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The properties and t/s-diagnosability of k-ary n-cube networks

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A Correction to this article was published on 02 December 2021

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Abstract

An increase in network system size increases the risk of node failure in a system. To maintain the reliability of the system, the faulty nodes need to be repaired or replaced with additional nodes, which implies that the approach of locating the faulty nodes in the system is a research topic of great significance. There are various kinds of diagnosis strategies, such as the t-diagnosis strategy, t/s-diagnosis strategy, t/t-diagnosis strategy and t/k-diagnosis strategy. When we use the t/s-diagnosis strategy to identify faulty nodes, some fault-free nodes may be identified as faulty nodes. In addition, the choice of the specific diagnosis model to identify faulty nodes is important; the Preparata, Metze and Chen (PMC) model is widely used. In this paper, we study the t/s-diagnosability of the k-ary n-cube under the PMC model. First, we obtain several structural properties of k-ary n-cubes. Then, we use these properties and determine that the 3-ary n-cube is \(\eta /\eta +h-1\)-diagnosable, where \(n\geqslant 2\), \(1\leqslant h\leqslant n-1\) and \(2hn-3(h-1)-\frac{(h-1)(h-2)}{2}-1<\eta \leqslant 2(h+1)n-3h-\frac{h(h-1)}{2}-1\), and that the k-ary n-cube is \(\eta /\eta +h-1\)-diagnosable, where \(k\geqslant 4\), \(n\geqslant 2\), \({1\leqslant h\leqslant n-1}\) and \(2hn-2(h-1)-\frac{(h-1)(h-2)}{2}-1<\eta \leqslant 2(h+1)n-2h-\frac{h(h-1)}{2}-1\).

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Acknowledgements

This work was supported in part by the Natural Science Foundation of China under Grant No.61862003 and No. 61761006, and in part by the Natural Science Foundation of the Guangxi Zhuang Autonomous Region of China under Grant No. 2018GXNSFDA281052.

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Authors and Affiliations

  1. School of Computers, Electronics and Information and Guangxi Key Laboratory of Multimedia Communications and Network Technology, Guangxi University, Nanning, 530004, Guangxi, China

    Yuhao Xie, Jiarong Liang & Wen Yin

  2. School of Public Policy and Management, Guangxi University, Nanning, 530004, Guangxi, China

    Changzhen Li

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  1. Yuhao Xie
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Correspondence to Changzhen Li.

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Xie, Y., Liang, J., Yin, W. et al. The properties and t/s-diagnosability of k-ary n-cube networks. J Supercomput 78, 7038–7057 (2022). https://doi.org/10.1007/s11227-021-04155-y

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