Skip to main content

Optimal and Online Preemptive Scheduling on Uniformly Related Machines

  • Conference paper
STACS 2004 (STACS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2996))

Included in the following conference series:

Abstract

We consider the problem of preemptive scheduling on uniformly related machines. We present a semi-online algorithm which, if the optimal makespan is given in advance, produces an optimal schedule. Using the standard doubling technique, this yields a 4 competitive deterministic and e≈ 2.71 competitive randomized online algorithms. In addition, it matches the performance of the previously known algorithms for the offline case, with a considerably simpler proof. Finally, we study the performance of greedy heuristics for the same problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aspnes, J., Azar, Y., Fiat, A., Plotkin, S., Waarts, O.: On-line load balancing with applications to machine scheduling and virtual circuit routing. Journal of the ACM 44, 486–504 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bar-Noy, A., Freund, A., Naor, J.: New algorithms for related machines with temporary jobs. Journal of Scheduling 3, 259–272 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Berman, P., Charikar, M., Karpinski, M.: On-line load balancing for related machines. Journal of Algorithms 35, 108–121 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen, B., van Vliet, A., Woeginger, G.J.: An optimal algorithm for preemptive on-line scheduling. Operations Research Letters 18, 127–131 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cho, Y., Sahni, S.: Bounds for list schedules on uniform processors. SIAM Journal on Computing 9, 91–103 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dobson, G.: Scheduling independent tasks on uniform processors. SIAM Journal on Computing 13, 705–716 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  7. Epstein, L.: Optimal preemptive scheduling on uniform processors with nondecreasing speed ratios. Operations Research Letters 29, 93–98 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Epstein, L.: Bin stretching revisited. Acta Informatica 39, 97–117 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Epstein, L., Favrholdt, L.M.: Optimal preemptive semi-online scheduling to minimize makespan on two related machines. Operations Research Letters 30, 269–275 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Epstein, L., Noga, J., Seiden, S.S., Sgall, J., Woeginger, G.J.: Randomized on-line scheduling for two related machines. Journal of Scheduling 4, 71–92 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Epstein, L., Sgall, J.: A lower bound for on-line scheduling on uniformly related machines. Operations Research Letters 26(1), 17–22 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Friesen, D.K.: Tighter bounds for LPT scheduling on uniform processors. SIAM Journal on Computing 16, 554–560 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gonzales, T.F., Sahni, S.: Preemptive scheduling of uniform processor systems. Journal of the ACM 25, 92–101 (1978)

    Article  Google Scholar 

  14. Horwath, E., Lam, E.C., Sethi, R.: A level algorithm for preemptive scheduling. Journal of the ACM 24, 32–43 (1977)

    Article  Google Scholar 

  15. Shachnai, H., Tamir, T., Woeginger, G.J.: Minimizing Makespan and Preemption Costs on a System of Uniform Machines. In: Craw, S., Preece, A.D. (eds.) ECCBR 2002. LNCS (LNAI), vol. 2416, pp. 859–871. Springer, Heidelberg (2002)

    Google Scholar 

  16. Shmoys, D.B., Wein, J., Williamson, D.P.: Scheduling parallel machines on-line. SIAM Journal on Computing 24, 1313–1331 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  17. Wen, J., Du, D.: Preemptive on-line scheduling for two uniform processors. Operations Research Letters 23, 113–116 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  18. Woeginger, G.J.: A comment on scheduling on uniform machines under chain-type precedence constraints. Operations Research Letters 26, 107–109 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ebenlendr, T., Sgall, J. (2004). Optimal and Online Preemptive Scheduling on Uniformly Related Machines. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24749-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21236-2

  • Online ISBN: 978-3-540-24749-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics