The t/s-diagnosability and t/s-diagnosis algorithm of folded hypercube under the PMC/MM model

• Published in: Theoretical computer science Vol. 887; pp. 85 - 98
• Main Authors: Lin, Yuhang, Lin, Limei, Huang, Yanze, Wang, Jiaru
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 02.10.2021
• Subjects: [formula omitted]-Diagnosability; Fault diagnosis; Folded hypercube; Reliability; Fault diagnosis; t/s-Diagnosability; Folded hypercube; Reliability
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2021.07.006

A t/s-diagnosable system refers to such a system that all the faulty nodes of the system can be isolated within a set of size at most s in the presence of at most t faulty nodes. Moreover, it increases the allowed faulty nodes, hence enhancing the diagnosability of the system. We can find that the t/s-diagnosability of n-dimensional folded hypercube FQn has not been studied under the PMC model and MM* model. In this paper, we determine the t/s-diagnosability of FQn under the PMC model and MM* model. First, we propose some new fault tolerant properties of FQn. Then we prove that the t/s-diagnosability of n-dimensional folded hypercube FQn is (n+1)g−12(g−1)(g+2) for 2≤g≤12(n−1) where s=(n+1)g−12(g−1)(g+2)+g−2 under both the PMC model and MM* model. In addition, we establish two t/s-diagnosis algorithms of complexity O(Nlog2N) and complexity O(N(log2N)2) to isolate the faulty nodes in a node subset of the system under the PMC model and MM* model, respectively. The comparison analysis results showed that the t/s-diagnosability of FQn is the largest, and it increases faster than the other types of diagnosability as n increases.