Locating a Tree in a Phylogenetic Network in Quadratic Time

TL;DR

This paper presents a quadratic-time algorithm to determine if a phylogenetic network contains a specific tree, focusing on binary nearly-stable networks, and establishes bounds on reticulations relative to taxa.

Contribution

It introduces an efficient quadratic-time algorithm for tree containment in binary nearly-stable networks and proves bounds on reticulations based on taxa count.

Findings

Quadratic-time algorithm for tree containment

Bound on reticulations linear in number of taxa

Applicable to binary nearly-stable networks

Abstract

A fundamental problem in the study of phylogenetic networks is to determine whether or not a given phylogenetic network contains a given phylogenetic tree. We develop a quadratic-time algorithm for this problem for binary nearly-stable phylogenetic networks. We also show that the number of reticulations in a reticulation visible or nearly stable phylogenetic network is bounded from above by a function linear in the number of taxa.