On the Fault Diameter for Supercubes

Abstract

Assume the N and s are positive integers with 2s ＜ N ≦ 2s+1. It is claimed by Auletta, Rescigno, and Scarano that the fault diameter of the supercube with N nodes, is exactly s + 1 if N € { 2s+1 -1, 2s+1 -2, 2s+2s-1 + 1},and s+2 otherwise. In this paper, we will argue that the above assertion is not correct. In stead, we will show that the fault diameter of the supercube with N nodes is s+1 if N €{2s+1 -2}∪{2s+1 – 2i∣ 0 ≦ i ≦ s-1},and s+2 otherwise. To get this goal, the shortest path routing algorithm for supercubes is also presented in this paper.