Related papers: A general approach to deriving diagnosability resu…
The $g$-good-neighbor conditional diagnosability is a new measure for fault diagnosis of systems. Xu et al. [Theor. Comput. Sci. 659 (2017) 53--63] determined the $g$-good-neighbor conditional diagnosability of $(n, k)$-star networks $S_{n,…
Let $G=(V, E)$ be a connected graph, a subset $S\subseteq V(G)$ is called an $R^{g}$-vertex-cut of $G$ if $G-F$ is disconnected and any vertex in $G-F$ has at least $g$ neighbours in $G-F$. The $R^{g}$-vertex-connectivity is the size of the…
The data center networks $D_{n,k}$, proposed in 2008, has many desirable features such as high network capacity. A kind of generalization of diagnosability for network $G$ is $g$-good-neighbor diagnosability which is denoted by $t_g(G)$.…
The processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly…
The concept of neighbor connectivity originated from the assessment of the subversion of espionage networks caused by underground resistance movements, and it has now been applied to measure the disruption of networks caused by cascading…
Extra connectivity and the pessimistic diagnosis are two crucial subjects for a multiprocessor system's ability to tolerate and diagnose faulty processor. The pessimistic diagnosis strategy is a classic strategy based on the PMC model in…
Connectivity and diagnosability are important parameters in measuring the fault tolerance and reliability of interconnection networks. The $R^g$-vertex-connectivity of a connected graph $G$ is the minimum cardinality of a faulty set…
In this paper, we study diagnosabilities of multiprocessor systems under two diagnosis models: the PMC model and the comparison model. In each model, we further consider two different diagnosis strategies: the precise diagnosis strategy…
System level diagnosis is an important approach for the fault diagnosis of multiprocessor systems. In system level diagnosis, diagnosability is an important measure of the diagnosis capability of interconnection networks. But as a measure,…
Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors.…
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…
Zhu et al. [Theoret. Comput. Sci. 758 (2019) 1--8] introduced the $h$-edge tolerable diagnosability to measure the fault diagnosis capability of a multiprocessor system with faulty links. This kind of diagnosability is a generalization of…
To measure the fault diagnosis capability of a multiprocessor system with faulty links, Zhu et al. [Theoret. Comput. Sci. 758 (2019) 1--8] introduced the $h$-edge tolerable diagnosability. This kind of diagnosability is a generalization of…
This paper considers a kind of generalized measure $\lambda_s^{(h)}$ of fault tolerance in a hypercube-like graph $G_n$ which contain several well-known interconnection networks such as hypercubes, varietal hypercubes, twisted cubes,…
The component connectivity is the generalization of connectivity which is an parameter for the reliability evaluation of interconnection networks. The $g$-component connectivity $c\kappa_{g}(G)$ of a non-complete connected graph $G$ is the…
Deep neural networks have achieved remarkable success in various challenging tasks. However, the black-box nature of such networks is not acceptable to critical applications, such as healthcare. In particular, the existence of adversarial…
Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network $G$. In 1996, F\`{a}brega and Fiol proposed the $g$-good-neighbor connectivity of $G$. In this paper, we show that $1\leq…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
Understanding the relationships between different properties of data, such as whether a connectome or genome has information about disease status, is becoming increasingly important in modern biological datasets. While existing approaches…
We consider the probability model of edge-fault tolerance of a network in the sense of connectivity with link faults. Using graph-theoretical notation, we define the edge-fault (EF) and Menger-type edge-fault (MEF) tolerances of a graph as…