Algorithms for Maximum Agreement Forest of Multiple General Trees

TL;DR

This paper extends algorithms for the Maximum Agreement Forest problem to multiple general phylogenetic trees, providing new parameterized and approximation algorithms, along with implementation and testing on real and simulated data.

Contribution

It introduces the first parameterized and approximation algorithms for the Maf problem on multiple general phylogenetic trees, broadening previous binary-focused work.

Findings

Parameterized algorithm with runtime $O(3^k n^2m)$ for rooted trees

3-approximation algorithm for rooted trees

Parameterized algorithm with runtime $O(4^k n^2m)$ for unrooted trees

Abstract

The Maximum Agreement Forest (Maf) problem is a well-studied problem in evolutionary biology, which asks for a largest common subforest of a given collection of phylogenetic trees with identical leaf label-set. However, the previous work about the Maf problem are mainly on two binary phylogenetic trees or two general (i.e., binary and non-binary) phylogenetic trees. In this paper, we study the more general version of the problem: the Maf problem on multiple general phylogenetic trees. We present a parameterized algorithm of running time $O(3^k n^2m)$ and a 3-approximation algorithm for the Maf problem on multiple rooted general phylogenetic trees, and a parameterized algorithm of running time $O(4^k n^2m)$ and a 4-approximation algorithm for the Maf problem on multiple unrooted general phylogenetic trees. We also implement the parameterized algorithm and approximation algorithm for the Maf problem on multiple rooted general phylogenetic trees, and test them on simulated data and biological data.