Generalized multihop shuffle networks

In this paper, we provide an in-depth study of the generalization of the well-known shuffle network for ultrafast multihop lightwave communication. 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 definition of the shuffle network, N = nk, where n is the number of nodes per stage, which was originally proposed as the shufflering network in [7]. Based on this definition, we divide the shuffle networks into two classes: extra-stage and reduced-stage. We derive an exact model and an approximate model of the expected number of hops for various network topologies. The results can be used to determine an optimal network topology when given a value of N.