GENERALIZED MULTIHOP SHUFFLE NETWORKS

In this paper, we provide an in-depth study of the generalization of t he well-known shuffle network for ultrafast multihop lightwave communi cation, In the classical definition of a shuffle network, i.e., N = kp (k) where N is the number of nodes and k is the number of stages with nodes of degree p, the realizable values of N are very sparse and many of the intermediate values of N are not realizable. We use a new defi nition of the shuffle network, N = nk, where n is the number of nodes per stage, which was originally proposed as the shuffle-ring network i n [7], Based on this definition, we divide the shuffle networks into t wo classes: extra-stage and reduced-stage, We derive an exact model an d an approximate model of the expected number of hops for various netw ork topologies, The results can be used to determine an optimal networ k topology when given a value of N.