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Abstract

We investigate an online version of a basic scheduling problem where a set of jobs has to be scheduled on a number of identical machines so as to minimize the makespan. The job processing times are known in advance and preemption of jobs is allowed. Machines are non-continuously available, i.e., they can break down and recover at arbitrary time instances not known in advance. New machines may be added as well. Thus machine availabilities change online.

We first show that no online algorithm can construct optimal schedules. We also show that no online algorithm can achieve a bounded competitive ratio if there may be time intervals where no machine is available. Then we present an online algorithm that constructs schedules with an optimal makespan of C\(^{OPT}_{\rm max}\) if a lookahead of one is given, i.e., the algorithm always knows the next point in time when the set of available machines changes. Finally we give an online algorithm without lookahead that constructs schedules with a nearly optimal makespan of C\(^{OPT}_{\rm max}\) + ε, for any ε >0, if at any time at least one machine is available. Our results demonstrate that not knowing machine availabilities in advance is of little harm.

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References

  1. 1.
    Kalyanasundaram, B., Pruhs, K.P.: Fault-tolerant scheduling. In: Proceedings of the 26th Annual ACM Symposium on the Theory of Computing, pp. 115–124 (1994)Google Scholar
  2. 2.
    Kalyanasundaram, B., Pruhs, K.P.: Fault-tolerant real-time scheduling. In: Burkard, R.E., Woeginger, G.J. (eds.) ESA 1997. LNCS, vol. 1284. Springer, Heidelberg (1997)Google Scholar
  3. 3.
    McNaughton, R.: Scheduling with deadlines and loss functions. Management Science 6, 1–12 (1959)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Sanlaville, E.: Nearly on line scheduling of preemptive independent tasks. Discrete Applied Mathematics 57, 229–241 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Sanlaville, E.: Private communication (1998)Google Scholar
  6. 6.
    Schmidt, G.: Scheduling on semi-identical processors. Z. Oper. Res. 28, 153–162 (1984)zbMATHCrossRefGoogle Scholar
  7. 7.
    Schmidt, G.: Scheduling independent tasks with deadlines on semi-identical processors. J. Oper. Res. Soc. 39, 271–277 (1988)zbMATHGoogle Scholar
  8. 8.
    Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28, 202–208 (1985)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Susanne Albers
    • 1
  • Günter Schmidt
    • 2
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Information and Technology ManagementUniversity of SaarlandSaarbrückenGermany

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