Dynamic Load Balancing for Distributed

In this paper we study diffusion schemes for dynamic load balancing on message passing multiprocessor networks. One of the main results concerns conditions under which these dynamic schemes converge and their rates of convergence for arbitrary topologies. These results use the eigenstructure of the iteration matrices that arise in dynamic load balancing. We completely analyze the hypercube network by explicitly computing the eigenstructure of its node adjacency matrix. Using a realistic model of interprocessor communications, we show that a diffusion approach to load balancing on a hypercube multiprocessor is inferior to another approach which we call the dimension exchange method. For a d-dimensional hypercube, we compute the rate of convergence to a uniform work distribution and show that after d + 1 iterations of a diffusion type approach, we can guarantee that the work distribution is approximately within e-* of the uniform distribution independent of the hypercube dimension d. Both static and dynamic random models of work distribution are studied. o 1989