Parameterized Algorithms for the Maximum Agreement Forest Problem on Multiple Rooted Multifurcating Trees

TL;DR

This paper develops fixed-parameter algorithms for the Maximum Agreement Forest problem on multiple rooted multifurcating phylogenetic trees, extending previous work from binary trees to more complex structures with different biological interpretations.

Contribution

It introduces two new parameterized algorithms with improved running times for the generalized problem involving multifurcating trees, considering different biological meanings of polytomies.

Findings

Algorithms run in $O(2.42^k m^3 n^4)$ and $O(2.74^k m^3 n^5)$ time

Addresses both hard and soft versions of the problem

Extends phylogenetic agreement forest analysis to multifurcating trees

Abstract

The Maximum Agreement Forest problem has been extensively studied in phylogenetics. Most previous work is on two binary phylogenetic trees. In this paper, we study a generalized version of the problem: the Maximum Agreement Forest problem on multiple rooted multifurcating phylogenetic trees, from the perspective of fixed-parameter algorithms. By taking advantage of a new branch-and-bound strategy, two parameterized algorithms, with running times $O(2.42^k m^3 n^4)$ and $O(2.74^k m^3 n^5)$, respectively, are presented for the hard version and the soft version of the problem, which correspond to two different biological meanings to the polytomies in multifurcating phylogenetic trees.