Maximum Covering Subtrees for Phylogenetic Networks

TL;DR

This paper addresses the problem of measuring how close a phylogenetic network is to a tree-based structure by introducing a polynomial-time algorithm for maximum covering subtrees, enhancing understanding of evolutionary history modeling.

Contribution

It provides the first polynomial-time algorithm for maximum covering subtrees in phylogenetic networks, including non-binary cases, solving an open problem in the field.

Findings

Maximum covering subtree problem is solvable in polynomial time.

The approach encodes the problem as a minimum-cost maximum flow.

Applicable to non-binary phylogenetic networks.

Abstract

Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of Francis, Semple, and Steel about the complexity of determining how far a phylogenetic network is from being tree-based, including non-binary phylogenetic networks. We show that finding a phylogenetic tree covering the maximum number of nodes in a phylogenetic network can be be computed in polynomial time via an encoding into a minimum-cost maximum flow problem.