A diagnosis algorithm by using graph-coloring under the PMC model

Abstract

Fault diagnosis is important to the design and maintenance of large multiprocessor systems. PMC model is the most well known and widely studied model in the system level diagnosis of multiprocessor systems. Under the PMC model, a diagnosis algorithm based on some graph-coloring techniques has been proposed in this paper. Given a syndrome \(\sigma \), the first part of the algorithm can locate all the definitely faulty vertices. Then in the second part of the algorithm a diagnosis graph corresponding to the syndrome can be constructed and the suspicious faulty sets can be determined by finding the maximal independent sets of the diagnosis graph. A weight is assigned to each suspicious faulty vertex set which can measure its occurring probability. The algorithm is shown to be correct, not based on any conjecture and can be applied to the fault identification for any multiprocessor system.

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References

  1. Barsi F, Grandoni F, Maestrini P (1976) A theory of diagnosability of digital systems. IEEE Trans Comput 100(6):585–593

    MathSciNet  Article  MATH  Google Scholar 

  2. Berthet GG, Nussbaumer HJ (1996) A unified theory for f1/f2-diagnosable communication networks. In: Dependable computing—EDCC-2. Springer, Berlin, Heidelberg, pp 421–438

  3. Bondy JA, Murty USR (1976) Graph theory with applications, vol 290. Macmillan, London

  4. Caruso A, Chessa S (2007) Worst-case diagnosis completeness in regular graphs under the pmc model. IEEE Trans Comput 56(7):917–924

    MathSciNet  Article  Google Scholar 

  5. Caruso A, Chessa S, Maestrini P, Santi P (2002) Diagnosability of regular systems. J Algorithms 45(2):126–143

    MathSciNet  Article  MATH  Google Scholar 

  6. Dahbura AT, Sabnani KK, King LL (1987) The comparison approach to multiprocessor fault diagnosis. IEEE Trans Comput C–36(3):373–378

    Article  Google Scholar 

  7. Dahbura AT, Masson GM (1984) An 0\((n^{2.5}p)\) fault identification algorithm for diagnosable systems. IEEE Trans Comput C–33(6):486–492

    Article  MATH  Google Scholar 

  8. Elbably ME (2005) Dynamic diagnosis algorithm to minimize the diagnosis complexity of digital systems. J Eng Appl Sci 52(4):753–763

    Google Scholar 

  9. Hakimi SL, Amin AT (1974) Characterization of connection assignment of diagnosable systems. IEEE Trans Comput 100(1):86–88

    MathSciNet  Article  MATH  Google Scholar 

  10. Harper LH (1966) Optimal numberings and isoperimetric problems on graphs. J Comb Theory 1(3):385–393

    MathSciNet  Article  MATH  Google Scholar 

  11. Krishnamoorthy MS, Krishnamurthy B (1987) Fault diameter of interconnection networks. Comput Math Appl 13(5–6):577–582

    MathSciNet  Article  MATH  Google Scholar 

  12. Lai PL, Tan JJ, Chang CP, Hsu LH (2005) Conditional diagnosability measures for large multiprocessor systems. IEEE Trans Comput 54(2):165–175

    Article  Google Scholar 

  13. Li TK, Tsai CH, Hsu HC (2012) A fast fault-identification algorithm for bijective connection graphs using the pmc model. Inf Sci 187:291–297

    MathSciNet  Article  MATH  Google Scholar 

  14. Liaw SC, Chang GJ (1999) Generalized diameters and Rabin numbers of networks. J Comb Optim 4:371–384

    MathSciNet  MATH  Google Scholar 

  15. Lombardi F (1986) Comparison-based diagnosis with faulty comparators. Electron Lett 22(22):1158–1160

    Article  Google Scholar 

  16. Manik M, Gramatová E (2009) Diagnosis of faulty units in regular graphs under the PMC model. In: 12th International symposium on design and diagnostics of electronic circuits & systems, 2009 (DDECS’09). IEEE, pp 202–205

