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An improved approximation algorithm for scheduling monotonic moldable tasks

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  • Wu, Fangfang
  • Zhang, Xiandong
  • Chen, Bo

Abstract

We are concerned with the problem of scheduling monotonic moldable tasks on identical processors to minimize the makespan. We focus on the natural case where the number m of processors as resources is fixed or relatively small compared with the number n of tasks. We present an efficient (3/2)-approximation algorithm with time complexity O(nmlog(nm)) (for m>n) and O(n2logn) (for m≤n). To the best of our knowledge, the best relevant known results are: (a) a (3/2+ϵ)-approximation algorithm with time complexity O(nmlog(n/ϵ)), (b) a fully polynomial-time approximation scheme for the case of m≥16n/ϵ, and (c) a polynomial-time approximation scheme with time complexity O(ng(1/ϵ)) when m is bounded by a polynomial in n, where g(·) is a super-exponential function. On the other hand, the novel general technique developed in this paper for removing the ϵ-term in the worst-case performance ratio can be applied to improving the performance guarantee of certain dual algorithms for other combinatorial optimization problems.

Suggested Citation

  • Wu, Fangfang & Zhang, Xiandong & Chen, Bo, 2023. "An improved approximation algorithm for scheduling monotonic moldable tasks," European Journal of Operational Research, Elsevier, vol. 306(2), pages 567-578.
    • Handle: RePEc:eee:ejores:v:306:y:2023:i:2:p:567-578
    DOI: 10.1016/j.ejor.2022.08.034
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    References listed on IDEAS

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    1. Dolgui, Alexandre & Kovalev, Sergey & Kovalyov, Mikhail Y. & Malyutin, Sergey & Soukhal, Ameur, 2018. "Optimal workforce assignment to operations of a paced assembly line," European Journal of Operational Research, Elsevier, vol. 264(1), pages 200-211.
    2. J Blazewicz & T C E Cheng & M Machowiak & C Oguz, 2011. "Berth and quay crane allocation: a moldable task scheduling model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1189-1197, July.
    3. Delorme, Xavier & Dolgui, Alexandre & Kovalev, Sergey & Kovalyov, Mikhail Y., 2019. "Minimizing the number of workers in a paced mixed-model assembly line," European Journal of Operational Research, Elsevier, vol. 272(1), pages 188-194.
    4. Claire Kenyon & Eric Rémila, 2000. "A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem," Mathematics of Operations Research, INFORMS, vol. 25(4), pages 645-656, November.
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    Cited by:

    1. Wu, Xiaohu & Loiseau, Patrick, 2023. "Efficient approximation algorithms for scheduling moldable tasks," European Journal of Operational Research, Elsevier, vol. 310(1), pages 71-83.

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