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The t/s-Diagnosability and Diagnostic Strategy of Balanced Hypercube Under Two Classic Diagnostic Models

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Abstract

Fault diagnosis plays a crucial role in the fault tolerability assessment of an interconnection network, which is of great value in the design and maintenance of large-scale multiprocessor systems. A t/s-diagnostic strategy, as the generalization of the t/t-diagnostic strategy, refers to the self-diagnosis of a multiprocessor system in which all faulty vertices can be identified in a set of size at most s in the presence of at most t faulty vertices. In this work, we show that the balanced hypercube BHn (n ⩾ 4) is ((2n + 1) ⌈g/2⌉ − ⌈g/2⌉2)/((2n + 1) ⌈g/2⌉ − ⌈g/2⌉2 + (g − 2))-diagnosable under both the Preparata, Metze, and Chien (PMC) and MM* models for 4 ⩽ ⌈g/2⌉ ⩽ n. Moreover, we propose two effective t/s-diagnosis algorithms under the PMC and MM* models with time complexity O(NlogN) and O(N(logN)2) (N = 22n is the order of BHn), respectively. Finally, comparison results indicate that t/s-diagnosability strengthens the self-diagnosable capability of the system compared with traditional diagnosabilities.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, China

    Xiao-Qing Liu  (柳晓青), Shu-Ming Zhou  (周书明) & Hong Zhang  (张 红)

  2. Center for Applied Mathematics of Fujian Province, Fujian Normal University, Fuzhou, 350117, China

    Xiao-Qing Liu  (柳晓青), Shu-Ming Zhou  (周书明) & Hong Zhang  (张 红)

  3. Department of Mathematics and Statistics, Oakland University, Rochester, MI, 48309, USA

    Eddie Cheng

Authors
  1. Xiao-Qing Liu  (柳晓青)
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  2. Shu-Ming Zhou  (周书明)
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  3. Eddie Cheng
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  4. Hong Zhang  (张 红)
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Corresponding author

Correspondence to Shu-Ming Zhou  (周书明).

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Conflict of Interest The authors declare that they have no conflict of interest.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61977016 and 61572010, the Natural Science Foundation of Fujian Province of China under Grant Nos. 2023J01539 and 2020J01164, the Fujian Alliance of Mathematics under Grant No. 2023SXLMMS04, and the China Scholarship Council under Grant No. 202108350054.

Xiao-Qing Liu received her B.S. degree in mathematics from Jinzhong University, Jinzhong, in 2020. She is a postgraduate candidate at the College of Mathematics and Statistics, Fujian Normal University, Fuzhou. Her research interests include interconnection networks, reliability analysis, and fault diagnosis of networks.

Shu-Ming Zhou received his Ph.D. degree in mathematics from Xiamen University, Xiamen, in June 2005. Now he is a professor and Ph.D. supervisor of Fujian Normal University, Fuzhou. His research interests include topics in algorithmic graph theory, combinational optimization, fault diagnosis, network science, social network, and big data processing.

Eddie Cheng received his Ph.D. degree in combinatorics and optimization from the University of Waterloo, Waterloo, in 1995. He is currently a distinguished professor of mathematics with the Department of Mathematics and Statistics, Oakland University

Hong Zhang received her B.S. and M.S. degrees in mathematics from Longdong University, Qingyang, in 2016, and Xinjiang University, Urumqi, in 2020, respectively. Now, she is a doctoral candidate at the College of Mathematics and Statistics, Fujian Normal University, Fuzhou. Her research interests include interconnection networks, reliability analysis of networks, and fault diagnosis.

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Liu, XQ., Zhou, SM., Cheng, E. et al. The t/s-Diagnosability and Diagnostic Strategy of Balanced Hypercube Under Two Classic Diagnostic Models. J. Comput. Sci. Technol. 39, 1207–1222 (2024). https://doi.org/10.1007/s11390-024-2732-5

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  • DOI: https://doi.org/10.1007/s11390-024-2732-5

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