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Abstract

For most scheduling problems the set of machines is fixed initially and remains unchanged for the duration of the problem. We consider two basic online scheduling problems with the modification that initially the algorithm possesses no machines, but that at any point additional machines may be purchased. Upper and lower bounds on the competitive ratio are shown for both problems.

Keywords

Schedule Problem Time Model Competitive Ratio Online Algorithm Optimal Cost 
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.
    Albers, S.: Better bounds for online scheduling. In: Proc. 29th Symp. Theory of Computing, pp. 130–139 (1997)Google Scholar
  2. 2.
    Chekuri, C., Motwani, R., Natarajan, B., Stein, C.: Approximation techniques for average completion time scheduling. In: Proc. 8th Symp. On Discrete Algorithms, pp. 609–618 (1997)Google Scholar
  3. 3.
    Chen, B., van Vliet, A., Woeginger, G.J.: New lower and upper bounds for on-line scheduling. Operations Research Letters 16, 221–230 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Chen, B., Vestjens, A.P.A.: Scheduling on identical machines: How good is LPT in an on-line setting? Operations Research Letters 21, 165–169 (1998)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Galambos, G., Woeginger, G.J.: An on-line scheduling heuristic with better worst case ratio than Graham’s list scheduling. SIAM Journal on Computing 22, 349–355 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell System Technical Journal 45, 1563–1581 (1966)Google Scholar
  7. 7.
    Noga, J., Seiden, S.: Scheduling two machines with release times. To appear at Integer Programming and Combinatorial Optimization (1999)Google Scholar
  8. 8.
    Shmoys, D.B., Wein, J., Williamson, D.P.: Scheduling parallel machines on-line. SIAM Journal on Computing 24, 1313–1331 (1995)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Csanád Imreh
    • 1
    • 2
  • John Noga
    • 3
  1. 1.Department of InformaticsJózsef Attila UniversitySzegedHungary
  2. 2.Stochastic Research Group, Hungarian Academy of SciencesTechnical UniversityBudapestHungary
  3. 3.Mathematics DepartmentTechnical University GrazGrazAustria

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