The (t,k)-diagnosability of Cayley graph generated by 2-tree

Abstract

Multiprocessor systems, which typically use interconnection networks (or graphs) as underlying topologies, are widely utilized for big data analysis in scientific computing due to the advancements in technologies such as cloud computing, IoT, social network. With the dramatic expansion in the scale of multiprocessor systems, the pursuit and optimization of strategies for identifying faulty processors have become crucial to ensuring the normal operation of high-performance computing systems. System-level diagnosis is a process designed to distinguish between faulty processors and fault-free processors in multiprocessor systems. The $(t,k)$-diagnosis, a generalization of sequential diagnosis, proceeds to identify at least k faulty processors and repair them in each iteration under the assumption that there are at most t faulty processors whenever $t\ge k$. We show that Cayley graph generated by 2-tree is $(2^{n-3},2n-4)$-diagnosable under the PMC model for $n\ge 5$ while it is $(\frac{2^{n-3}(2n-6)}{2n-4},2n-4)$-diagnosable under the MM^⁎ model for $n\ge 4$. As an empirical case study, the $(t,k)$-diagnosabilities of the alternating group graph $A{G}_n$ under the PMC model and the MM* model have been determined.