On a class of rearrangeable networks

Benes networks are nonblocking rearrangeable networks that can realize arbitrary permutations without conflict. A class of 2 log_b N stage networks which are equivalent to the Benes networks is introduced. Networks in this class can be either symmetric or asymmetric in their structure, regular or irregular in their interstage 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 of 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 representation introduces a portability concept for the routing scheme on this class of networks. With this 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