Large Sorting and Routing Problems on the Hypercube and Related Networks

In this paper we present upper and lower bounds for the problems of sorting and routing n items using p processors on the hypercube, the shuffle, the butterfly and the Cube-Connected-Cycles. We consider problems where n is large; more precisely we assume that n = Ω (p2). The main results of this paper are an algorithm for routing n packets in O((n/p) log p) time, and an algorithm for sorting n integers in the range 0, 1, …, R – 1 in time.