Least resolved trees for two-colored best match graphs

TL;DR

This paper introduces a new efficient algorithm for recognizing 2-colored best match graphs and constructing their least resolved trees, which are important in phylogenetic analysis of gene evolution.

Contribution

The paper presents a novel $O(|V|+|E|\log^2|V|)$-time algorithm for recognizing 2-BMGs and building their least resolved trees, extending to binary-explainable cases.

Findings

Algorithm is efficient and outperforms previous methods

Successfully constructs least resolved trees for 2-BMGs

Empirical tests confirm practical efficiency

Abstract

2-colored best match graphs (2-BMGs) form a subclass of sink-free bi-transitive graphs that appears in phylogenetic combinatorics. There, 2-BMGs describe evolutionarily most closely related genes between a pair of species. They are explained by a unique least resolved tree (LRT). Introducing the concept of support vertices we derive an $O(|V|+|E|\log^2|V|)$-time algorithm to recognize 2-BMGs and to construct its LRT. The approach can be extended to also recognize binary-explainable 2-BMGs with the same complexity. An empirical comparison emphasizes the efficiency of the new algorithm.