Xiao-Yan Li’s research while affiliated with Fuzhou University and other places

BCube stands as a renowned server-centric data center network (DCN), boasting numerous advantages, such as low diameter, high aggregate throughput, and abundant parallel paths. As DCNs expand rapidly, followed by the daily increasing likelihood of failures, fault tolerance has become an important issue in DCNs. Hamiltonian paths constitute a pivotal network topology for parallel and distributed computing, suitable for designing deadlock-free routing algorithms, fault-tolerant routing algorithms, and congestion avoidance. The partitioned edge fault (PEF) model is a recently proposed fault model that exploits the properties of networks to achieve fault tolerance with an exponential scale. In this paper, we explore the existence of Hamiltonian paths in BCube under the PEF model. Since one switch failure will result in multiple faulty links, we also extend the conclusions related to Hamiltonian paths to analyze the fault tolerance of BCube under the PEF model when switch failures occur. Moreover, we provide algorithms to embed a Hamiltonian path between arbitrary two distinct servers into BCube under the PEF model. Experimental analysis and comparisons demonstrate that our approach exhibits exponential enhancements over the other known results, and BCube DCNs possess remarkable fault tolerance in response to both link and switch failures under the PEF model. As a by-product, we obtain a deadlock-free routing based on the constructed Hamiltonian path and assess the routing performance compared to the benchmark routing algorithms.

With the surge of bandwidth demand for cloud applications and the exponential growth of data, data center networks (DCNs) are expanding rapidly, followed by the daily increasing likelihood of failures. Such failures, whether due to device or link issues, are inevitable and often lead to packet loss, transmission delays, and even system downtime. Thus, it is crucial to assess the fault-tolerant capabilities of data center networks using appropriate reliability metrics when failures occur. BCube is a well-known server-centric data center network with many advantages, such as rich low-diameter paths, high throughput, and excellent expandability. Not only do the recently proposed matroidal connectivity and conditional matroidal connectivity have reasonable fault assumptions that align well with the structural characteristics of data center networks, but they also significantly enhance the fault tolerance performance of DCNs. This paper determines the matroidal connectivity and conditional matroidal connectivity of BCube, which is the first study to apply the two reliability metrics in DCNs. Then, we extend the conclusions about (conditional) matroidal connectivity to analyze the fault tolerance of BCube in the occurrence of switch failures. In addition, we develop an efficient algorithm to identify the structural features of minimum faulty edge sets, where the cardinality of these edge sets corresponds to the conditional matroidal connectivity of BCube. Finally, we experimentally evaluate the effects of both link and switch failures on BCube’s performance under the matroidal restriction. The experimental analyses reveal that BCube DCNs exhibit high fault tolerance under matroidal constraints, with the ability to withstand both link and switch failures.

The rapid expansion of infrastructure topology, especially noticeable in high-performance computing systems and data center networks, significantly increases the likelihood of failures in network components. While traditional (edge) connectivity has long been the standard for measuring the reliability of interconnection networks, this approach becomes less effective as networks grow more complex. To address this, two innovative metrics, named matroidal connectivity and conditional matroidal connectivity, have emerged. These metrics provide the flexibility to impose constraints on faulty edges across different dimensions and have shown promise in enhancing the edge fault tolerance of interconnection networks. In this paper, we explore (conditional) matroidal connectivity of the k-dimensional folded Petersen network FPk, which is constructed by iteratively applying the Cartesian product operation on the well-known Petersen graph and possesses a regular, vertex- and edge-symmetric architecture with optimal connectivity and logarithmic diameter. Specifically, the faulty edge set F is partitioned into k subsets according to the dimensions of FPk. We then arrange these subsets by their cardinality, imposing the restriction whereby the cardinality of the ith largest subset dose not exceed 3 ⋅ 10i−1 for 1 ≤ i ≤ k. Subsequently, we show that FPk − F is connected with |F|≤∑i=1k(3 ⋅ 10i−1) and determine the exact value of matroidal connectivity and conditional matroidal connectivity.

