A branch-&-price approach to the unrooted maximum agreement forest problem

TL;DR

This paper introduces a novel branch-&-price algorithm for the unrooted maximum agreement forest problem, significantly improving computational performance for comparing unrooted binary trees in computational biology.

Contribution

It presents the first branch-&-price approach for this problem, integrating a dynamic programming solution for the weighted maximum agreement subtree problem.

Findings

State-of-the-art performance demonstrated

Effective polynomial-time pre-processing used

Algorithm outperforms existing methods

Abstract

We propose the first branch-&-price algorithm for the maximum agreement forest problem on unrooted binary trees: given two unrooted X-labelled binary trees we seek to partition X into a minimum number of blocks such that the induced subtrees are disjoint and have the same topologies in both trees. We provide a dynamic programming algorithm for the weighted maximum agreement subtree problem to solve the pricing problem. When combined with rigorous polynomial-time pre-processing our branch-&-price algorithm exhibits (beyond) state-of-the-art performance.