The Gamma network

Abstract

The Gamma network is an interconnection network connecting N=2' inputs to N outputs. It consists of log ₂ N stages with N switches per stage, each of which is a 3 input, 3 output crossbar. The stages are linked via “power of two” and identity connections in such a way that redundant paths exist between the input and output terminals. In this network, a path from a source to a destination may be represented using one of the redundant forms of the difference between the source and destination numbers. The redundancy in paths may thus be studied using the theory of redundant number systems. Results are obtained on the distribution of paths connecting inputs to outputs, and the permuting capabilities of the Gamma network. Switch settings for certain frequently used permutations and control mechanisms are also considered in this paper. This network has an interesting application in solving tridiagonal systems using the odd-even elimination algorithm.