The k-ary n-cube network: modeling, topological properties and routing strategies

Abstract

The class of k-ary n-cubes represents the most commonly used interconnection topology for parallel and distributed systems. The main shortcoming of this topology is exponential growth of its size, which is k n , as n increases. In this paper, we describe a technique for modeling k-ary n-cube networks. The proposed technique is used to define and to analyze a variation of this topology, which we call incomplete k-ary n-cubes, or incomplete n: k cubes for short. We show that n: k cubes and incomplete n: k cubes are members of the class of linear recursive networks reported in [1] with generators ( k−1) β k and ( k−1) β respectively, where β is any positive integer. The significance of linearity of an incomplete n: k cube lies in the ability of having control over the growth (in size) of this type of networks. Thus, it is possible to design a communication network which satisfies most of the n: k cube properties but with significantly smaller size. In addition, an efficient routing algorithm for the class of incomplete n: k cube networks is presented.