Non-blocking and self-routing properties of sort-Clos networks

A large class of connection networks with non-blocking and self-routing properties is studied in this paper. We extend the address numbering scheme and the self-routing algorithm in the multistage interconnection networks (MIN) to the Clos network. We show that if the set of connection requests is ordered, a non-blocking route assignment can be easily obtained according to properly defined numbering scheme. Thus, the well-known Batcher-banyan network is generalized to the sort-Clos network, and we obtain a whole family of non-blocking and self-routing networks which are not necessarily constructed from and limited to 2 x 2 switch elements. The Clos network can be considered as a cascade combination of an omega network and a reverse omega network. As far as routing is concerned, we show that this symmetric structure is very general such that any combination of a MIN and its reverse network would possess the same routing property as the classical Clos network. In this context, the non-blocking and self-routing properties of omega and reverse omega networks are examined to make the theory more coherent.