On hypercube-based hierarchical interconnection network design

Abstract

Hierarchical interconnection networks (HINs) have been proposed as a cost-effective way to interconnect large numbers of processors in a multicomputer system. This paper considers two issues concerning the design of binary hypercube-based HINs—the optimum cluster size and the optimum number of levels in the hierarchy. The network cost is measured in terms of the total link cost L and the performance of the network is measured by the average internode distance P. The goal is to minimize the cost-benefit ratio as represented by the LP product. The optimum cluster size is dependent on the underlying degree of locality in communication. For all of the various locality characterizations that we consider, the optimum cluster size in a two-level binary hypercube-based HIN, obtained numerically, is shown to be either 4 or 8, over a wide range of network sizes. It is shown that increasing the number of levels to 3 yields at most a moderate improvement in the cost-benefit ratio, depending on the type of locality characterization considered. For some locality characterizations, the cost-benefit ratio deteriorates. Thus, an appropriate design for a binary hypercube-based HIN appears to be a two-level hierarchy, with a cluster size of either 4 or 8.