Diagnosabilities of exchanged hypercube networks under the pessimistic one-step diagnosis strategy

The exchanged hypercube EH（s, t） （where s ≥ 1 and t ≥ 1） is obtained by systematically reducing links from a regular hypercube Q,＋t＋l. One-step diagnosis of exchanged hypercubes which involves only one testing phase during which processors test each other is discussed. The diagnosabilities of exchanged hypercubes are studied by using the pessimistic one-step diagno- sis strategy under two kinds of diagnosis models： the PMC model and the MM model. The main results presented here are the two proofs that the degree of diagnosability of the EH（s, t） under pessimistic one-step tl/tl fault diagnosis strategy is 2s where I ≤ s ≤ t （respectively, 2t, where 1 ≤ t ≤ s） based on the PMC model and that it is also 2s where 1 ≤ s ≤ t （respectively, 2t, where 1 ≤ t ≤ s） based on the MM＊ model.

Transitivity of varietal hypercube networks

The varietal hypercube VQn is a variant of the hypercube Qn and has better properties than Qn with the same number of edges and vertices. This paper proves that VQn is vertex-transitive. This property shows that when VQn is used to model an interconnection network, it is high symmetrical and obviously superior to other variants of the hypercube such as the crossed cube.

t/k-fault diagnosis algorithm of n-dimensional hypercube network based on the MM*model

Compared with accurate diagnosis, the system’s selfdiagnosing capability can be greatly increased through the t/kdiagnosis strategy at most k vertexes to be mistakenly identified as faulty under the comparison model, where k is typically a small number. Based on the Preparata, Metze, and Chien(PMC)model, the n-dimensional hypercube network is proved to be t/kdiagnosable. In this paper, based on the Maeng and Malek(MM)*model, a novel t/k-fault diagnosis(1≤k≤4) algorithm of ndimensional hypercube, called t/k-MM*-DIAG, is proposed to isolate all faulty processors within the set of nodes, among which the number of fault-free nodes identified wrongly as faulty is at most k. The time complexity in our algorithm is only O(2~n n~2).

Fault diagnosis for t/(t+1)-diagnosable system based on the PMC model

In this paper, a t/(t+1)-diagnosable system is studied, which can locate a set S with |S|≤t+1 containing all faulty units only if the system has at most t faulty units. On the basis of the characterization of the t/(t+1)-diagnosable system, a necessary and sufficient condition is presented to judge whether a system is t/(t+1)-diagnosable. Meanwhile, this paper exposes some new and important properties of the t/(t+1)-diagnosable system to present the t/(t+1)-diagnosability of some networks. Furthermore, the following results for the t/(t+1)-diagnosability of some special networks are obtained: a hypercube network of n -dimensions is (3n-5)/(3n-4)-diagnosable, a star network of n -dimensions is (3n-5)/(3n-4)-diagnosable (n≥5) and a 2D-mesh (3D-mesh) with n 2(n 3) units is 8/9-diagnosable (11/12-diagnosable). This paper shows that in general, the t/(t+1)-diagnosability of a system is not only larger than its t/t -diagnosability , but also its classic diagnosability, specially the t/(t+1)-diagnosability of the hypercube network of n -dimensions is about 3 times as large as its classic t -diagnosability and about 1.5 times as large as its t/t -diagnosability.

An Artificial Neural Network-Based Response Surface Method for Reliability Analyses of c-φ Slopes with Spatially Variable Soil

This paper presents an artificial neural network（ANN）-based response surface method that can be used to predict the failure probability of c-φslopes with spatially variable soil.In this method,the Latin hypercube sampling technique is adopted to generate input datasets for establishing an ANN model;the random finite element method is then utilized to calculate the corresponding output datasets considering the spatial variability of soil properties;and finally,an ANN model is trained to construct the response surface of failure probability and obtain an approximate function that incorporates the relevant variables.The results of the illustrated example indicate that the proposed method provides credible and accurate estimations of failure probability.As a result,the obtained approximate function can be used as an alternative to the specific analysis process in c-φslope reliability analyses.

Fault-Tolerant Cycles Embedding in Folded Hypercubes

The generalized conditional fault-tolerant embedding is investigated, in which the n-dimensional folded hypercube networks （denoted by FQn） acts as the host graph, and the longest fault-free cycle represents the guest graph. Under the conditions looser than that of previous works, it is shown that FQn has a cycle with length at least 2n -21F, I when the number of faulty vertices and non-critical edges is at most 2n-4; where ｜Fv｜ is the number of faulty vertices. It provides further theoretical evidence for the fact that FQn has excellent node-fault-tolerance and edge-fault-tolerance when used as a topology of large scale computer networks.