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Scheduling shared continuous resources on many-cores

Author

Listed:
  • Ernst Althaus

    (Johannes Gutenberg-Universität Mainz)

  • André Brinkmann

    (Johannes Gutenberg-Universität Mainz)

  • Peter Kling

    (Simon Fraser University)

  • Friedhelm Meyer Heide

    (Paderborn University)

  • Lars Nagel

    (Johannes Gutenberg-Universität Mainz)

  • Sören Riechers

    (Paderborn University)

  • Jiří Sgall

    (Charles University)

  • Tim Süß

    (Johannes Gutenberg-Universität Mainz)

Abstract

We consider the problem of scheduling a number of jobs on m identical processors sharing a continuously divisible resource. Each job j comes with a resource requirement . The job can be processed at full speed if granted its full resource requirement. If receiving only an x-portion of $$r_j$$ r j , it is processed at an x-fraction of the full speed. Our goal is to find a resource assignment that minimizes the makespan (i.e., the latest completion time). Variants of such problems, relating the resource assignment of jobs to their processing speeds, have been studied under the term discrete–continuous scheduling. Known results are either very pessimistic or heuristic in nature. In this article, we suggest and analyze a slightly simplified model. It focuses on the assignment of shared continuous resources to the processors. The job assignment to processors and the ordering of the jobs have already been fixed. It is shown that, even for unit size jobs, finding an optimal solution is NP-hard if the number of processors is part of the input. Positive results for unit size jobs include a polynomial-time algorithm for any constant number of processors. Since the running time is infeasible for practical purposes, we also provide more efficient algorithm variants: an optimal algorithm for two processors and a -approximation algorithm for m processors.

Suggested Citation

  • Ernst Althaus & André Brinkmann & Peter Kling & Friedhelm Meyer Heide & Lars Nagel & Sören Riechers & Jiří Sgall & Tim Süß, 2018. "Scheduling shared continuous resources on many-cores," Journal of Scheduling, Springer, vol. 21(1), pages 77-92, February.
    • Handle: RePEc:spr:jsched:v:21:y:2018:i:1:d:10.1007_s10951-017-0518-0
    DOI: 10.1007/s10951-017-0518-0
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    References listed on IDEAS

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    1. Weglarz, Jan & Józefowska, Joanna & Mika, Marek & Waligóra, Grzegorz, 2011. "Project scheduling with finite or infinite number of activity processing modes - A survey," European Journal of Operational Research, Elsevier, vol. 208(3), pages 177-205, February.
    2. Jozefowska, Joanna & Weglarz, Jan, 1996. "Discrete-continuous scheduling problems -- Mean completion time results," European Journal of Operational Research, Elsevier, vol. 94(2), pages 302-309, October.
    3. Joanna Józefowska & Marek Mika & Rafał Różycki & Grzegorz Waligóra & Jan Weglarz, 2000. "Solving the discrete-continuous project scheduling problem via its discretization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(3), pages 489-499, December.
    4. Jacek Błażewicz & Klaus H. Ecker & Erwin Pesch & Günter Schmidt & Jan Węglarz, 2007. "Handbook on Scheduling," International Handbooks on Information Systems, Springer, number 978-3-540-32220-7, December.
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