"Hypermeshes": Optical Interconnection Networks for Parallel Computing

Abstract

A formal model for a class of optical mesh-based interconnection networks called "hypermeshes" is proposed and characterized. Hypermeshes are based on the concept of orthogonal crossbar switches, with N nodes arranged in n-dimensional mesh structure where all nodes aligned along a dimension are interconnected with an optical multichannel switch. The optical multichannel switches can be modeled as hypergraph "hyperedges" which can perform multiple data transfers over their members simultaneously. The hyperedges can be implemented with space division multiplexing (SDM) in the electrical or optical domains or with wavelength division multiplexing (WDM) over a single fiber in the optical domain. The use of WDM over a fiber also reduces the hypermesh "interconnection complexity" to rival that of a 2D mesh. An architectural characterization is performed and the combinatorial properties, including rearrangeability, permutation capability, partitionability, embedding capability, and bisection bandwidth, are characterized. It is shown that every algorithm which can execute conflict-free on an omega network can execute conflict-free on a hypermesh and that every graph which can be embedded into a hypercube with dilation k can be embedded into a hypermesh with dilation ≤ k. Hypermeshes are shown to have high bisection bandwidths, thereby minimizing the time for many common algorithms such as parallel sorting. It is shown that under the constraint of equivalent aggregate bandwidth the hypermeshes are considerably more powerful computational models than meshes, generalized hypercubes, and other orthogonal graphs. Two attractive optical implementations of hypermeshes using optical technology recently advocated in the literature are also proposed.