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Algorithms for Scheduling Deadline-Sensitive Malleable Tasks

Author

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  • Xiaohu Wu

    (National Engineering Research Center of Mobile Network Technologies, Beijing University of Posts and Telecommunications, China)

  • Patrick Loiseau

    (Inria, FairPlay team, Palaiseau, France)

Abstract

Due to the ubiquity of batch data processing, the related problems of scheduling malleable batch tasks have received significant attention. We consider a fundamental model where a set of tasks is to be processed on multiple identical machines and each task is specified by a value, a workload, a deadline and a parallelism bound. Within the parallelism bound, the number of machines assigned to a task can vary over time without affecting its workload. In this paper, we identify a boundary condition and prove by construction that a set of malleable tasks with deadlines can be finished by their deadlines if and only if it satisfies the boundary condition. This core result plays a key role in the design and analysis of scheduling algorithms: (i) when several typical objectives are considered, such as social welfare maximization, machine minimization, and minimizing the maximum weighted completion time, and, (ii) when the algorithmic design techniques such as greedy and dynamic programming are applied to the social welfare maximization problem. As a result, we give four new or improved algorithms for the above problems.

Suggested Citation

  • Xiaohu Wu & Patrick Loiseau, 2024. "Algorithms for Scheduling Deadline-Sensitive Malleable Tasks," SN Operations Research Forum, Springer, vol. 5(2), pages 1-38, June.
    • Handle: RePEc:spr:snopef:v:5:y:2024:i:2:d:10.1007_s43069-024-00300-4
    DOI: 10.1007/s43069-024-00300-4
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    References listed on IDEAS

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    1. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    2. Wu, Xiaohu & Loiseau, Patrick, 2023. "Efficient approximation algorithms for scheduling moldable tasks," European Journal of Operational Research, Elsevier, vol. 310(1), pages 71-83.
    3. W. A. Horn, 1974. "Some simple scheduling algorithms," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(1), pages 177-185, March.
    4. Viswanath Nagarajan & Joel Wolf & Andrey Balmin & Kirsten Hildrum, 2019. "Malleable scheduling for flows of jobs and applications to MapReduce," Journal of Scheduling, Springer, vol. 22(4), pages 393-411, August.
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