An algorithm for finding the K-best allocations of a tree structured program

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 Ω = {A₁,…, A_K} of a given task allocation problem is a set of allocations such that no allocation A which is not contained in Ω is better than any A_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).