Three-Round Adaptive Diagnosis in Twisted Cubes

Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 20)

Abstract

In this paper, we propose a scheme to solve the problem of adaptive fault diagnosis in n-dimensional twisted cubes in at most three test rounds, provided that the number of faulty vertices is at most n for n ≥ 9. First, each vertex tests one specific neighbour and is tested by another specific neighbour to provide a basic syndrome in two rounds in our scheme. Then, we assign other necessary tests to diagnose the vertices that cannot be identified according to the previous syndrome in one more round. The scheme is optimal for at most three rounds since the adaptive diagnosis needs at least three rounds to complete.

Keywords

Interconnection networks twisted cubes hypercubes adaptive diagnosis Hamiltonian distributed systems multiprocessors 

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References

  1. 1.
    Preparata, F.P., Metze, G., Chien, R.T.: On the connection assignment problem of diagnosable systems. IEEE Transactions on Electronic Computers EC-16, 848–854 (1967)MATHCrossRefGoogle Scholar
  2. 2.
    Hakimi, S.L., Amin, A.T.: Characterization of connection assignment of diagnosable systems. IEEE Transactions on Computers 23, 86–88 (1974)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Nakajima, K.: A new approach to system diagnosis, pp. 697–706 (September 1981)Google Scholar
  4. 4.
    Fujita, S., Araki, T.: Three-Round Adaptive Diagnosis in Binary n-Cubes. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 442–451. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Hilbers, P.A.J., Koopman, M.R.J., van de Snepscheut, J.L.A.: The Twisted Cube. In: Treleaven, P.C., Nijman, A.J., de Bakker, J.W. (eds.) PARLE 1987. LNCS, vol. 258, pp. 152–159. Springer, Heidelberg (1987)CrossRefGoogle Scholar
  6. 6.
    Abraham, S., Padmanabhan, K.: The twisted cube topology for multiprocessors: A study in network asymmetry. Journal of Parallel and Distributed Computing 13, 104–110 (1991)CrossRefGoogle Scholar
  7. 7.
    Chang, C.P., Wang, J.N., Hsu, L.H.: Topological properties of twisted cube. Informatics and Computer Science: An International Journal 113, 147–167 (1999)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Lai, P.L., Tasi, C.: Embedding of tori and grids into twisted cubes. Theoretical Computer Science 411(40-42), 3763–3773 (2010)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    West, D.B.: Introduction to Graph Theory. Prentice Hall (2001)Google Scholar
  10. 10.
    Fana, J., Linb, X., Panc, Y., Jiaa, X.: Optimal fault-tolerant embedding of paths in twisted cubes. Journal of Parallel and Distributed Computing 67, 205–214 (2007)CrossRefGoogle Scholar
  11. 11.
    Araki, T.: Optimal adaptive fault diagnosis of cubic hamiltonian graphs, pp. 162–167 (May 2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Computer Science and Information EngineeringNational Dong Hwa University, ShoufengHualienTaiwan , R.O.C.

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