On Determining if Tree-based Networks Contain Fixed Trees

TL;DR

This paper proves that determining whether a phylogenetic network is based on a fixed tree is NP-hard, but also fixed parameter tractable, addressing an open question in phylogenetics.

Contribution

It establishes the NP-hardness of the problem and shows it is fixed parameter tractable, advancing understanding of phylogenetic network analysis.

Findings

NP-hardness of deciding if a network is based on a fixed tree

The problem is fixed parameter tractable

Addresses an open question in phylogenetics

Abstract

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is N based on T? We show that it is NP-hard to decide, by reduction from 3-Dimensional Matching (3DM), and further, that the problem is fixed parameter tractable.