Acta Mathematica Sinica

, Volume 22, Issue 2, pp 587–594 | Cite as

Preemptive Semi–online Algorithms for Parallel Machine Scheduling with Known Total Size

ORIGINAL ARTICLES
First Online:
Received:
Accepted:

Abstract

This paper investigates preemptive semi-online scheduling problems on m identical parallel machines, where the total size of all jobs is known in advance. The goal is to minimize the maximum machine completion time or maximize the minimum machine completion time. For the first objective, we present an optimal semi–online algorithm with competitive ratio 1. For the second objective, we show that the competitive ratio of any semi–online algorithm is at least \( \frac{{2m - 3}} {{m - 1}} \) for any m > 2 and present optimal semi–online algorithms for m = 2, 3.

Keywords

Semi–online Preemptive scheduling Competitive analysis 

MR (2000) Subject Classification

90B35 90C27 68Q25 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Liu, W. P., Sidney, J. B., van Vliet, A.: Ordinal algorithm for parallel machines scheduling. Operations Research Letters, 21, 235–242 (1997)MathSciNetGoogle Scholar
  2. 2.
    He, Y., Yang, Q. F., Tan, Z. Y.: Semi on-line seheduling on parallel machines (I). Applied Mathematics-A Journal of Chinese University, 18A, 105–114 (2003) (in Chinese)Google Scholar
  3. 3.
    He, Y., Yang, Q. F., Tan, Z. Y.: Semi on-line seheduling on parallel machines (II). Applied Mathematics-A Journal of Chinese University, 18A, 213–222 (2003) (in Chinese)Google Scholar
  4. 4.
    He, Y., Jiang, Y. W.: Optimal algorithms for semi-online preemptive scheduling on two uniform machines. Acta Informatica, 40, 367–383 (2004)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Kellerer, H., Kotov, V., Speranza, M. G., Tuza, Z.: Semi on-line algorithms for the partition problem. Operations Research Letters, 21, 235–242 (1997)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    He, Y.: Semi on-line scheduling problem for maximizing the minimum machine completion time. Acta Mathematica Applicate Sinica, 17, 107–113 (2001)MATHGoogle Scholar
  7. 7.
    Tan, Z. Y., He, Y.: On-line and semi on-line scheduling on parallel machines with non-simultaneous machine available times. Journal of Systems Science and Mathematical Science, 22(4), 414–421 (2002) (in Chinese)MATHGoogle Scholar
  8. 8.
    Tan, Z. Y., He, Y.: Semi on-line scheduling on two uniform machines. System Engineering–Theory & Practice, 21(2), 53–57 (2001) (in Chinese)Google Scholar
  9. 9.
    He, Y., Yang, Q. F., Tan, Z. Y., Yao, E. Y.: Algorithms for semi on-line multiprocessor scheduling problem. Journal of Zhejiang University SCIENCE, 3, 60–64 (2002)Google Scholar
  10. 10.
    Jiang, Y. W., Tan, Z. Y., He, Y.: Preemptive machine covering on parallel machines. Journal of Combinatorial Optimization, 10, 345–363 (2005)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    He, Y., Jiang, Y. W.: Optimal semi-online preemptive algorithms for machine covering on two uniform machines. Theoretical Computer Science, 339, 293–314 (2005)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    McNaughton, R.: Scheduling with deadings and loss functions. Management Sciences, 6, 1–12 (1959)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhou 310027P. R. China
  2. 2.State Key Lab of CAD & CGZhejiang UniversityHangzhou 310027P. R. China

Personalised recommendations