The Generalized Diffusion method for the load balancing problem

This paper defines the Generalized Diffusion (GDF) method by the introduction of a parameter T in the Diffusion (DF) method and studies its convergence analysis for a weighted network graph. In particular, it is proved that GDF converges if and only if tau is an element of (0, 1/parallel toAparallel to(infinity)), where A is the adjacency matrix of the network graph G (V: E). This is a more relaxed condition than the one required by the DF method. Next, we consider a multiparametric version of GDF. which involves a set of parameters tau(i), i = 1, 2, ..., \V\, instead of a single parameter tau. By applying local Fourier analysis we are able to find a closed form formula which produces optimum values for the set of the parameters tau(i) in the sense that the rate of convergence of GDF is maximized for ring and 2D-torus network graphs.