Computing the Unrooted Maximum Agreement Subtree in Sub-quadratic Time

This paper presents the first sub-quadratic time algorithm for the Unrooted Maximum Agreement Subtree (UMAST) problem: Given a set A of n items (e.g., species) and two unrooted trees T and T, each with {otn} leaves uniquely labeled by the items of A, we want to compute the largest subset B of A such that the subtrees of T and T' induced by B are isomorphic. The UMAST problem is closely related to some problems in biology, in particular, the one of finding the consensus between evolutionary trees (or phylogenies) of a set of species. The previous best algorithm for the UMAST problem requires time O(n2+o(1)) [5]; the algorithm in this paper improves the time bound to O(n1.75+o(1)). The rooted version of this problem has also attracted a lot of attention; the time complexity has recently been improved from O(n2) [5] to O(n1-5 log {otn}) [6].