Embedding phylogenetic trees in networks of low treewidth

TL;DR

This paper introduces an algorithm for embedding phylogenetic trees into networks by leveraging the network's treewidth, enabling efficient validation of inferred phylogenetic networks.

Contribution

It presents the first fixed-parameter algorithm for the Tree Containment problem based on the network's treewidth, with a runtime of 2^{O(t^2)}·|N|.

Findings

Algorithm solves Tree Containment in 2^{O(t^2)}·|N| time

Uses treewidth as a parameter for efficient computation

First fixed-parameter algorithm for this problem

Abstract

Given a rooted, binary phylogenetic network and a rooted, binary phylogenetic tree, can the tree be embedded into the network? This problem, called \textsc{Tree Containment}, arises when validating networks constructed by phylogenetic inference methods.We present the first algorithm for (rooted) \textsc{Tree Containment} using the treewidth $t$ of the input network $N$ as parameter, showing that the problem can be solved in $2^{O(t^2)}\cdot|N|$ time and space.