Locating the vertices of a steiner tree in an arbitrary metric space

Given a tree each of whose terminal vertices is associated with a given poin t in a compact metric space, the problem is to optimally associate a point in this space to each nonterminal vertex of the tree. The optimali ty criterion is the minimizat ion o f the sum of the lengths, in the metric space, over all edges of the tree. This note shows how a dynamic programming solution to this problem generalizes a number of previously published algori thms in diverse metr ic spaces, each of which has direct and significant applications to biological systematics or evolutionary theory.