A Pessimistic Fault Diagnosability of Large-Scale Connected Networks via Extra Connectivity
Limei Lin, Yanze Huang, Li Xu, Sun‐Yuan Hsieh · IEEE Transactions on Parallel and Distributed Systems · 2021
Thet/kt/k-diagnosabilityandhh-extra connectivityare regarded as two important indicators to improve the network reliability. The t/k-diagnosis strategy can significantly improve the self-diagnosing capability of a network at the expense of no more thankfault-free nodes being mistakenly diagnosed as faulty. Theh-extra connectivity can tremendously improve the real fault tolerability of a network by insuring that each remaining component has no fewer than h+1 nodes. However, there is few result on the inherent relationship between these two indicators. In this article, we investigate the reason that caused the serious flawed results in (Liu, 2020), and we propose a diagnosis algorithm to establish the t/k-diagnosability for a large-scale connected networkGunder the PMC model by considering its h-extra connectivity. Let κh(G) be the h-extra connectivity of G. Then, we can deduce that G is κh(G)/h-diagnosable under the PMC model with some basic conditions. All κh(G)faulty nodes can be correctly diagnosed in the large-scale connected network G and at most h fault-free nodes would be misdiagnosed as faulty. The complete fault tolerant method adopts combinatorial properties and linearly many fault analysis to conquer the core of our proofs. We will apply the newly found relationship to directly obtain the κh(G)/h-diagnosability of a series of well known networks, including hypercubes, folded hypercubes, balanced hypercubes, dual-cubes, BC graphs, star graphs, Cayley graphs generated by transposition trees, bubble-sort star graphs, alternating group graphs, split-star networks, k-ary n-cubes and (n,k)-star graphs.