Coset networks as connectors in parallel processors

Abstract

An active area of research regarding parallel computer systems deals with the design of interconnection networks. Among all interconnection networks, permutation networks play a special role as all other networks can be constructed using such networks. It was recently shown that many permutation networks reported in the literature are manifestations of coset decompositions of symmetric groups. This result is generalized here to obtain several other previously unknown permutation networks which satisfy such decompositions. In addition, analyses of the edge-count, propagation delay, fan-out, and setup time of such networks are provided. The results lead to some anomolous behavior as well as several trade-offs among these parameters. For example, it is shown that a complete bipartite graph is the fastest and most economical direct realization of a permutation network. Furthermore, it is shown that the fan-out of a network is inversely proportional to the propagation delay whereas the setup time may or may not relate to the propagation delay at all depending on the network in question. Finally, two constant fan-out implementations of these networks using O (n ^1.59) 2 × 1 multiplexers and 2 × 2 switches are presented.