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Approximation algorithms for scheduling monotonic moldable tasks on multiple platforms

Author

Listed:
  • Fangfang Wu

    (Fudan University)

  • Zhongyi Jiang

    (Changzhou University)

  • Run Zhang

    (Fudan University)

  • Xiandong Zhang

    (Fudan University)

Abstract

We consider scheduling monotonic moldable tasks on multiple platforms, where each platform contains a set of processors. A moldable task can be split into several pieces of equal size and processed simultaneously on multiple processors. Tasks are not allowed to be processed spanning over platforms. This scheduling model has many applications, ranging from parallel computing to the berth and quay crane allocation and the workforce assignment problem. We develop several approximation algorithms aiming at minimizing the makespan. More precisely, we provide a 2-approximation algorithm for identical platforms, a Fully Polynomial Time Approximation Scheme (FPATS) under the assumption of large processor counts and a 2-approximation algorithm for a fixed number of heterogeneous platforms. Most of the proposed algorithms combine a dual approximation scheme with a novel approach to improve the dual approximation algorithm. All results can be extended to the contiguous case, i.e., a task can only be executed by contiguously numbered processors.

Suggested Citation

  • Fangfang Wu & Zhongyi Jiang & Run Zhang & Xiandong Zhang, 2023. "Approximation algorithms for scheduling monotonic moldable tasks on multiple platforms," Journal of Scheduling, Springer, vol. 26(4), pages 383-398, August.
    • Handle: RePEc:spr:jsched:v:26:y:2023:i:4:d:10.1007_s10951-022-00774-2
    DOI: 10.1007/s10951-022-00774-2
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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.
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