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

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.