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)(m )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 <= 2n, 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).