Fast self-routing permutation switching on an asymptotically minimum cost network

Abstract

A self-routing permutation network with O((n lg n)) switches and O(lg/sup 2/n) routing time, where lg denotes log/sub 2/, is presented. More generally, a permutation network with O(kn/sup 1+1/k/) cost and O(k lg n) routing time for any k, 1<or=k lg n, is described. This improves D. Nassimi and J. Sahni's (1982) routing algorithm that gives O(k lg/sup 3/ n) routing time for the same cost expression. The only networks capable of permutation switching with O(n lg n) cost and O(lg n) routing time are the AKS sorting network and E. Upfal's (1989) packet routing network, but the constants hidden in the complexities of these networks are so large that they remain impractical until n gets very large.<<ETX>>