Chapter 3 - A Dense, Massively Parallel Architecture

Abstract

Publisher Summary The chapter focuses on networks in which each processor is connected by bidirectional links to several other ones. The family of dense graphs has fixed maximum node degree, which has two advantages. First, the diameter of these graphs is small. With node degree four, up to a diameter of 10 graphs with more nodes than DeBruijn networks of the same diameter can be found. The graphs have various numbers of nodes; thus, the size of the network can be highly adopted to any environmental constraint on the processor number. These advantages come for the price of lacking an optimal standard routing algorithm. The chapter presents the results of some empirical studies on diameter and mean distance of a ring-connected chain (RCC). These results were compared to DeBruijn networks, which is a well-known family of graphs. This family of graphs has several advantages in the context of massive parallel architectures. Beneath high density and degrees of freedom, the RCC has a building algorithm, which is easy to understand and easy to implement. A straightforward but not optimal routing algorithm for the class of graphs is also presented in the chapter. The straightforward routing algorithm calculates a path from any start node to an arbitrary, fixed end node.