Randomized 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. Assuming the multiaccepting model, we show that the probability of routing all N packets on the N-node, base-b generalized hypercube in asymptotically optimal C log(b) N time (constant C greater than or equal to 1) approaches exponentially one, as N increases. Furthermore, our derived upper bound on the above probability improves on previous results, especially for the binary hypercube, for which bounds can be further improved. Comparison tables of these upper bounds are also provided.