Linear-Time Tree Containment in Phylogenetic Networks

TL;DR

This paper presents a linear-time algorithm for the Tree Containment problem in certain classes of phylogenetic networks, significantly improving efficiency for complex network structures.

Contribution

The authors develop a fast, linear-time algorithm for Tree Containment in reticulation visible and nearly stable networks, extending previous methods to more general network classes.

Findings

Linear-time algorithm for specific phylogenetic networks

Improved efficiency over previous algorithms

Applicable to complex network classes

Abstract

We consider the NP-hard Tree Containment problem that has important applications in phylogenetics. The problem asks if a given leaf-labeled network contains a subdivision of a given leaf-labeled tree. We develop a fast algorithm for the case that the input network is indeed a tree in which multiple leaves might share a label. By combining this algorithm with a generalization of a previously known decomposition scheme, we improve the running time on reticulation visible networks and nearly stable networks to linear time. While these are special classes of networks, they rank among the most general of the previously considered classes.