We consider the problem of allocating n tasks of a distributed program to m processors of a distributed system in order to minimize total communication and processing costs. If the intertask communication can be represented by a tree and if the communication costs are uniform, it is known that an optimal allocation can be determined in O (nm) time. A K-optimal solution set = {1,..., K} of a given task allocation problem is a set of allocations such that no allocation which is not contained in is better than any i, i = 1,..., K. In this paper, an algorithm is presented which computes a K-optimal set for the considered task allocation problem in O (Knm). Copyright 1995, 1999 Academic Press, Inc.