An O(log2 N) Depth Asymptotically Nonblocking Self-Routing Permutation Network

A self-routing multi-logN permutation network is presented and studied. This network has 3 1 0 ~ N 2 depth and N(log~N)(31og~, N -2)/2 nodes, where N is the number of network inputs and 7 a constant very close to 1. A parallel routing algorithm runs in 3 l o m 2 time on thii network. The overall system (network and algorithm) can work in pipeline and it is asymptotically nonblocking in the sense that its blocking probability vanishes when N increases, hence the quasi-totality of the information synchronously arrives in 3 l o W 2 steps at the network outputs. Thi network presents very good fault tolerance, a modular architecture, and it is suitable for information exchange in very large scale parallel processors and communication systems.