Recursive hierarchical fully-connected networks: A class of low-degree small-diameter interconnection networks

In this paper we propose a new class of interconnection networks called recursive hierarchical fully-connected (RHFC) networks for high-performance parallel processing. The degree of a partially-linked RHFC network is equal to that of its nucleus graph plus a fixed integer, leading to the scalability of such networks. The diameters of suitably constructed RHFC networks are asymptotically optimal within a small constant factor with respect to their node degrees. We then present the construction of recursive hierarchical swapped (RHS) networks and multi-dimensional hypernets, both of which are subclasses of RHFC networks and can emulate a hypercube efficiently. We conclude that RHFC networks ore highly modularized, make the use of fixed-degree building blocks possible for any practically realizable system, and lead to the construction of high-performance interconnection networks with reasonable cost.