Analysis of nearest neighbor load balancing algorithms for random loads

Nearest neighbor load balancing algorithms, like diffusion, are popular due to their simplicity, flexibility, and robustness. We show that they are also asymptotically very efficient when a random rather than a worst case initial load distribution is considered. We show that diffusion needs $\Th{(\log n)^{2/d}}$ balancing time on a $d$-dimensional mesh network with $n^d$ processors. Furthermore, some but not all of the algorithms known to perform better than diffusion in the worst case also perform better for random loads. We also present new results on worst case performance regarding the maximum load deviation