Optimal and alternating-direction load balancing schemes

Abstract

We discuss iterative nearest neighbor load balancing schemes on processor networks which are represented by a cartesian product of graphs like e.g. tori or hypercubes. By the use of the Alternating-Direction Loadbalancing scheme, the number of load balance iterations decreases by a factor of 2 for this type of graphs. The resulting flow is analyzed theoretically and it can be very high for certain cases. Therefore, we furthermore present the Mixed-Direction scheme which needs the same number of iterations but results in a much smaller flow. Apart from that, we present a simple optimal diffusion scheme for general graphs which calculates a minimal balancing flow in the 12 norm. The scheme is based on the spectrum of the graph representing the network and needs only m-1 iterations in order to balance the load with m being the number of distinct eigenvalues. © Springer-Verlag Berlin Heidelberg 1999.