On the optimum value offor a variant of the Diffusion Method: A Generalization
Gregory Karagiorgos, George A. Kollias, Nikolaos M. Missirlis, Elias Tsigaridas · 2004
In this paper we find an exact formula for the eigenvalues of the iteration matrix of the Generalized Diffusion method (GDF) used in load balancing. This provides us with the optimum value of the extrapolation parameter, i.e. the parameter endowing GDF with extra flexibility compared to other iterative methods. We apply our technique to the broad class of n-D torus interconnection topologies and specialize our main result in the case of rings, 2-D tori, n-D hypercubes and n-D, k-ary hypercubes. Simulation results are then presented demonstrating the validity of our theoretical approach.