Max-Throughput for (Conservative) k-of-n Testing

  • Lisa Hellerstein
  • Özgür Özkan
  • Linda Sellie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

We define a variant of k-of-n testing that we call conservative k-of-n testing. We present a polynomial-time, combinatorial algorithm for maximizing the throughput of conservative k-of-n testing, in a parallel setting. This extends previous work of Kodialam and Condon et al. on the parallel pipelined filter ordering problem, which is the special case where k = 1 (or k = n) [1,2,3]. We also consider the problem of maximizing throughput for standard k-of-n testing, and describe a polynomial-time algorithm for it based on the ellipsoid method.

Keywords

Testing Strategy Precedence Constraint Rate Limit Combinatorial Algorithm Conservative Variant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kodialam, M.S.: The Throughput of Sequential Testing. In: Aardal, K., Gerards, B. (eds.) IPCO 2001. LNCS, vol. 2081, pp. 280–292. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Condon, A., Deshpande, A., Hellerstein, L., Wu, N.: Flow algorithms for two pipelined filter ordering problems. In: PODS, ACM, pp. 193–202 (2006)Google Scholar
  3. 3.
    Condon, A., Deshpande, A., Hellerstein, L., Wu, N.: Algorithms for distributional and adversarial pipelined filter ordering problems. ACM Transactions on Algorithms 5 (2009)Google Scholar
  4. 4.
    Liu, Z., Parthasarathy, S., Ranganathan, A., Yang, H.: A generic flow algorithm for shared filter ordering problems. In: Lenzerini, M., Lembo, D. (eds.) PODS, ACM, pp. 79–88 (2008)Google Scholar
  5. 5.
    Deshpande, A., Hellerstein, L.: Parallel pipelined filter ordering with precedence constraints. Pre-publication version (To appear in ACM Transactions on Algorithms), http://cis.poly.edu/string~hstein/pubs/filterwithconstraint.pdf
  6. 6.
    Salloum, S.: Optimal testing algorithms for symmetric coherent systems. PhD thesis, Univ. of Southern California (1979)Google Scholar
  7. 7.
    Salloum, S., Breuer, M.A.: An optimum testing algorithm for some symmetric coherent systems. J. Mathematical Analysis and Applications 101, 170–194 (1984)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Ben-Dov, Y.: Optimal testing procedure for special structures of coherent systems. Management Science 27, 1410–1420 (1981)CrossRefMATHGoogle Scholar
  9. 9.
    Chang, M.F., Shi, W., Fuchs, W.K.: Optimal diagnosis procedures for k-out-of-n structures. IEEE Trans. Computers 39, 559–564 (1990)CrossRefGoogle Scholar
  10. 10.
    Hellerstein, L., Özkan, Ö., Sellie, L.: Max-throughput for (conservative) k-of-n testing. CoRR abs/1109.3401 (2011)Google Scholar
  11. 11.
    Salloum, S., Breuer, M.: Fast optimal diagnosis procedures for k-out-of-n:g systems. IEEE Transactions on Reliability 46, 283–290 (1997)CrossRefGoogle Scholar
  12. 12.
    Ünlüyurt, T.: Sequential testing of complex systems: a review. Discrete Applied Mathematics 142, 189–205 (2004); Boolean and Pseudo-Boolean FunctionsMathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Garey, M.R.: Optimal task sequencing with precedence constraints. Discrete Math. 4, 37–56 (1973)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Boros, E., Ünlüyurt, T.: Diagnosing double regular systems. Ann. Math. Artif. Intell. 26, 171–191 (1999)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Lisa Hellerstein
    • 1
  • Özgür Özkan
    • 1
  • Linda Sellie
    • 1
  1. 1.Department of Computer Science and EngineeringPolytechnic Institute of NYUBrooklynUSA

Personalised recommendations