A Unified Theory of Interconnection Network Structure

The relationship between the topology of interconnection networks and their functional properties is examined. Graph theoretical characterizations are derived for delta networks , which have a simple routing scheme, and for bidelta networks, which have the delta property in both directions. Delta networks are shown to have a recursive structure. Bidelta networks are shown to have a unique topology. The definition of bidelta network is used to derive in a uniform manner the labeling schemes that define the ome-ga networks, indirect binary cube networks, flip networks, baseline networks, modified data manipulators, and two new networks; these schemes are generalized to arbitrary radices. The labeling schemes are used to characterize networks with simple routing. In another paper, we characterize the networks with optimal performance/cost ratio. Only the mul-tistage shuffle-exchange networks have both optimal performance/cost ratio and simple routing. This helps explain why few fundamentally different geometries have been proposed .