Least resolved trees for two-colored best match graphs

Abstract

In phylogenetic combinatorics, 2-colored best match graphs (2-BMGs) form a subclass of sink-free bi-transitive digraphs that describe the most closely related genes between a pair of species in an evolutionary scenario. They are explained by a unique least resolved tree (LRT). In this paper, the concept of support vertices is introduced and used to derive an $O(|V|+|E|\log^2|V|)$-time algorithm that recognizes a 2-BMG and constructs its LRT. The approach can be extended to allow the recognition of binary-explainable 2-BMGs with the same complexity. An empirical comparison emphasizes the efficiency of the new algorithm.