Optimal Diffusion for Load Balancing in Heterogeneous Networks

In [7] we studied the local Extrapolated Diffusion (EDF) method for the load balancing problem in case of homogeneous torus networks. The present paper develops the convergence theory of the local EDF for heterogeneous torus networks. In particular, we determine its quasi-optimal iteration parameters and the corresponding quasi-optimal convergence factor using local mode analysis. As a result dynamic load balancing becomes an efficient procedure since the parameters of local EDF are computed via a closed form formulae resulting in the maximization of its rate of convergence. Moreover, it is shown how the convergence factor depends upon the communication edge weights and the processor speeds of the network.