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Algorithms for Scheduling Deadline-Sensitive Malleable Tasks

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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.

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Data Availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Notes

  1. We refer readers to [9, 19] for more details on the general techniques to design scheduling algorithms.

  2. In this paper, we use the terms “demand” and “workload” interchangeably.

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Funding

The work of Patrick Loiseau has been partially supported by MIAI @ Grenoble Alpes (ANR-19- P3IA-0003), by the French National Research Agency (ANR) through grant ANR-20-CE23-0007 and through the “Investissements d’avenir” program (ANR-15-IDEX- 02); and by the Alexander von Humboldt Foundation.

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Authors and Affiliations

  1. National Engineering Research Center of Mobile Network Technologies, Beijing University of Posts and Telecommunications, China, 10 Xitucheng Road, Haidian District, Beijing, 100876, China

    Xiaohu Wu

  2. Inria, FairPlay team, Palaiseau, France, 5 Avenue Henry Le Chatelier, 91120, Palaiseau, France

    Patrick Loiseau

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  1. Xiaohu Wu
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Correspondence to Xiaohu Wu.

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Wu, X., Loiseau, P. Algorithms for Scheduling Deadline-Sensitive Malleable Tasks. Oper. Res. Forum 5, 30 (2024). https://doi.org/10.1007/s43069-024-00300-4

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