Conditional diagnosability of arrangement graphs under the PMC model

Processor fault diagnosis has played an important role in measuring the reliability of a multiprocessor system, and the diagnosabilities of many well-known multiprocessor systems have been investigated. The conditional diagnosability has been widely accepted as a measure of diagnosability by assuming an additional condition that any fault-set can't contain all the neighbors of any node in a multiprocessor system. This paper considers the conditional diagnosability of an (n,k)(n,k)-arrangement graph An,kAn,k, a flexible interconnection network model for multiprocessor systems, under the classical PMC diagnostic model, and determines that the conditional diagnosability of An,kAn,k(k≥2,n≥k+2)(k≥2,n≥k+2) is (4k−4)(n−k)−3(4k−4)(n−k)−3, which is about four times its traditional diagnosability.