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

Abstract

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 t1/t1-diagnosability, the t/k-diagnosability can better reflect the fault modes of a practical system. The m-ary n-cube Qnm (in order not to be confused with the “k” of the t/k-diagnosability, we replace k-ary n-cube Qnk with m-ary n-cube Qnm) 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 Qnm. 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, Qnm is tk,n/k-diagnosable, where tk,n=2(k+1)n−12(k+1)(k+2)+1. Based on this, we provide a comparison among the t-diagnosability, the t1/t1-diagnosability, and the t/k-diagnosability of Qnm.