A Systematic Analysis of Equivalence in Multi-Stage Networks

Many approaches to switching in optoelectronic and optical networks decompose the switching function across multiple stages or hops. This paper addresses the problem of determining whether two multi-stage or multi-hop networks are functionally equivalent. Various ad-hoc methods have been used in the past to establish such equivalences. A systematic method for determining equivalence is presented based on properties of the link permutations used to interconnect stages of the network. This method is of use in laying out multistage networks, in determining optimal channel assignments for multi-hop networks, and in establishing the routing required in such networks. A purely graphical variant of the method, requiring no mathematics or calculations, is also described.