Routing a class of concatenated omega networks

Benes networks are known to be nonblocking rearrangeable networks which can realize arbitrary permutations. Topological equivalence extends the nonblocking rearrangeability to a class of multistage interconnection networks (MIN), which has the same topology as Benes networks. There is another class of well-known multistage interconnection networks, which is not yet known as either nonblocking rearrangeable networks or blocking networks, such as omega+omega networks. In this paper we extend the labeling scheme used in Benes-equivalent networks to a class of concatenated omega networks with modified central stage connection. The class of concatenated omega networks are proved to be nonblocking rearrangeable. A looping algorithm is proposed to routing through the networks to realize arbitrary permutation for the whole class of 2log₂N stage networks