Strict-sense non-blocking conditions for shuffle/exchange networks with vertical replication

The strict-sense non-blocking conditions of an interconnection network built by vertical replication or a Banyan network with additional stages are known only it the expanded Banyan network has a recursive construction. We consider a shuffle/exchange network as the basic building block to be replicated vertically. Since this network does not have a recursive construction, the previous analysis cannot be applied. By relying on the topological properties of the channel graph in a shuffle/exchange network, we find that the non-blocking conditions for this network an numerically the same needed for a recursive Banyan network