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Parallel solutions for preemptive makespan scheduling on two identical machines

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  • Leah Epstein

    (University of Haifa)

Abstract

We consider online preemptive scheduling of jobs arriving one by one, to be assigned to two identical machines, with the goal of makespan minimization. We study the effect of selecting the best solution out of two independent solutions constructed in parallel in an online fashion. Two cases are analyzed, where one case is purely online, and in the other one jobs are presented sorted by non-increasing sizes. We show that using two solutions rather than one improves the performance significantly, but that an optimal solution cannot be obtained for any constant number of solutions constructed in parallel. Our algorithms have the best possible competitive ratios out of algorithms for each one of the classes.

Suggested Citation

  • Leah Epstein, 2023. "Parallel solutions for preemptive makespan scheduling on two identical machines," Journal of Scheduling, Springer, vol. 26(1), pages 61-76, February.
    • Handle: RePEc:spr:jsched:v:26:y:2023:i:1:d:10.1007_s10951-022-00764-4
    DOI: 10.1007/s10951-022-00764-4
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    References listed on IDEAS

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    1. Peter Sanders & Naveen Sivadasan & Martin Skutella, 2009. "Online Scheduling with Bounded Migration," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 481-498, May.
    2. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
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    Cited by:

    1. Leah Epstein, 2023. "Parallel solutions for ordinal scheduling with a small number of machines," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-24, August.
    2. Jiang, Yiwei & Wu, Mengjing & Chen, Xin & Dong, Jianming & Cheng, T.C.E. & Blazewicz, Jacek & Ji, Min, 2024. "Online early work scheduling on parallel machines," European Journal of Operational Research, Elsevier, vol. 315(3), pages 855-862.
    3. Epstein, Leah, 2024. "Tighter bounds for the harmonic bin packing algorithm," European Journal of Operational Research, Elsevier, vol. 316(1), pages 72-84.

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