On the performance merits of bypass channels in hypermeshes and k-ary n-cubes

Low-dimensional k-ary n-cubes have been popular in recent multicomputers. These networks, however, suffer from high switching delays due to their high message distance. To overcome this problem, Dally has proposed a variation, called express k-ary n-cubes, with express channels that allow non-local messages to partially bypass clusters of nodes within a dimension. K-ary n-cubes are graph topologies where a channel connects exactly two nodes. This study argues that hypergraph topologies, where a channel connects any number of nodes, thus providing total bypasses within a dimension, represent potential candidates for future high-performance networks. It presents a comparative analysis, of a regular hypergraph, referred to as the distributed crossbar switch hypermesh (DCSH), and the express k-ary n-cube. The analysis considers channel bandwidth constraints which apply in different implementation technologies. The results conclude that the DCSH's total bypass strategy yields superior performance characteristics to the partial bypassing of its express cube counterpart.