The extra local diagnosability and diagnosis algorithm of networks under the PMC model

Abstract

The fault diagnosis has played an important role in the reliability of the large-scale Networks. In practical applications, we do not require global diagnosis and it suffices to determine the working status of some specific vertices (i.e. processors) in the area of the information transmission. Therefore, the sub-network containing the specific vertex v needs to be designed, and then we can judge whether v is faulty after analyzing the syndrome which is obtained by using the diagnosis model in this sub-network. This approach is known as local diagnosis. Since the faulty network should have local connectivity, we consider the h-extra fault model that, after removing all faulty vertices, each component of the network contains more than h vertices. Then we introduce the concept of h-extra local diagnosability and propose a sufficient condition for estimating the extra local diagnosability of the vertex v under the PMC diagnosis model. Additionally, the structure $T(v;h)$ which is the sub-network containing v is designed and we propose the algorithm for correctly identifying the faulty or fault-free status of v. Finally, the simulation demonstrates that, under the PMC model, our diagnosis algorithm is still effective in $T(v;h)$ even with a large number of faulty vertices.