Topological Equivalence of Half Crossover Networks and Banyan Networks.

Topological equivalence between the half crossover network and the banyan network is proven using a pair of equivalence relationships. This proof is important to the photonic switching and optical computing research efforts, because the use of the half crossover interconnections between arrays of optical logic elements can result in a lossless, compact free-space photonic switching network that is topologically equivalent to the banyan network. By transitivity, the half crossover network is also topologically equivalent to the Omega network, which is based on shuffle interconnections.