Advertisement

Optimal Preemptive Scheduling for General Target Functions

  • Leah Epstein
  • Tamir Tassa
Conference paper
  • 467 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3153)

Abstract

We study the problem of optimal preemptive scheduling with respect to a general target function. Given n jobs with associated weights and mn uniformly related machines, one aims at scheduling the jobs to the machines, allowing preemptions but forbidding parallelization, so that a given target function of the loads on each machine is minimized. This problem was studied in the past in the case of the makespan. Gonzalez and Sahni [7] and later Shachnai, Tamir and Woeginger [12] devised a polynomial algorithm that outputs an optimal schedule for which the number of preemptions is at most 2(m–1). We extend their ideas for general symmetric, convex and monotone target functions. This general approach enables us to distill the underlying principles on which the optimal makespan algorithm is based. More specifically, the general approach enables us to identify between the optimal scheduling problem and a corresponding problem of mathematical programming. This, in turn, allows us to devise a single algorithm that is suitable for a wide array of target functions, where the only difference between one target function and another is manifested through the corresponding mathematical programming problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alon, N., Azar, Y., Woeginger, G., Yadid, T.: Approximation schemes for scheduling on parallel machines. Journal of Scheduling 1(1), 55–66 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Coffman Jr., E.G., Lueker, G.S.: Approximation algorithms for extensible bin packing. In: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), pp. 586–588 (2001)Google Scholar
  3. 3.
    Dell’Olmo, P., Kellerer, H., Speranza, M.G., Tuza, Z.: A 13/12 approximation algorithm for bin packing with extendable bins. Information Processing Letters 65(5), 229–233 (1998)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Dell’Olmo, P., Speranza, M.G.: Approximation algorithms for partitioning small items in unequal bins to minimize the total size. Discrete Applied Mathematics 94, 181–191 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Ebenlendr, T., Sgall, J.: Optimal and online preemptive scheduling on uniformly related machines. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 199–210. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Epstein, L., Sgall, J.: Approximation schemes for scheduling on uniformly related and identical parallel machines. Algorithmica 39(1), 151–162 (2004)MathSciNetGoogle Scholar
  7. 7.
    Gonzalez, T., Sahni, S.: Preemptive scheduling of uniform processor systems. Journal of the ACM 25(1), 92–101 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Hochbaum, D.S., Shanthikumar, J.G.: Convex separable optimization is not much harder than linear optimization. Journal of the ACM 37(4), 843–862 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hochbaum, D.S., Shmoys, D.B.: A polynomial approximation scheme for scheduling on uniform processors: using the dual approximation approach. SIAM Journal on Computing 17(3), 539–551 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Horvath, E.C., Lam, S., Sethi, R.: A level algorithm for preemptive scheduling. Journal of the ACM 24(1), 32–43 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Liu, J.W.S., Yang, A.T.: Optimal scheduling of independent tasks on heterogeneous computing systems. In: Proceedings ACM National Conference, vol. 1, pp. 38–45. ACM, New York (1974)Google Scholar
  12. 12.
    Shachnai, H., Tamir, T., Woeginger, G.J.: Minimizing makespan and preemption costs on a system of uniform machines. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 859–871. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Leah Epstein
    • 1
  • Tamir Tassa
    • 2
  1. 1.School of Computer ScienceThe Interdisciplinary CenterHerzliyaIsrael
  2. 2.Department of Mathematics and Computer Science, The Open University, Ramat Aviv, Tel Aviv, and Department of Computer ScienceBen Gurion UniversityBeer ShevaIsrael

Personalised recommendations