A simulation scheme in rearrangeable networks

In this paper, we present a new simulation scheme for verifying the rearrangeability of the 2log₂N- or (2log₂N-1)-stage networks. Instead of the exhaustive method which is actually impossible due to the prohibitively large amount of cases, the proposed scheme simulates just for the representative cases for the possible permutations. First of all, a cyclic characteristic of the center stages in the network is discussed. From the graph theoretical point of view, we show that any permutation can be decomposed into two subpermutations and in addition, show that each subpermutation can be divided further into groups called loops so that they can match the center-stage cycles. By using these two concepts, it is shown that any possible permutation for N=16 falls into one of the categories and is proved that all of them can be realized without conflict on the network