Topology and Routing Algorithm 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, when the size of a network have been increases added nodes must be 2i times more than its nodes and increase the degree of nodes , which affects scalable characteristic. The paper puts forward a scalable hypercube based on the Combination Gray Code with Johnson Code(GJCode(s, t)). The GJCode(s, t) has flexible scalable characteristics and the important properties of both Gray Code and Johnson Code which is there exists a link between two nodes only if their binary addresses differ in a single bit. 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 very simple and easy to be implemented in hardware with low implementation cost. The GJCode(s, t) can be applied in parallel computer systems and networks on chip.