A kernel for the maximum agreement forest problem on multiple binary phylogenetic trees

TL;DR

This paper introduces a new kernelization approach for the maximum agreement forest problem on multiple binary phylogenetic trees, providing bounds on tree size after reduction and establishing the first kernels for cases with more than two trees.

Contribution

It develops a modified chain reduction rule and proves size bounds for trees, resulting in the first kernelization results for multiple trees in the MAF problem.

Findings

Bounded the size of trees after reduction to O(t * r * k) leaves.

Proved the tightness of the bound r for both unrooted and rooted trees.

First kernelization results for the MAF problem with more than two trees.

Abstract

The maximum agreement forest (MAF) problem in phylogenetics takes as input a set t >= 2 of binary phylogenetic trees T on the same set of taxa X. It asks for a partition of X into the smallest number of blocks such that the subtrees induced by these blocks are disjoint and have common topology across all the trees in T. We produce a modified version of the well-known chain reduction rule in order to prove that after exhaustive application of reduction rules each tree has O( t * r * k ) leaves, where k is the natural parameter (the number of blocks) and r=min{max{k,3},t+1}}. We prove this bound for both the unrooted and rooted version of the problem, and demonstrate that the bound r, the length to which common chains are truncated, is tight. Our results constitute the first kernels for MAF in the t>2 regime.