusfield, and Sridhar (2009) showed that a set of three-state characters has a perfect phylogeny if and only if every subset of three characters has a perfect phylogeny. They also gave a complete characterization of the sets of three three-state characters that do not have a perfect phylogeny. However, it is not clear from their characterization how to find a subset of three characters that does not have a perfect phylogeny without testing all triples of characters. In this note, we build upon their result by giving a simple characterization of when a set of three-state characters does not have a perfect phylogeny that can be inferred from testing all pairs of characters.