Fault detection and localization are vital for ensuring the stability of data center networks (DCNs). Specifically, adaptive fault diagnosis is deemed a fundamental technology in achieving the fault tolerance of systems. The highly scalable data center network (HSDC) is a promising structure of server-centric DCNs, as it exhibits the capacity for incremental scalability, coupled with the assurance of low cost and energy consumption, low diameter, and high bisection width. In this paper, we first determine that both the connectivity and diagnosability of the m-dimensional complete HSDC, denoted by HSDCm(m), are m. Further, we propose an efficient adaptive fault diagnosis algorithm to diagnose an HSDCm(m) within three test rounds, and at most N+4m(m−2) tests with m≥3 (resp. at most nine tests with m=2), where N=m·2m is the total number of nodes in HSDCm(m). Our experimental outcomes demonstrate that this diagnosis scheme of HSDC can achieve complete diagnosis and significantly reduce the number of required tests.

In the realm of multiprocessor systems, the evaluation of interconnection network reliability holds utmost significance, both in terms of design and maintenance. The intricate nature of these systems calls for a systematic assessment of reliability metrics, among which, two metrics emerge as vital: connectivity and diagnosability. The Rg$R_g$-conditional connectivity is the minimum number of processors whose deletion will disconnect the multiprocessor system and every processor has at least g fault-free neighbors. The Rg$R_g$-conditional diagnosability is a novel generalized conditional diagnosability, which is the maximum number of faulty processors that can be identified under the condition that every processor has no less than g fault-free neighbors. In this paper, we first investigate the Rg$R_g$-conditional connectivity of generalized exchanged X-cubes GEX(s,t)$G\!E\!X(s,t)$ and present the lower (upper) bounds of the Rg$R_g$-conditional diagnosability of GEX(s,t)$G\!E\!X(s,t)$ under the PMC model. Applying our results, the Rg$R_g$-conditional connectivity and the lower (upper) bounds of Rg$R_g$-conditional diagnosability of generalized exchanged hypercubes, generalized exchanged crossed cubes, and locally generalized exchanged twisted cubes under the PMC model are determined. Our comparative analysis highlights the superiority of Rg$R_g$-conditional diagnosability, showcasing its effectiveness in guiding reliability studies across a diverse set of networks.

Modern large-scale computing systems always demand better connectivity indicators for reliability evaluation. However, as more processing units have been rapidly incorporated into emerging computing systems, existing indicators (e.g., $\ell$ -component edge connectivity and $\ell$ -extra edge connectivity) have gradually failed to provide the required fault tolerance. In addition, these indicators require, for example, that the faulty network should have at least $\ell$ components (or that each component should have at least $\ell$ nodes). These fault assumptions are not flexible enough to deal with diversified structural demands in practice circumstances. In order to address these challenges simultaneously, this article proposes two novel indicators for network reliability by utilizing the partition matroid technique, named matroidal connectivity and conditional matroidal connectivity. We first investigate the accurate values of (conditional) matroidal connectivity of k -ary n -cube $Q_{n}^{k}$ , which is an appealing option as the underlying topology for modern parallel computing systems. Moreover, we propose an $O(k^{n-1})$ algorithm for determining structural features of minimum edge sets whose cardinality is the conditional matroidal connectivity of $Q_{n}^{k}$ . Simulation results are presented to verify our algorithm's correctness and further investigate the distribution pattern of edge sets subject to the restriction of partition matroid. We also present comparative analyses illustrating the superior edge fault tolerance of our findings in relation to prior research, which even exhibits an exponential enhancement when $k\geq 4$ .

Star networks play an essential role in designing parallel and distributed systems. With the massive growth of faulty edges and the widespread applications of the longest paths and cycles, it is crucial to embed the longest fault-free paths and cycles in edge-faulty networks. However, the traditional fault model allows a concentrated distribution of faulty edges and thus can only tolerate faults that depend on the minimum degree of the network vertices. This paper introduces an improved fault model called the partitioned fault model, which is an emerging assessment model for fault tolerance. Based on this model, we first explore the longest fault-free paths and cycles by proving the edge fault-tolerant Hamiltonian laceability, edge fault-tolerant strongly Hamiltonian laceability, and edge fault-tolerant Hamiltonicity in the n -dimensional star network Sn . Furthermore, based on the theoretical proof, we give an O(nN) algorithm to construct the longest fault-free paths in star networks based on the partitioned fault model, where N is the number of vertices in Sn . We also make comparisons to show that our result of edge fault tolerance has exponentially improved other known results.