ON A CLASS OF REARRANGEABLE NETWORKS

Benes networks are known as the nonblocking rearrangeable networks which can realize arbitrary permutations without conflict. In this paper, we introduce a class of 2 log(b) N stage networks which are equivalent to the Benes networks. Networks in this class can be either symmetric or asymmetric in their structure, regular or irregular in their inter-stage connections, and even, 2 log(b) N or 2 log(b) N - 1 stages. All networks in this class are nonblocking rearrangeable. A switch labeling scheme is proposed to provide testing the topological and functional equivalency for this class of networks. This switch labeling scheme can also provide a novel matrix representation for network configuration. This new representation introduces a portability concept for the routing scheme on this class of networks. With this new representation, a general routing scheme is also developed. This routing scheme can realize arbitrary permutation for the whole class of 2 log(b) N stage networks.