From Local to Global: An Analysis of Nearest Neighbor Balancing on Hypercubes

This paper will focus on the issue of load balancing on a hypercube network of N processors. We will investigate a typical nearest neighbor balancing strategy - in which workloads among neighboring processors are averaged at discrete time steps. The computation model allows tasks, described by independent random variables, to be generated and terminated at all times. We assume that the random variables at all nodes have equal expected value and their variances are bounded by a constant d 2 , and we let the difference DIFF between the actual load on each node and the average load on the system describe the deviation of the load on a node from the global average value. The following analytical results are obtained: The expected value of DIFF, denoted by E(DIFF), is 0. The variance of DIFF, denoted by Var(DIFF), is independent of time t , and Var(DIFF)≤ 1.386 d 2 + 0.231 log N .