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)-arrangement graph A_n,k, a flexible interconnection network model for multiprocessor systems, under the classical PMC diagnostic model, and determines that the conditional diagnosability of A_n,k (k≥2, n≥k+2) is (4k-4)(n-k)-3, which is about four times its traditional diagnosability.