Modeling Several Multistage Interconnection Networks with Unified Cayley Formulation

摘要

With the semi-direct product of two groups, several schemes for designing interconnection networks with constant degree are unified under a general framework in this paper theoretically. A new family of Cayley graph, called CSC(q, p, l, k) is introduced on this general framework, which shows a better scalability. We have verified that CSC(q, p, l, k) includes some well-known significant multistage interconnection networks as its subclasses, for example, Cube- Connected Cycles (CCC), the k-degree Cayley graph recently proposed, the new three degree network and Star- Connected Cycles (SCC). This work can induce computer designers to obtain desired networks by a proper choice of parameters which is attractive for some applications which are built on large scale networks. Secondly, this unified framework of Cayley graph can avoid to repeatedly exploit some "new" interconnection networks.