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Scheduling and packing malleable and parallel tasks with precedence constraints of bounded width

Author

Listed:
  • Elisabeth Günther

    (Technische Universität Berlin)

  • Felix G. König

    (TomTom International BV)

  • Nicole Megow

    (Max-Planck-Institut für Informatik)

Abstract

We study the problems of non-preemptively scheduling and packing malleable and parallel tasks with precedence constraints to minimize the makespan. In the scheduling variant, we allow the free choice of processors; in packing, each task must be assigned to a contiguous subset. Malleable tasks can be processed on different numbers of processors with varying processing times, while parallel tasks require a fixed number of processors. For precedence constraints of bounded width, we resolve the complexity status of the problem with any number of processors and any width bound. We present an FPTAS based on Dilworth’s decomposition theorem for the NP-hard problem variants, and exact efficient algorithms for all remaining special cases. For our positive results, we do not require the otherwise common monotonous penalty assumption on the processing times of malleable tasks, whereas our hardness results hold even when assuming this restriction. We complement our results by showing that these problems are all strongly NP-hard under precedence constraints which form a tree.

Suggested Citation

  • Elisabeth Günther & Felix G. König & Nicole Megow, 2014. "Scheduling and packing malleable and parallel tasks with precedence constraints of bounded width," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 164-181, January.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:1:d:10.1007_s10878-012-9498-3
    DOI: 10.1007/s10878-012-9498-3
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    References listed on IDEAS

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    1. Blazwicz, Jacek & Liu, Zhen, 1996. "Scheduling multiprocessor tasks with chain constraints," European Journal of Operational Research, Elsevier, vol. 94(2), pages 231-241, October.
    2. Drozdowski, Maciej, 1996. "Scheduling multiprocessor tasks -- An overview," European Journal of Operational Research, Elsevier, vol. 94(2), pages 215-230, October.
    3. Gerhard J. Woeginger, 2000. "When Does a Dynamic Programming Formulation Guarantee the Existence of a Fully Polynomial Time Approximation Scheme (FPTAS)?," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 57-74, February.
    4. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
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    Cited by:

    1. Elisabeth Lübbecke & Marco E. Lübbecke & Rolf H. Möhring, 2019. "Ship Traffic Optimization for the Kiel Canal," Operations Research, INFORMS, vol. 67(3), pages 791-812, May.
    2. Andrzej Kozik, 2017. "Handling precedence constraints in scheduling problems by the sequence pair representation," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 445-472, February.
    3. 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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