Analysis of the generalized dimension exchange method for dynamic load balancing

Abstract

The dimension exchange method is a distributed load balancing method for point-to-point networks. We add a parameter, called the exchange parameter, to the method to control the splitting of load between a pair of directly connected processors, and call this parameterized version the generalized dimension exchange (GDE) method. The rationale for the introduction of this parameter is that splitting the workload into equal halves does not necessarily lead to an optimal result (in terms of the convergence rate) for certain structures. We carry out an analysis of this new method, emphasizing its termination aspects and potential efficiency. Given a specific structure, one needs to determine a value to use for the exchange parameter that would lead to an optimal result. To this end, we first derive a sufficient and necessary condition for the termination of the method. We then show that equal splitting, proposed originally by others as a heuristic strategy, indeed yields optimal efficiency in hypercube structures. For chains, rings, meshes, and tori, however, optimal choices of the exchange parameter are found to be closely related to the scales of these structures. Finally, to further investigate the potential of the GDE method, we extend it to allow exchange parameters of different values to be used over the set of edges, and based on this extension, we compare the GDE method with the diffusion method.