O(log N) deterministic packet routing scheme

We present a deterministic O(log N) time algorithm for the problem of routing an arbitrary permutation on an N-processor bounded-degree network with bounded buffers. Unlike all previous deterministic solutions to this problem, our routing scheme does not reduce the routing problem to sorting and does not use the M. Ajtai, J. Komlos and E. Szemeredi sorting network. Consequently, the constant in the run time of our routing scheme is substantially smaller, and the network topology is significantly simpler.