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Approximation Schemes for the Min-Max Starting Time Problem

  • Leah Epstein
  • Tamir Tassa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)

Abstract

We consider the off-line scheduling problem of minimizing the maximal starting time. The input to this problem is a sequence of n jobs and m identical machines. The goal is to assign the jobs to the machines so that the first time in which all jobs have already started their processing is minimized, under the restriction that the processing of the jobs on any given machine must respect their original order. Our main result is a polynomial time approximation scheme for this problem in the case where m is considered as part of the input. As the input to this problem is a sequence of jobs, rather than a set of jobs where the order is insignificant, we present techniques that are designed to handle ordering constraints. Those techniques are combined with common techniques of assignment problems in order to yield a polynomial time approximation scheme.

Keywords

Schedule Problem Approximation Scheme Parallel Machine Competitive Ratio List Schedule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alon, N., et al.: Approximation schemes for scheduling on parallel machines. Journal of Scheduling 1(1), 55–66 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Epstein, L., van Stee, R.: Minimizing the maximum starting time on-line. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 449–460. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Graham, R.L.: Bounds for certain multiprocessor anomalies. Bell System Technical Journal 45, 1563–1581 (1966)Google Scholar
  4. 4.
    Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math 17, 416–429 (1969)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hochbaum, D., Shmoys, D.: 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
  6. 6.
    Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: theoretical and practical results. Journal of the Association for Computing Machinery 34(1), 144–162 (1987)MathSciNetGoogle Scholar
  7. 7.
    Horowitz, E., Sahni, S.: Exact and approximate algorithms for scheduling nonidentical processors. Journal of the Association for Computing Machinery 23, 317–327 (1976)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Jansen, K., Porkolab, L.: Improved approximation schemes for scheduling unrelated parallel machines. In: Andersson, S.I. (ed.) Summer University of Southern Stockholm 1993. LNCS, vol. 888, pp. 408–417. Springer, Heidelberg (1999)Google Scholar
  9. 9.
    Lenstra, J.K., Rinnooy Kan, A.H.G.: Complexity os scheduling under precedence constraints. Operations Research 26, 22–35 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Mehta, S.R., Chandrasekaran, R., Emmons, H.: Order-presrving allocation of jobs to two machines. Naval Research Logistics Quarterly 21, 846–847 (1975)Google Scholar
  11. 11.
    Naor, J., Bar-Noy, A., Freund, A.: On-line load balancing in a hierarchical server topology. In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 77–88. Springer, Heidelberg (1999)Google Scholar
  12. 12.
    Sahni, S.: Algorithms for scheduling independent tasks. Journal of the Association for Computing Machinery 23, 116–127 (1976)zbMATHMathSciNetGoogle Scholar
  13. 13.
    Schuurman, P., Woeginger, G.: Polynomial time approximation algorithms for machine scheduling: Ten open problems. Journal of Scheduling 2, 203–213 (1999)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Leah Epstein
    • 1
  • Tamir Tassa
    • 2
  1. 1.School of Computer ScienceThe Interdisciplinary CenterHerzliyaIsrael
  2. 2.Department of Applied MathematicsTel-Aviv UniversityRamat Aviv, Tel AvivIsrael

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