THE MESH WITH BINARY TREE NETWORKS: AN ENHANCED MESH WITH LOW BUS-LOADING

Abstract

The literature abounds with enhanced mesh models and numerous results for them. These models employ buses connecting a large (usually a polynomial) number of processors resulting in high bus loading and a very low bus data rate. In this paper we propose an enhanced mesh model called the mesh with binary-tree (multiple bus) network (MBTN) with low bus loading. We measure the cost of the model in terms of its loading, degree (connections per processor), number of buses and layout area. We also devise an algorithm to perform prefix computations on the MBTN. The MBTN's parameters can be selected to provide a wide range of tradeoffs between its cost and performance. Most importantly, for every major existing enhanced mesh model, there is a choice of parameters that makes the MBTN superior to the existing model. Key to the MBTN is a novel implementation of a binary-tree algorithm on a multiple bus network (MBN). We propose two constant loading MBNs that can run binary tree algorithms optimally. We also show that any network (such as the MBTN) that is capable of running binary tree algorithms efficiently can also solve linear recurrences efficiently. These results may be of independent interest.