The GJCode(s, t): A Scalable Hypercube Based on the Combination Gray Code with Johnson Code

Abstract

Hypercubes utilizing Gray Code are used widely as the interconnection networks of parallel computer systems. But an n-dimensional hypercube has 2n nodes, which limits scalability of networks when the degree of nodes is invariable. The paper puts forward a scalable hypercube based on the Combination Gray Code with Johnson Code (GJCode (s, t)). The GJCode (s, t) has good scalable characteristics and the important properties of both Gray Code and Johnson Code. In the GJCode (s, t), there are two adjustable parameters which offer a good tradeoff between the cost of networks and their performance in terms of the demand of application systems. The paper discusses the performance of several variations of the hypercube and proposes the routing algorithm for the GJCode (s, t), which can make packets pass along the shortest distance path and is simple in hard implementation. The GJCode (s, t) can be applied in parallel computer systems and networks on chip.