Optimal wormhole routing in the (n,d)-torus

The authors consider wormhole routing in a d-dimensional torus of side length n. In particular they present an optimal randomized algorithm for routing worms of length up to O(n/(d log n)/sup 2/), one per node, to random destinations. Previous algorithms only work optimally for two dimensions, or are a factor of log n away from the optimal running time. As a by-product they develop an algorithm for the 2-dimensional torus that guarantees an optimal runtime for worms of length up to O(n/(log n)/sup 2/) with much higher probability than all previous algorithms.