Reliability Evaluation of Generalized ExchangedX-Cubes Based on the Condition ofg-Good-Neighbor

Xiaoyan Li,Shuming Zhou,Cheng-Kuan Lin,Hongbin Zhuang,Wenzhong Guo,Hongju Cheng

doi:10.1155/2020/9793082

Xiaoyan Li, Shuming Zhou + Show 4 more

Open Access

https://doi.org/10.1155/2020/9793082

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Abstract

In the cloud computing environment with massive information services and decision-making resources, the accuracy and reliability of information are more important than previous single closed systems. Therefore, ensuring the reliability of information and the stable operation of the system are the core problems in the research fields such as the Internet Plus and the Internet of Things. The connectivity and diagnosability are two important measures for the fault tolerance of multiprocessor systems. Theg-good-neighbor conditional connectivity (Rg-connectivity) is the minimum number of nodes that make the graph disconnected, and each node has at leastgneighbors in every remaining component. Theg-good-neighbor conditional diagnosability (g-GNCD) is the maximum number of faulty processors that has been correctly identified in a system, and any fault-free processor has no less thangfault-free neighbors. ExchangedX-cubes are a class of irregular networks, obtained by deleting links from hypercubes and some variant networks of hypercubes (X-cubes). They not only combine the advantages ofX-cubes but also reduce the interconnection complexity. ExchangedX-cubes classify its nodes into two different classes clusters with a unique connecting rule. In this paper, we propose the generalized exchangedX-cubes framework so that architecture can be constructed by different connecting rules. Furthermore, we study theRg-connectivity andg-GNCD of generalized exchangedX-cubes under the PMC and MM∗models. As applications, theRg-connectivity andg-GNCD of generalized exchanged hypercubes, dual-cube-like networks, generalized exchanged crossed cubes, and locally generalized exchanged twisted cubes are determined, respectively.

Highlights

With the expansion of network scale and the improvement of complexity, the reliability and stability of the system become more and more important
We study the Rg-connectivity and g-good-neighbor conditional diagnosability (g-GNCD) of generalized exchanged X-cubes under the PMC and MM∗ models
A multiprocessor system can be usually enlightened as a simple connected graph, where each processor represents a node of the graph, and each link between two processors represents an edge between two nodes in the graph

Summary

Introduction

With the expansion of network scale and the improvement of complexity, the reliability and stability of the system become more and more important. Peng et al [13] proposed the notion of g-good-neighbor conditional diagnosability (g-GNCD), which is the maximum number of faulty processors that can be identified under the condition that every fault-free processor has no less than g fault-free neighbors. Yuan et al [7] studied the g-good-neighbor conditional diagnosabilities of k-ary n-cube networks under the PMC model and the MM∗ model. Lin et al [16] evaluated the g-good-neighbor conditional diagnosabilities of ðn, kÞ-arrangement graphs under the PMC model and the MM∗ model. Guo et al [17] studied the g -good-neighbor conditional diagnosability of the crossed cubes under the PMC model and the MM∗ model. We propose the generalized exchanged X-cubes framework so that architecture can be constructed by different connecting rules.

Preliminaries

Applications to a Family of Famous Networks

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Conclusion