Kwon Kyung Hee, Lee Gye Sung

The Transactions of the Korea Information Processing Society (1994 ~ 2000), Vol. 6, No. 1, pp. 75-82, Jan. 1999
10.3745/KIPSTE.1999.6.1.75,   PDF Download:

Abstract

Recently, a new hypercube-like interconnection network, the Z-cube, was proposed. The Z-cube retains most good topological properties, however, its node degree is 3/4 of hypercube's one. Considering hardware implementations, the Z-cube is a good alternative to the hypercube. In this paper, we obtained the diameter, fault diameter and the average distance between two nodes to evaluate the communication performance of the Z-cube. The recursive structure, the shortest path between two nodes in Z-cube and recurrence relation on the average distance were deduced, and node disjoint path was introduced. Although it is generally expected that the communication performance in an interconnection network with reduced node degree falls as much as that, this paper shows that the Z-cube's diameter is the same as the hypercube's one and the average distance between two nodes in Z-cube is about 1.125 times the average distance between two nodes in the hypercube and the fault diameter of Z-cube ranges approximately from 1.4 times to 1.7 times the fault diameter of the hypercube.

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