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This paper presents an O(n1.75+o(1)) 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 n 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.