With the rapid development of cloud computing, big data, and artificial intelligence, data center networks have become the core of modern computing infrastructure. As an important type of data center network, determining theh-component diagnosability ofk-dimensional DCell networksDCellk,nwith n-port switch has become a critical issue for enhancing network’s diagnostic capabilities and assessing network’s vulnerability. However, there is currently scarce research on the h-component diagnosability ofDCellk,nbased on the mutual testing model. In this paper, we innovatively propose theh-component diagnosability and diagnostic algorithm of DCell networks based on the mutual testing model. We first theoretically prove and determine that the h-component diagnosability of DCellk,n is ctPMC h (DCellk,n) = (h− 1)n + hk− (2h− 2) for 2 ≤h≤ 3 andk≥ (h− 2)n+ (4 −h),n≥h+ 1. It implies that the data center networkDCellk,ncan identify (h− 1)n+hk− (2h− 2) faulty nodes when the count of remaining components is at leasth(2 ≤ h ≤ 3). Furthermore, we also propose a novel and broadly applicableh-componentt-diagnosable algorithm ICFD-P based on iterative testing, combinatorial properties and linearly many fault analysis to diagnose all faulty nodes inDCellk,n, effective as a general framework in interconnection networks. We apply the algorithm ICFD-P to simulated data and real data to diagnose faulty nodes. The simulation experiments highlight the effectiveness and robustness of the designed ICFD-P strategy within and even beyond the allowed range of diagnosability inDCellk,n, combined with its enhanced fault diagnosis capability and theoretical foundation for reliability and security, make it a valuable tool for maintaining the stability and security of such networks.

Data center DCell networks are particularly well-suited for large, reliability-critical data centers due to their scalability, fault tolerance, and efficient bandwidth utilization. The reliability and diagnosis of DCell networks are of paramount importance in ensuring smooth operation and continuous availability of data center services. Traditional fault diagnosis models, which focus on global fault detection, are more suited to simpler networks. In contrast, complex DCell networks require fault diagnosis under specific conditions to accommodate dynamic changes and constraints. This paper studies the cyclic diagnosability of DCell networks under different system-level diagnostic models, which is a novel fault diagnosis strategy. Cyclic diagnosability, denoted as$ct_{c}(G)$, represents the maximum size of a set of fault vertices$D$in a network$G$, so that the self-diagnosis system can identify all vertices in$D$under the condition that at least two connected components of$G-D$contain a cycle. We show that for$k$-dimensional DCell with$n$-port switches$DCell_{k,n}$, when$k \geq 2$,$3 \leq n \leq 5$, or$k \geq \frac {n}{2} + 1$,$n \geq 6$, the cyclic diagnosability is$4k+2n-5$under the PMC and MM* models based on the indistinguishability of the constructed set and the linear multiple fault analysis technology. Additionally, we propose two practical cyclic fault diagnosis algorithms with low time complexity: PMC-Based Cyclic Fault Diagnosis (PMCCFD) and MM*-Based Cyclic Fault Diagnosis (MMCFD) for the PMC and MM* models to improve fault detection and recovery in large-scale DCell networks. We also implement the PMCCFD and MMCFD algorithms on both synthetic and real data. Furthermore, we verify the availability/efficiency of algorithms PMCCFD and MMCFD in terms of accuracy rate, recall, false negative rate, negative predictive value, and F1Score.

Fault diagnosability can reflect the actual self diagnosing capability of a multiprocessor system better. However, people usually focus on the overall information and neglect the important local information. In order to reflect the locality of a system at a node better, this paper proposes a novel fault diagnosis strategy, called x-block local fault diagnosability (x-BLFD), where the x-block condition requires more than x connected fault-free nodes. Then, we characterize some important properties about the x-BLFD of multiprocessors interconnected networks under the Preparata/Metze/Chien model (P/M/C), and further propose the x-BLFD in an$f(x)$-extended block network with the minimum$(x+1)$-subnetwork degree at some node. We also establish an approximate algorithm to calculate the x-BLFD of a large-scale diagnosable network at some node, and analyze the experimental performance of large-scale networks. Furthermore, we apply our proposed conclusion to obtain the x-BLFD of 16 well-known networks at some node directly under P/M/C, including dual cubes, hierarchical cubic networks, DQcubes, twisted hypercubes, Bicube networks, crossed cubes, folded hypercubes, k-ary n-cubes, balanced hypercubes, BC graphs,$(n,k)$-star graphs, Cayley graphs generated by transposition trees, bubble-sort star graphs, split-star networks, data center networks, and$(n,k)$-arrangement graphs. Finally, we compare the x-BLFD with the diagnosability, conditional diagnosability, pessimistic diagnosability, and$t/k$-diagnosability by a large number of detailed numerical analysis. It can be seen that the x-BLFD is greater than all the other types of fault diagnosabilities.