The t/k-diagnosability of m-ary n-cube networks

A crucial index used to evaluate the reliability of a multiprocessor system is diagnosability. The t / k-diagnosis strategy greatly improves the diagnosability of a system by allowing up to k fault-free processors to be misdiagnosed as faulty processors. Compared with the t -diagnosability and t 1 / t 1-diagnosability, the t / k-diagnosability can better reflect the fault modes of a practical system. The m -ary n -cube Q n m (in order not to be confused with the “ k ” of the t / k-diagnosability, we replace k -ary n -cube Q n k with m -ary n -cube Q n m) is a significant and common network topology, which is used as the underlying network in the construction of many distributed memory multiprocessors. In this paper, we explore several useful lemmas and the t / k-diagnosability of Q n m. According to the sufficient condition for determining that a system is t / k-diagnosable, we show that for n ≥ 2, m ≥ 4, and 0 ≤ k ≤ 2 n, Q n m is t k , n / k-diagnosable, where t k , n = 2 ( k + 1 ) n − 1 2 ( k + 1 ) ( k + 2 ) + 1. Based on this, we provide a comparison among the t -diagnosability, the t 1 / t 1-diagnosability, and the t / k-diagnosability of Q n m.