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

The authors 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. They then present the construction of recursive hierarchical swapped (RES) networks and multi-dimensional hypernets, both of which are subclasses of RHFC networks and can emulate a hypercube efficiently. They conclude that RHFC networks are 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.