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A focus of research for crossbar switches has been to reduce the number of switch elements, each of which not only occupies a relatively large area but also costs a lot when implemented with optical devices. We point out that conventional crossbar switches, where is the switch size, actually function as switches and thus have redundant switch elements to be removed. We show that ILLIAC torus networks, which have a less number of switching elements than crossbar switches of an identical switch size, are equivalent to true crossbar switches. We describe in detail how the crossbar switches can be embedded into the equivalent torus networks. We also discuss switch control complexity of the equivalent torus networks and show that it can be reduced to (1).

Embedding N × N Crossbar Switches into ILLIAC(N, N − 1) Torus Networks for Optical Interconnection Networks