Optimal and Alternating-Direction Load Balancing Schemes

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 ow 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 ow. Apart from that, we present a simple optimal diiusion scheme for general graphs which calculates a minimal balancing ow in the l2 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.