The average diffusion method for the load balancing problem

This paper proposes the Average Diffusion (ADF) method for solving the load balancing problem. It is shown that a sufficient and necessary condition for the ADF method to converge to the uniform distribution of loads is the induced network of processors to be d-regular, connected and not bipartite. Next, we proceed and apply Fourier analysis determining the convergence factor gamma in terms of the diffusion parameters c(ij) (weighted case) when the network of processors is a ring and 2D-torus. it is shown that c(ij) = 1 and c(ij) is an element of (0, (1)/(2)) when the network is a ring and 2D-torus, respectively, thus solving partially the open problem which concerns the determination of the diffusion parameters c(ij).