Diagnosability of crossed cubes under the comparison diagnosis model

Diagnosability of a multiprocessor system is an important study topic in the parallel processing area. As a hypercube variant, the crossed cube has many attractive properties. The diameter, wide diameter and fault diameter of it are all approximately half those of the hypercube. The power with which the crossed cube simulates trees and cycles is stronger than the hypercube. Because of these advantages, the crossed cube has attracted much attention from researchers. In this paper, we show that the n-dimensional crossed cube is n-diagnosable under a major diagnosis model-the comparison diagnosis model proposed by Malek and Maeng (1981) if n ⩾ 4. According to this, the polynomial algorithm presented by Sengupta and Dahbura (1992) may be used to diagnose the n-dimensional crossed cube, provided that the number of the faulty nodes in the n-dimensional crossed cube does not exceed n. The conclusion also indicates that the diagnosability of the n-dimensional crossed cube is the same as that of the n-dimensional hypercube when n ⩾ 5 and better than that of the n-dimensional hypercube when n = 4