Journal of Classification 12:101-112 (1995) An Efficient Algorithm for Supertrees Mariana Constantinescu Universit6 de Moncton David Sankoff Universit6 de Montr6eal Abstract: Given k rooted binary trees A t,A2,..,Ak, with labeled leaves, we gen- erate C, a unique system of lineage constraints on common ancestors. We then present an algorithm for constructing the set of rooted binary trees B, compatible with all of A I,A2,..,Ak. The running time to obtain one such supertree is O(k2n2), where n is the number of distinct leaves in all of the trees A I,A2,..,Ak. Keywords: Tree compatibility; Constraints on trees; Supertrees; Consensus trees. 1. Introduction The evolutionary history of n species can be described by a rooted tree with labeled leaves in which the internal nodes represent hypothetical ances- tral species and the leaves represent the given species. Various methods have been proposed in the literature to reconstruct the evolutionary tree (phylo- geny) from data on n given species. Many of these methods require the gen- eration and evaluation of all possible trees on n labeled leaves. This becomes unfeasible for large n because there are 1.3.5...(2n - 3) = (2n - 2)!/(2n-l(n - 1)!), Cayley (1881), possible unordered binary trees with n labeled leaves. In some contexts however it is possible to restrict the set of trees to be examined so that the problem becomes tractable for relatively Authors' Addresses: Mariana Constantinescu, D6partement d'Informatique, Universit6 de Moncton, Moncton (Nouveau Brunswick) E1A 3E9, and David Sankoff, Centre de Recherches Math6matiques, Universit6 de Montr6al, C. P., Succ. A, Montr6al (Quebec) H3C 3J7, Canada.