The authors study a routing problem that arises on SIMD parallel architectures whose communication network forms a toroidal mesh. They assume there exists a set of k message descriptors {(xi,yi)•i=1,2,...,k}, where (xi,yi) indicates that the ith message’s recipient is offset from its sender by xi hops in one mesh dimension, and yi hops in the other. Every processor has k messages to send, and all processors use the same set of message descriptors. The SIMD constraint implies that at any routing step, every processor is actively routing messages with the same descriptors as any other processor. The authors call this Isomorphic Routing. The present objective is to find the isomorphic routing schedule with the minimum makespan. The authors consider a number of variations on the problem, yielding complexity results from O(k) to NP-complete. Most of the present results follow after we transform the problem into a scheduling problem, where it is related to other well-known scheduling problems.
