A note on efficient computation of hybridization number via softwired clusters

TL;DR

This paper introduces a fixed parameter tractable algorithm for computing the hybridization number of two rooted binary phylogenetic trees, avoiding MAAFs by leveraging softwired cluster equivalences, thus providing a new combinatorial perspective.

Contribution

It presents a novel FPT algorithm that bypasses MAAFs by connecting hybridization number computation with softwired cluster problems.

Findings

Algorithm runs in (6r)^r.poly(n) time

Avoids use of Maximum Acyclic Agreement Forests

Provides new combinatorial insights into hybridization number

Abstract

Here we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted binary phylogenetic trees on taxon set X in time (6r)^r.poly(n), where n=|X|. The novelty of this approach is that it avoids the use of Maximum Acyclic Agreement Forests (MAAFs) and instead exploits the equivalence of the problem with a related problem from the softwired clusters literature. This offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem.