Online Scheduling Revisited

  • Rudolf Fleischer
  • Michaela Wahl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1879)

Abstract

We present a new online algorithm, MR, for non-preemptive scheduling of jobs with known processing times on m identical machines which beats the best previous algorithm for m ≥ 64. For m → ∞ its competitive ratio approaches 1 + \( \sqrt {\frac{{1 + 1n{\mathbf{ }}2}} {2}} \) > 1.9201.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Albers. Better bounds for online scheduling. In Proceedings of the 29th ACM Symposium on the Theory of Computation (STOC’97), pages 130–139, 1997. To appear in SIAM Journal on Computing.Google Scholar
  2. 2.
    Y. Bartal, A. Fiat, H. Karloff, and R. Vohra. New algorithms for an ancient scheduling problem. Journal of Computer and System Sciences, 51:359–366, 1995. A preliminary version was published in Proceedings of the 24th ACM Symposium on the Theory of Computation (STOC’92), pages 51–58, 1992.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Y. Bartal, H. Karloff, and Y. Rabani. A better lower bound for on-line scheduling. Information Processing Letters, 50:113–116, 1994.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, Cambridge, England, 1998.MATHGoogle Scholar
  5. 5.
    R. Chandrasekaran, B. Chen, G. Galambos, P. R. Narayanan, A vanVliet, and G. J. Woeginger. A note on’ An on-line scheduling heuristic with better worst case ratio than Graham’s list scheduling’. SIAM Journal on Computing, 26(3):870–872, 1997.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    B. Chen, A vanVliet, and G. J. Woeginger. A lower bound for randomized on-line scheduling algorithms. Information Processing Letters, 51:219–222, 1994.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    B. Chen, A vanVliet, and G. J. Woeginger. New lower and upper bounds for on-line scheduling. Operations Research Letters, 16:221–230, 1994.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    B. Chen, A vanVliet, and G. J. Woeginger. An optimal algorithm for preemptive on-line scheduling. Operations Research Letters, 18:300–306, 1994. A preliminary version was published in Proceedings of the 2nd European Symposium on Algorithms (ESA’94). Springer Lecture Notes in Computer Science 855, pages 300–306, 1994.Google Scholar
  9. 9.
    U. Faigle, W. Kern, and G. Turán. On the performance of on-line algorithms for partition problems. Acta Cybernetica, 9:107–119, 1989/90.MATHMathSciNetGoogle Scholar
  10. 10.
    A. Fiat and G. Woeginger, editors. Online Algorithms —The State of the Art. Springer Lecture Notes in Computer Science 1442. Springer-Verlag, Heidelberg, 1998.Google Scholar
  11. 11.
    G. Galambos and G. J. Woeginger. An on-line scheduling heuristic with better worst case ratio than Graham’s list scheduling. SIAM Journal on Computing, 22(2):349–355, 1993.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    M. R. Garey and D. S. Johnson. Computers and Intractability —A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York, 1979.MATHGoogle Scholar
  13. 13.
    T. Gormley, N. Reingold, E. Torng, and J. Westbrook. Generating adversaries for request-answer games. In Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms (SODA’ 00), pages 564–565, 2000.Google Scholar
  14. 14.
    R. L. Graham. Bounds for certain multiprocessing anomalies. Bell System Technical Journal, 45:1563–1581, 1966.Google Scholar
  15. 15.
    D. S. Hochbaum, editor. Approximation Algorithms for NP-Hard Problems. PWS Publishing Company, Boston, MA, 1996.Google Scholar
  16. 16.
    D. R. Karger, S. J. Phillips, and E. Torng. A better algorithm for an ancient scheduling problem. Journal of Algorithms, 20(2):400–430, 1996. A preliminary version was published in Proceedings of the 5th ACM-SIAM Symposium on Discrete Algorithms (SODA’94), pages 132–140, 1994.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    S. Seiden. Randomized algorithms for that ancient scheduling problem. In Proceedings of the 5th Workshop on Algorithms and Data Structures (WADS’97). Springer Lecture Notes in Computer Science 1272, pages 210–223, 1997.Google Scholar
  18. 18.
    J. Sgall. A lower bound for randomized on-line multiprocessor scheduling. Information Processing Letters, 63:51–55, 1997.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Rudolf Fleischer
    • 1
  • Michaela Wahl
    • 2
  1. 1.Department of Computer ScienceUniversity of WaterlooUK
  2. 2.Max-Planck-Institut für InformatikSaarbrücken

Personalised recommendations