A Class of Static and Dynamic Hierarchical Interconnection Networks

Abstract

A TCN is a hierarchical interconnection network where isomorphic clusters are connected using a complete graph at the highest level of hierarchy. We extend the concept of TCN to the dynamic domain and reduce the hardware complexity in the static domain. The resulting networks outperform both its non-hierarchical and hierarchical counterparts, while improving on the congestion and fault-tolerance characteristics of the latter; they also have optimal connectivity, high bisection width, low degree, cost and diameter, and low average distance under both uniform and non-uniform traffic. For instance, with dynamic clusters we obtain the same delay as the corresponding non hierarchical multistage network at 1/2 the cost; while the maximum and average delays are typically 2/3 and 3/4 of those in a comparable HMIN, at approximately the same cost. In the static case, using hypercube clusters, the degree, diameter and cost are approximately 1/2, 3/4 and 3/8 of the same parameters in a comparable size hypercube; while the diameter and average distance are typically 1/2 and 3/4 of those in traditional HINs. In case of mesh clusters, the diameter and cost are reduced even further, by an amount proportional to their square root.