With the application and rapid development of high-performance computing and cloud computing technology, the scale of the interconnection network has appeared to grow exponentially. Network attacks have become increasingly sophisticated and stealthy. To reach a high reliable network system, widespread attention has been paid to fault diagnosis. In this article, we put forward a reliable and adaptive self-diagnosis strategy, the $h$-extra $r$-component conditional diagnosability, denoted by $ct_{r}^{h}(G)$. Then, we provide a theoretical derivation to characterize the $h$-extra $r$-component conditional diagnosability of bubble sort networks $B_{n}$ under the PMC model. Furthermore, we develop a fast and adaptive fault self-diagnosis algorithm FAFD-PMC to detect all faulty units. Extensive experiments are implemented and applied to synthetic networks and real networks in terms of accuracy (ACCR), true negative rate, false positive rate, recall, and precision, which demonstrates the ACCR/efficiency of our algorithm.

With the proliferation of interconnection networks in mission-critical systems ranging from cloud computing infrastructures to large-scale data centers, the escalating structural complexity has intensified network vulnerability to malicious attacks and cyber warfare incidents. This article establishes a theoretical framework for evaluating network self-diagnostic capability through a novel $h$-extra $r$-component diagnosability metric, denoted as $\widehat{ec}_{r}^{h}(G)$, which quantifies a network’s resilience under compound fault patterns. The proposed metric requires that after removing specific nodes, the remaining subgraph is required to preserve at least $r$ connected components where every component maintains a node count exceeding $h$. Through rigorous combinatorial analysis, we derive closed-form expressions for star networks $S_{n}$, $\widehat{ec}_{2}^{1}(S_{n})=4n-9$ and $\widehat{ec}_{3}^{1}(S_{n})=6n-15$ when $n\geq 6$, establishing the tight diagnosability bounds for this fundamental network topology. To enable practical implementation, we design a Trial System-based Fault Diagnosis Algorithm (TSFD) that features adaptive syndrome verification and parallel fault localization mechanisms. Extensive simulations demonstrate the accuracy of 98.99% fault detection with linear-time complexity $O(Nd)$ in $n$-dimensional star networks. This work advances network reliability theory by introducing a multi-feature diagnosability measure for system-level diagnosis and developing an efficient diagnosis algorithm validated through large-scale network emulation.

With the scale of multiprocessor systems constantly increasing, the large number of interconnected processors (or nodes) makes faulty nodes inevitable. The fault diagnosis of multiprocessor systems therefore is a key technique for the system’s robustness. In this paper, we first propose a novel diagnostic metric, the $h$ -extra $r$ -component diagnosability, denoted $ECD^{h}_{r}(G)$ , which characterizes one special pattern of faults. We derive some theoretical results for the ECD of hypercube, denoted $ECD^{h}_{r}(Q_{n})$ , under the PMC model. Diagnostic algorithms is proposed and implemented to detect faulty nodes that will disconnect hypercube $Q_{n}$ into $r$ components each containing at least $h+1$ nodes. We also test the ECD-PMC algorithm to the hypercube network with different number of faulty processors satisfying the $h$ -extra $r$ -component condition. Extensive simulation results show that our proposed method achieves very good performance in terms of ACCR, TPR, FPR, and TNR.

In this paper, we propose a new digragh model for system level fault diagnosis, which is called the $(f_1,f_{2})$-bounded Preparata–Metze–Chien (PMC) model (shortly, $(f_1,f_{2})$-BPMC). The $(f_1,f_{2})$-BPMC model projects a system such that the number of faulty processors that test faulty processors with the test results $0$ does not exceed $f_{2}$$(f_2\leq f_{1})$ provided that the upper bound on the number of faulty processors is $f_{1}$. This novel testing model compromisingly generalizes PMC model (Preparata, F.P., Metze, G. and Chien R.T. (1967) On the connection assignment problem of diagnosable systems. IEEE Tran. Electron. Comput.,EC-16, 848–854) and Barsi–Grandoni–Maestrini model (Barsi, F., Grandoni, F. and Maestrini, P. (1976) A theory of diagnosability of digital systems. IEEE Trans. Comput.C-25, 585–593). Then we present some characterizations for one-step diagnosibility under the $(f_1,f_{2})$-bounded PMC model, and determine the diagnosabilities of some special regular networks. Meanwhile, we establish the characterizations of $f_1/(n-1)$-diagnosability and three configurations of $f_1/(n-1)$-diagnosable system under the $(f_1,f_{2})$-BPMC model.