On the performance of a class of multihop shuffle networks

A generalization of the well-known shuffle network is proposed for 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 base p, the realizable values of N are very discrete and many of the intermediate values of N are not realizable. In this paper, we propose a new definition of a shuffle network as N = nk where n is the number of nodes per stage with base p. Based on this new definition, we divide the shuffle networks into two classes: extra-stage and reduced-stage. Study results can be used to determine an optimal network topology when given a value of N.