Fast load balancing in Cayley graphs and in circuits

Abstract

We compare two load balancing techniques for Cayley graphs based on information and load exchange between neighbouring vertices. In the first scheme, called natural diffusion, each vertex gives (or receives) a fixed part of the load difference to (from) its direct neighbours. In the second scheme, called Cayley diffusion, each vertex successively gives (or receives) a part of the load difference to (or from) direct neighbours incident to the edges labelled by the elements of the generator set of the Cayley graph. We prove that the convergence of the Cayley diffusion is faster than the natural diffusion, at least for some particular graphs (cube, circuit with an even number of vertices, graphs from the symmetric group). Furthermore we compute the fastest possible way to distribute load in a circuit using local load balancing strategies.