  17. Masson GM, Blough DM, Gregory GM (1996) System diagnosis. In: Fault-tolerant computer system design. Prentice-Hall, Inc., NJ, pp 478–536

  18. Metze G, Preparata FP, Chien RT (1967) On the connection assignment problem of diagnosable systems. IEEE Trans Comput 6:848–854

    MATH  Google Scholar 

  19. Meyer GGL, Masson GM (1978) An efficient fault diagnosis algorithm for symmetric multiple processor architectures. IEEE Trans Comput 100(11):1059–1063

    Article  MATH  Google Scholar 

  20. Meyer GGL (1981) A fault diagnosis algorithm for asymmetric modular architectures. IEEE Trans Comput 100(1):81–83

    MathSciNet  Article  MATH  Google Scholar 

  21. Pelc A (1991) Undirected graph models for system-level fault diagnosis. IEEE Trans Comput 40(11):1271–1276

    MathSciNet  Article  Google Scholar 

  22. Peng Y, Hong BR, Qiao YQ (2000) The characterization of t-diagnosable systems based on the generalized comparison model and a parallel algorithm for diagnosis. Chin J Comput 23(2):126–133

    MathSciNet  Google Scholar 

  23. Rangarajan S, Fussell D (1991) Probabilistic diagnosis algorithms tailored to system topology. In: Twenty-first international symposium on fault-tolerant computing, 1991 (FTCS-21). Digest of papers. IEEE, pp 230–237

  24. Rangarajan S, Fussell D (1992) Diagnosing arbitrarily connected parallel computers with high probability. IEEE Trans Comput 41(5):606–615

    Article  Google Scholar 

  25. Shi TL, Lu M (2012) Fault-tolerant diameter for three family interconnection networks. J Comb Optim 23:471–482

    MathSciNet  Article  MATH  Google Scholar 

  26. Wang H, Bian X, Ding F, Han G (2002) The application of a distributed system-level diagnosis algorithm in dynamic positioning system. In: Proceedings of the 4th world congress on intelligent control and automation, 2002, vol 3. IEEE, pp 2274–2278

  27. Xiong W, Zhang Z, Lai HJ (2014) Spanning 3-connected index of graphs. J Comb Optim 27:199–208

    MathSciNet  Article  MATH  Google Scholar 

  28. Xuan HN, Zhang DF, Zhang M (2003) The equation diagnosis on pmc fault model. Acta Electron Sin 31(5):694–697

    MathSciNet  Google Scholar 

  29. Yang H, Elhadef M, Nayak A, Yang X (2008) Network fault diagnosis: an artificial immune system approach. In: 14th IEEE international conference on parallel and distributed systems, 2008 (ICPADS’08). IEEE, pp 463–469

  30. Yang XF (2004) A fast pessimistic one-step diagnosis algorithm for hypercube multicomputer systems. J Parallel Distrib Comput 64(4):546–553

    Article  MATH  Google Scholar 

  31. Yang XF, Tang YY (2007) Efficient fault identification of diagnosable systems under the comparison model. IEEE Trans Comput 56(12):1612–1618

    MathSciNet  Article  Google Scholar 

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Acknowledgments

This work is partially supported by the following grants: the Center of Identification Technology Research Grant of West Virginia University, National Natural Science Foundation of China Grants No. 11101322, National Security Agency of USA, Nos. H98230-12-1-0233 &  H98230-14-1-0154, and National Science Foundation of USA, No. DMS-126480.

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Correspondence to Cun-Quan Zhang.

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Zhu, Q., Guo, G., Tang, W. et al. A diagnosis algorithm by using graph-coloring under the PMC model. J Comb Optim 32, 960–969 (2016). https://doi.org/10.1007/s10878-015-9923-5

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Keywords

  • Interconnection networks
  • Diagnosis algorithm
  • PMC model