Allocating Modules to Processors in a Distributed System with Limited Memory

Abstract

We consider the problem of finding a minimum-cost assignment of program modules to processors in a distributed system where one of the processors has limited memory. This problem is NP-hard, even if the communication graph is a tree. We show that a fully polynomial-time approximation scheme exists for the case where the communication graph is a partial k-tree. A faster approximation scheme is presented for the case of trees with uniform costs. Both schemes are derived from algorithms for the allocation problem without memory constraints. We also show that, if the communication graph is unrestricted, there is no fully polynomial-time approximation scheme for the memory-constrained problem unless P = NP.