ON LOWER BOUNDS FOR THE COMMUNICATION VOLUME IN DISTRIBUTED SYSTEMS

In this paper we derive a lower bound for the total communication volume when mapping arbitrary task graphs onto a distributed processor system. For a K processor system this lower bound can be computed with only the K (possibly) largest eigen values of the adjacency matrix of the task graph and the eigen values of the adjacency matrix of the processor graph. We also derive the eigen values of the adjacency matrix of the processor graph for a hypercube multiprocessor and illustrate the concept with a simple example for the two processor case.