Advertisement

On Adaptive Fault Diagnosis for Multiprocessor Systems

  • Kumiko Nomura
  • Toshinori Yamada
  • Shuichi Ueno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)

Abstract

We first consider adaptive serial diagnosis for multiprocessor systems. We present an adaptive diagnosis algorithm using N+t.1 tests, which is the smallest possible number, for an N-processor system modeled by a (2t.1)-connected graph with at most t faulty processors. We also present an adaptive diagnosis algorithm using minimum number of tests for a system modeled by cube-connected cycles. We consider adaptive parallel diagnosis as well. We show that for adaptive parallel diagnosis of an N-processor system modeled by a hypercube, three testing rounds are necessary and suficient if the number of faulty processors is at most logN-⌈log(logN-⌈log logN⌉+4)⌉+2. We also show that three testing rounds are necessary and sufficient for adaptive parallel diagnosis of a system modeled by cube-connected cycles of dimension greater than three.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Beigel, W. Hurwood, and N. Kahale. Fault diagnosis in a flash. Proc. of 36th FOCS, pages 571–580, 1995.Google Scholar
  2. 2.
    R. Beigel, S.R. Kosaraju, and G.F. Sullivan. Locating faults in a constant number of testing rounds. Proc. of 1st SPAA, pages 189–198, 1989.Google Scholar
  3. 3.
    R. Beigel, G. Margulis, and D.A. Spielman. Fault diagnosis in a small constant number of parallel rounds. Proc. of 5th SPAA, pages 21–29, 1993.Google Scholar
  4. 4.
    R.P. Bianchini, Jr., and R. Buskens. An adaptive distributed system level-diagnosis algorithm and its implementation. Proc. of 21st Int. Symp. on Fault Tolerant Computing, pages 222–229, 1991.Google Scholar
  5. 5.
    R.P. Bianchini, Jr., K. Goodwin, and D.S. Nydick. Practical application and implementation of distributed system-level diagnosis thoery. Proc. of 20st Int. Symp. on Fault Tolerant Computing, pages 332–339, 1984.Google Scholar
  6. 6.
    A. Bjöklund. Optimal adaptive fault diagnosis of hypercubes. Proc. of SWAT, LNCS 1851, pages 527–534, 2000.Google Scholar
  7. 7.
    P.M. Blecher. On a logical problem. Discrete Mathematics, 43:107–110, 1983.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    C. Feng, L.N. Bhuyan, and F. Lombardi. Adaptive system-level diagnosis for hypercube multiprocessors. IEEE Trans. Computers, 45:1157–1170, 1996.CrossRefzbMATHGoogle Scholar
  9. 9.
    S.L. Hakimi and A.T. Amin. Characterization of connection assignment of diagnossable systems. IEEE Trans. Computers, 23:86–88, 1974.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    S.L. Hakimi and K. Nakajima. On adaptive system daignosis. IEEE Trans. Computers, 33:234–240, 1984.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    S.L. Hakimi, M. Otsuka, E.F. Schmeichel, and G.F. Sullivan. A parallel fault identification algorithm. Journal of Algorithm, 11:231–241, 1990.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    S.L. Hakimi and E.F. Schmeichel. An adaptive algorithm for system level daignosis. Journal of Algorithms, 5:524–530, 1984.Google Scholar
  13. 13.
    E. Kranakis and A. Pelc. Better adaptive daignosis of hypercubes. IEEE Trans. Computers, 49:1013–1020, 2000.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    E. Kranakis, A. Pelc, and A. Spatharis. Optimal adaptive fault diagnosis for simple multiprocessor systems. Networks, 34:206–214, 1999.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    K. Nakajima. A new approach to system daignosis. Proc. 19th allerton Conf. Commun. Contr. and Computing, pages 697–706, 1981.Google Scholar
  16. 16.
    F.P. Preparata, G. Metze, and R.T. Chien. On the connection assignment problem of daiganosable systems. IEEE Trans. Electronic Computers, 16:848–854, 1967.CrossRefzbMATHGoogle Scholar
  17. 17.
    Pei Yuan Wu. Partial solution to problem 81-6. Journal of Algorithms, 12:379–380, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Kumiko Nomura
    • 1
  • Toshinori Yamada
    • 1
  • Shuichi Ueno
    • 1
  1. 1.Dept. of Communications and Integrated SystemsGraduate School of Science and Engineering Tokyo Institute of TechnologyTokyoJapan

Personalised recommendations