A quadratic kernel for computing the hybridization number of multiple trees

TL;DR

This paper demonstrates that the problem of computing the hybridization number for multiple rooted binary phylogenetic trees is fixed-parameter tractable and provides a quadratic kernel for it.

Contribution

It extends fixed-parameter tractability results from two trees to an arbitrary set of trees and introduces a quadratic kernel for the problem.

Findings

The hybridization number problem is fixed-parameter tractable for multiple trees.

A quadratic kernel for the problem is constructed.

The approach generalizes previous results from two trees to many trees.

Abstract

It has recently been shown that the NP-hard problem of calculating the minimum number of hybridization events that is needed to explain a set of rooted binary phylogenetic trees by means of a hybridization network is fixed-parameter tractable if an instance of the problem consists of precisely two such trees. In this paper, we show that this problem remains fixed-parameter tractable for an arbitrarily large set of rooted binary phylogenetic trees. In particular, we present a quadratic kernel.