THE OPTIMAL ROUTING ALGORITHM IN HIERARCHICAL CUBIC NETWORK AND ITS PROPERTIES

Abstract

A Hierarchical Cubic Network (HCN) is a hierarchical hypercube network proposed by Ghose [4]. The HCN is topologically superior to many other similar networks. in particular, the hypercube. It has a considerably lower diameter than a comparable hypercube and is realized using almost half the number of links per node as a comparable hypercube. In this paper, we propose the shortest routing algorithm in HCN(nln) and show that the diameter of HCN(n,n) with 2(2n) nodes is n + [(n + 1)/3] + 1 which is about 2/3 of that of a comparable hypercube. We also propose the optimal routing algorithm in HCN(m,n) where m less than or equal to n and obtain that its diameter is n + [(m + 1)/3] + 1. Typical parallel algorithms run in HCN(m. n) with the same time complexity as a hypercube and the hypercube topology can be emulated with O(1) time complexity in it.