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Semi-online scheduling with non-increasing job sizes and a buffer

Author

Listed:
  • Leah Epstein

    (University of Haifa)

  • Hanan Zebedat-Haider

    (The college of Sakhnin)

Abstract

This work considers a semi-online version of scheduling on m identical machines, where the objective is to minimize the makespan. In the variant studied here, jobs are presented sorted by non-increasing sizes, and a buffer of size k is available for storing at most k jobs. Every arriving job has to be either placed into the buffer until its assignment, or else it has to be assigned immediately to a machine. We prove a lower bound greater than 1 on the competitive ratio of the problem for any m and any buffer size. To complement this negative result, we design a simple algorithm for any m whose competitive ratio tends to 1 as the buffer size grows. Using those results, we show the best possible competitive ratio is $$1+\Theta (\frac{m}{k})$$ 1 + Θ ( m k ) . We provide additional bounds for small values of m. In particular, we show that for $$m=2$$ m = 2 the case $$k=1$$ k = 1 is not different from the case without a buffer, while $$k=2$$ k = 2 admits an improved competitive ratio.

Suggested Citation

  • Leah Epstein & Hanan Zebedat-Haider, 2025. "Semi-online scheduling with non-increasing job sizes and a buffer," Journal of Combinatorial Optimization, Springer, vol. 49(4), pages 1-23, May.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:4:d:10.1007_s10878-025-01293-4
    DOI: 10.1007/s10878-025-01293-4
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    References listed on IDEAS

    as
    1. Leah Epstein, 2018. "A survey on makespan minimization in semi-online environments," Journal of Scheduling, Springer, vol. 21(3), pages 269-284, June.
    2. György Dósa & Leah Epstein, 2010. "Online scheduling with a buffer on related machines," Journal of Combinatorial Optimization, Springer, vol. 20(2), pages 161-179, August.
    Full references (including those not matched with items on IDEAS)

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