Abstract
Diagnosability of a multiprocessor system is an important measure of the reliability of interconnection networks. System-level diagnosis is a primary strategy to identify the faulty processors in a multiprocessor system. Based on a sound assumption proposed by Zhu et al. recently, we proposed a new diagnosability named non-inclusion diagnosability and showed that the non-inclusion diagnosability \( t_N(Q_n)\) of the hypercube under the PMC model is \( 2n-2\). That is, assume that if two vertex sets \( F_1\) and \( F_2\) are both consistent with a syndrome and \( F_1\subset F_2\), then \( F_2\) is not the faulty set which we are looking for; the faulty set F is 1-step diagnosable if \( |F|\leqslant 2n-2\) in \( Q_n\) under the PMC model.
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Acknowledgements
Many of the ideas in this paper were inspired by a course in the School of Mathematical Sciences, BNU. The authors thank the editor and anonymous referees for their helpful comments and kind suggestions on the original manuscript which resulted in this final version.
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This work was supported by the National Natural Science Foundation of China (Nos. 61672025, 60974082, 61179040 and 61075117), Shandong Provincial Natural Science Foundation (No. ZR2021MF012).
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Ma, MJ., Xu, M., Ding, TT. et al. The Non-inclusion Diagnosability of Hypercubes Under the PMC Model. J. Oper. Res. Soc. China (2022). https://doi.org/10.1007/s40305-022-00421-9
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DOI: https://doi.org/10.1007/s40305-022-00421-9