Fast Compatibility Testing for Rooted Phylogenetic Trees

TL;DR

This paper introduces a new, efficient algorithm for testing compatibility of multiple rooted phylogenetic trees, which operates quickly regardless of the trees' node degrees, improving performance over previous methods.

Contribution

The authors present a $ ilde{O}(M_ ext{P})$ algorithm for tree compatibility that is independent of node degrees, enabling faster analysis of both resolved and unresolved trees.

Findings

Algorithm runs in $ ilde{O}(M_ ext{P})$ time

Performance independent of node degrees

Effective on highly resolved and unresolved trees

Abstract

We consider the following basic problem in phylogenetic tree construction. Let $\mathcal{P} = \{T_1, \ldots, T_k\}$ be a collection of rooted phylogenetic trees over various subsets of a set of species. The tree compatibility problem asks whether there is a tree $T$ with the following property: for each $i \in \{1, \dots, k\}$, $T_i$ can be obtained from the restriction of $T$ to the species set of $T_i$ by contracting zero or more edges. If such a tree $T$ exists, we say that $\mathcal{P}$ is compatible. We give a $\tilde{O}(M_\mathcal{P})$ algorithm for the tree compatibility problem, where $M_\mathcal{P}$ is the total number of nodes and edges in $\mathcal{P}$. Unlike previous algorithms for this problem, the running time of our method does not depend on the degrees of the nodes in the input trees. Thus, it is equally fast on highly resolved and highly unresolved trees.