Intermittent Fault Diagnosability of Hyper Petersen Network

  • Hua JiangEmail author
  • Jiarong Liang


The problem of permanent fault diagnosis has been discussed widely, and the diagnosability of many well-known networks have been explored. Faults of a multiprocessor system generally include permanent and intermittent, with intermittent faults regarded as the most challenging to diagnose. In this paper, we investigate the intermittent fault diagnosability of hyper Petersen networks. First, we derive that an \(n\)-dimensional hyper Petersen network \(HP_{n}\) with fault-free edges is \((n - 1)_{i}\)-diagnosable under the PMC model. Then, we investigate the intermittent fault diagnosability of \(HP_{n}\) with faulty edges under the PMC model. Finally, we prove that an \(n\)-dimensional hyper Petersen network \(HP_{n}\) is \((n - 2)_{i}\)-diagnosable under the MM* model.


Fault diagnosability Intermittent fault PMC model Hyper Petersen network Multiprocessor system 



  1. 1.
    F. P. Preparata, G. Metze and R. T. Chien, On the connection assignment problem of diagnosis systems, IEEE Transactions on Electronic Computers, Vol. 16, No. 6, pp. 848–854, 1967.CrossRefzbMATHGoogle Scholar
  2. 2.
    A. Kavianpour and K. H. Kim, Diagnosability of hypercubes under the pessimistic one-step diagnosis strategy, IEEE Transactions on Computers, Vol. 40, No. 2, pp. 232–237, 1991.CrossRefGoogle Scholar
  3. 3.
    J. X. Fan, Diagnosability of the Möbius cubes, IEEE Transactions on Parallel and Distributed Systems, Vol. 9, pp. 923–928, 1998.CrossRefGoogle Scholar
  4. 4.
    G. Y. Chang, G. J. Chang and G. H. Chen, Diagnosabilities of regular networks, IEEE Transactions on Parallel and Distributed Systems, Vol. 16, pp. 314–323, 2005.CrossRefGoogle Scholar
  5. 5.
    P. L. Lai, J. J. M. Tan, C. P. Chang and L. H. Hsu, Conditional diagnosability measures for large multiprocessor systems, IEEE Transactions on Computers, Vol. 54, No. 2, pp. 165–175, 2005.CrossRefGoogle Scholar
  6. 6.
    S. L. Peng, C. K. Lin, J. J. M. Tan and L. H. Hsu, The g-good-neighbor conditional diagnosability of hypercube under PMC model, Applied Mathematics and Computation, Vol. 218, pp. 10406–10412, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    M. Xu, K. Thulasiraman and X. D. Hu, Conditional diagnosability of matching composition networks under the PMC model, IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 56, pp. 875–879, 2009.CrossRefGoogle Scholar
  8. 8.
    Q. Zhu, On conditional diagnosability and reliability of the BC networks, The Journal of Supercomputing, Vol. 45, pp. 173–184, 2008.CrossRefGoogle Scholar
  9. 9.
    M. C. Yang, Conditional diagnosability of balanced hypercubes under the PMC model, Information Sciences, Vol. 222, pp. 754–760, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    L. Lin, L. Xu, D. Wang and S. Zhou, The g-good-neighbor conditional diagnosability of arrangement graphs, IEEE Transactions on on Dependable and Secure Computing, Vol. 15, No. 3, pp. 542–548, 2018.CrossRefGoogle Scholar
  11. 11.
    J. Yuan, A. X. Liu, X. Ma, X. L. Liu, X. Qin and J. F. Zhang, The g-good-neighbor conditional diagnosability of k-Ary n-Cubes under the PMC model and MM model, IEEE Transactions on Parallel and Distributed Systems, Vol. 26, pp. 1165–1177, 2015.CrossRefGoogle Scholar
  12. 12.
    J. Yuan, A. X. Liu, X. Qin, J. F. Zhang and J. Li, g-good-neighbor conditional diagnosability measures for 3-ary n-cube networks, Theoretical Computer Science, Vol. 626, pp. 144–162, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    A. K. Somani and O. Peleg, On diagnosability of large fault sets in regular topology-based computer systems, IEEE Transactions on Computers, Vol. 45, No. 8, pp. 892–903, 1996.CrossRefzbMATHGoogle Scholar
  14. 14.
    M. Malek, A Comparison connection assignment for diagnosable of multiprocessor systems. In Proceedings of Seventh International Symposium on Computer Architecture, pages 31–36, 1980.Google Scholar
  15. 15.
    J. Maeng and M. Malek, A comparison connection assignment for self-diagnosis of multiprocessors systems. In Proceedings of 11th International Symposium Fault-Tolerant Computing, pages 173–175, 1981.Google Scholar
  16. 16.
    D. Li and M. Lu, The g-good-neighbor conditional diagnosability of star graphs under the PMC and MM* model, Theoretical Computer Science, Vol. 674, No. 25, pp. 53–59, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    S. Y. Wang and W. P. Han, The g-good-neighbor conditional diagnosability of n-dimensional hypercubes under the MM* model, Information Processing Letters, Vol. 116, No. 9, pp. 574–577, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    M. Wang, Y. Lin and S. Wang, The 2-good-neighbor diagnosability of Cayley graphs generated by transposition trees under the PMC model and MM* model, Theoretical Computer Science, Vol. 628, No. 16, pp. 92–100, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    J. R. Liang, H. Feng and X. Du, Intermittent fault diagnosability of interconnection networks, Journal of Computer Science and Technology, Vol. 32, pp. 1279–1287, 2017.MathSciNetCrossRefGoogle Scholar
  20. 20.
    D. A. Thomas, K. Ayers and M. Pecht, The trouble not identified’ phenomenon in automotive electronics, Microelectronics Reliability, Vol. 42, No. 4–5, pp. 641–651, 2002.CrossRefGoogle Scholar
  21. 21.
    J. Gracia-Morn, J. C. Baraza-Calvo, D. Gil-Toms, L. J. Saiz-Adalid and P. J. Gil-Vicente, Effects of intermittent faults on the reliability of a reduced instruction set computing (RISC) microprocessor, IEEE Transactions on Reliability, Vol. 63, No. 1, pp. 114–153, 2014.Google Scholar
  22. 22.
    S. Mallela and G. M. Masson, Diagnosable systems for intermittent faults, IEEE Transactions on Computers, Vol. 27, No. 6, pp. 560–566, 1978.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    W. A. Syed, S. Khan, P.l Phillips and S. Perinpanayagam, Intermittent fault finding strategies. In The 2nd International Through-life Engineering Services Conference, Procedia CIRP 11, pages 74–79, 2013.Google Scholar
  24. 24.
    G. Chartrand and R. J. Wilson, The Petersen Graph, Graphs and Applications, pages 69–100, 1985.Google Scholar
  25. 25.
    S. K. Das and A. K. Banerjee, Hyper Petersen network: yet another hypercube-like topology. In Proceedings of the 4th Symposium on the Frontiers of Massively Parallel Computation (Froniters92), pages 270–277, 1992.Google Scholar
  26. 26.
    S. K. Das, S. Öhring and A. K. Banerjee, Embedding into hyper petersen networks: yet another hypercube-like interconnection topology, VLSI Design, Vol. 2, pp. 335–351, 1995.CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Automation Science and EngineeringSouth China University of TechnologyGuangzhouChina
  2. 2.Information Network CenterGuangxi UniversityNanningChina
  3. 3.School of Computer, Electronics and InformationGuangxi UniversityNanningChina

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