IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v129y2004i1p65-8010.1023-banor.0000030682.25673.c0.html
   My bibliography  Save this article

Scheduling Malleable Tasks on Parallel Processors to Minimize the Makespan

Author

Listed:
  • Jacek Błażewicz
  • Maciej Machowiak
  • Jan Węglarz
  • Mikhail Kovalyov
  • Denis Trystram

Abstract

The problem of optimal scheduling n tasks in a parallel processor system is studied. The tasks are malleable, i.e., a task may be executed by several processors simultaneously and the processing speed of a task is a nonlinear function of the number of processors allocated to it. The total number of processors is m and it is an upper bound on the number of processors that can be used by all the tasks simultaneously. It is assumed that the number of processors is sufficient to process all the tasks simultaneously, i.e. n≤m. The objective is to find a task schedule and a processor allocation such that the overall task completion time, i.e. the makespan, is minimized. The problem is motivated by real-life applications of parallel computer systems in scientific computing of highly parallelizable tasks. An O(n) algorithm is presented to solve this problem when all the processing speed functions are convex. If these functions are all concave and the number of tasks is a constant, the problem can be solved in polynomial time. A relaxed problem, in which the number of processors allocated to each task is not required to be integer, can be solved in O(nmax {m,nlog 2 m}) time. It is proved that the minimum makespan values for the original and relaxed problems coincide. For n=2 or n=3, an optimal solution for the relaxed problem can be converted into an optimal solution for the original problem in a constant time. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Jacek Błażewicz & Maciej Machowiak & Jan Węglarz & Mikhail Kovalyov & Denis Trystram, 2004. "Scheduling Malleable Tasks on Parallel Processors to Minimize the Makespan," Annals of Operations Research, Springer, vol. 129(1), pages 65-80, July.
    • Handle: RePEc:spr:annopr:v:129:y:2004:i:1:p:65-80:10.1023/b:anor.0000030682.25673.c0
    DOI: 10.1023/B:ANOR.0000030682.25673.c0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/B:ANOR.0000030682.25673.c0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/B:ANOR.0000030682.25673.c0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Artigues, Christian & Lopez, Pierre & Haït, Alain, 2013. "The energy scheduling problem: Industrial case-study and constraint propagation techniques," International Journal of Production Economics, Elsevier, vol. 143(1), pages 13-23.
    2. Ana Rita Antunes & Marina A. Matos & Ana Maria A. C. Rocha & Lino A. Costa & Leonilde R. Varela, 2022. "A Statistical Comparison of Metaheuristics for Unrelated Parallel Machine Scheduling Problems with Setup Times," Mathematics, MDPI, vol. 10(14), pages 1-19, July.
    3. Wu, Xiaohu & Loiseau, Patrick, 2023. "Efficient approximation algorithms for scheduling moldable tasks," European Journal of Operational Research, Elsevier, vol. 310(1), pages 71-83.
    4. Margaux Nattaf & Christian Artigues & Pierre Lopez & David Rivreau, 2016. "Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 459-492, March.
    5. Roland Braune, 2022. "Packing-based branch-and-bound for discrete malleable task scheduling," Journal of Scheduling, Springer, vol. 25(6), pages 675-704, December.
    6. 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.
    7. Gorczyca, Mateusz & Janiak, Adam, 2010. "Resource level minimization in the discrete-continuous scheduling," European Journal of Operational Research, Elsevier, vol. 203(1), pages 32-41, May.
    8. Simon Emde & Hamid Abedinnia & Anne Lange & Christoph H. Glock, 2020. "Scheduling personnel for the build-up of unit load devices at an air cargo terminal with limited space," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 397-426, June.
    9. 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.
    10. Emde, Simon & Gendreau, Michel, 2017. "Scheduling in-house transport vehicles to feed parts to automotive assembly lines," European Journal of Operational Research, Elsevier, vol. 260(1), pages 255-267.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:129:y:2004:i:1:p:65-80:10.1023/b:anor.0000030682.25673.c0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.