Distributed computation in a three-dimensional mesh with communication delays

We study the problem of scheduling a divisible load in a three-dimensional mesh network in which processors communicate by means of circuit-switched routing. The objective is to find a distribution of load shares among processors which minimizes the processing time for a given computation volume. We model and solve the problem with a set of algebraic equations. Whereas other algorithms distribute all data in a single sweep, our load distribution algorithm scatters data in a sequence of sweeps, each sweep brings data to a set of processors located in the same distance from the source of the distribution. The second feature which distinguishes our algorithm is that processors start computation in the reverse order their distance from the originator as opposed to previous solutions in which processors begin computation in the order of that distance. We evaluate the performance of our algorithm and show that it improves on previous results obtained for mesh networks.