Nested crossbar connection networks for optically interconnected processor arrays for vector–matrix multiplication

Abstract

A family of new interconnection networks, termed the nested crossbar, has been developed. These networks are particularly well suited to optical interconnects due to their high bisection width and high degree of space invariance. Algorithms have been developed for computing vector-matrix multiplication with nested crossbar connected processor arrays with time growth rates between O(1) and O(N(1/2)). (N is the number of elements in the vector.) When these algorithms are implemented on holographic optically interconnected very large scale integrated processor arrays, the nested crossbar networks have area and time growth rates close to fundamental lower bounds. The nested crossbar networks also allow the use of a minimum number of transmitters and detectors.