Improved Probabilistic Routing on Generalized Hypercubes

We propose and theoretically analyze a new probabilistic permutation routing algorithm, which is based on two-phases of 1-1 permutation routing. We show that the probability of routing all N packets on the N-node, base-b generalized hypercube in asymptotically optimal C logbN time (constant C≥1) approaches exponentially one, as N increases. Further, for any generalized hypercube and especially for the binary hypercube (b=2), our derived upper bound on the above probability improves on existing ones. Comparison tables of these upper bounds are also provided.