A simple fixed parameter tractable algorithm for computing the hybridization number of two (not necessarily binary) trees

TL;DR

This paper introduces a new fixed parameter tractable algorithm for computing the hybridization number of two rooted phylogenetic trees, utilizing terminals and softwired cluster insights for a simple, practical bounded-search approach.

Contribution

It presents a novel fixed parameter tractable algorithm that simplifies the computation of hybridization numbers by leveraging terminals and softwired cluster concepts.

Findings

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

Uses terminals and softwired clusters for simplicity

Provides an alternative combinatorial perspective

Abstract

Here we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted, not necessarily binary phylogenetic trees on taxon set X in time (6^r.r!).poly(n)$, where n=|X|. The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on X, and several insights from the softwired clusters literature. This yields a surprisingly simple and practical bounded-search algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem.