Advertisement

Optimal Preemptive Scheduling on Uniform Processors with Non-decreasing Speed Ratios

  • Leah Epstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)

Abstract

We study preemptive scheduling on uniformly related pro- cessors, where jobs are arriving one by one in an on-line fashion. We consider the class of machine sets where the speed ratios are non- decreasing as speed increases. For each set of machines in this class, we design an algorithm of optimal competitive ratio. This generalizes the known result for identical machines, and solves other interesting cases.

Keywords

Algorithms scheduling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Y. Bartal, A. Fiat, H. Karloff, and R. Vohra. New algorithms for an ancient scheduling problem. J. Comput. Syst. Sci., 51(3):359–366, 1995.CrossRefMathSciNetGoogle Scholar
  2. 2.
    B. Chen, A. van Vliet, and G. J. Woeginger. Lower bounds for randomzed online scheduling. Information Processing Letters, 51:219–222, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    B. Chen, A. van Vliet, and G. J. Woeginger. An optimal algorithm for preemptive on-line scheduling. Operations Research Letters, 18:127–131, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    L. Epstein, J. Noga, S.S. Seiden, J. Sgall, and G.J. Woeginger. Randomized online scheduling on two uniform machines. In Annual ACM-SIAM Symposium on Discrete Algorithms, pages 317–326, 1999. To appear in Journal of Scheduling.Google Scholar
  5. 5.
    L. Epstein and J. Sgall. A lower bound for on-line scheduling on uniformly related machines. Oper. Res. Lett., 26(1):17–22, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    T. F. Gonzales and S. Sahni. Preemptive scheduling of uniform processor systems. J. Assoc. Comput. Mach., 25:92–101, 1978.MathSciNetGoogle Scholar
  7. 7.
    E. Horwath, E. C. Lam, and R. Sethi. A level algorithm for preemptive scheduling. J. Assoc. Comput. Mach., 24:32–43, 1977.MathSciNetGoogle Scholar
  8. 8.
    J. Sgall. A lower bound for randomized on-line multiprocessor scheduling. Inf. Process. Lett., 63(1):51–55, 1997.CrossRefMathSciNetGoogle Scholar
  9. 9.
    J. Sgall. On-line scheduling. In A. Fiat and G. J. Woeginger, editors, Online Algorithms: The State of the Art, volume 1442 of LNCS, pages 196–231. Springer-Verlag, 1998.CrossRefGoogle Scholar
  10. 10.
    A. P. A. Vestjens. Scheduling uniform machines on-line requires nondecreasing speed ratios. Technical Report Memorandum COSOR 94-35, Eindhoven University of Technology, 1994. To appear in Math. Programming.Google Scholar
  11. 11.
    J. Wen and D. Du. Preemptive on-line scheduling for two uniform processors. Oper. Res. Lett., 23:113–116, 1998.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Leah Epstein
    • 1
  1. 1.School of Computer and Media SciencesThe Interdisciplinary CenterHerzliyaIsrael

Personalised recommendations