The Metric Relationship Between Extra Connectivity and Extra Diagnosability of Multiprocessor Systems

As multiprocessor systems scale up, $h$-extra connectivity and $h$-extra diagnosability serve as two pivotal metrics for assessing the reliability of the underlying interconnection networks. To ensure that each component of the survival graph holds no fewer than $h + 1$ vertices, the $h$-extra connectivity and $h$-extra diagnosability have been proposed to characterize the fault tolerability and self-diagnosing capability of networks, respectively. Many efforts have been made to establish the quantifiable relationship between these metrics but it is less than optimal. This work addresses the flaws of the existing results and proposes a novel proof to determine the metric relationship between $h$-extra connectivity and $h$-extra diagnosability under the PMC and MM^* models. Our approach overcomes the defect of previous results by abandoning the network’s regularity and independence number. Furthermore, we apply the suggested metric to establish the $h$-extra diagnosability of a new network class, named generalized exchanged X-cube-like network $GEXC(s,t)$, which takes dual-cube-like network, generalized exchanged hypercube, generalized exchanged crossed cube, and locally generalized exchanged twisted cube as special cases. Finally, we propose the $h$-extra diagnosis strategy ($h$-EDS) and design two self-diagnosis algorithms AhED-PMC and AhED-MM^*, and then conduct experiments on $GEXC(s,t)$ and the real-world network DD-$g648$ to show the high accuracy and superior performance of the proposed algorithms.