Maximum Agreement Subtree of a Set of Evolutionary Trees

The maximum agreement subtree approach is one method of reconciling different evolution trees for the same set of species. Recently, dynamic programming ideas were used by Steele and Warnow to provide polynomial time algorithms for finding a maximum agreement subtree of two trees. Their methods do not generalize to sets of more than two trees. In this paper we prove that the maximum agreement subtree problem is NPcomplete for three trees with unbounded degrees. We also develop a new method for finding the maximum agreement subtree of k trees of degree d. This new method enables us to find the maximum agreement subtree in time O(nd + kn3 ).