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The Complexity of Parallel Machine Scheduling of Unit-Processing-Time Jobs under Level-Order Precedence Constraints

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  • Tianyu Wang

    (Institut Mines-Télécom Atlantique, LS2N, UMR CNRS 6004)

  • Odile Bellenguez-Morineau

    (Institut Mines-Télécom Atlantique, LS2N, UMR CNRS 6004)

Abstract

In this paper, we prove that parallel machine scheduling problems where jobs have unit processing time and level-order precedence constraints are NP-complete, while minimizing the makespan or the total completion time. These problems are NP-complete even when preemption is allowed. We then adapt the proof to other open problems with out-tree or opposing-forests precedence constraints.

Suggested Citation

  • Tianyu Wang & Odile Bellenguez-Morineau, 2019. "The Complexity of Parallel Machine Scheduling of Unit-Processing-Time Jobs under Level-Order Precedence Constraints," Journal of Scheduling, Springer, vol. 22(3), pages 263-269, June.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:3:d:10.1007_s10951-018-0596-7
    DOI: 10.1007/s10951-018-0596-7
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    References listed on IDEAS

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    1. T. C. Hu, 1961. "Parallel Sequencing and Assembly Line Problems," Operations Research, INFORMS, vol. 9(6), pages 841-848, December.
    2. Peter Brucker & M. R. Garey & D. S. Johnson, 1977. "Scheduling Equal-Length Tasks Under Treelike Precedence Constraints to Minimize Maximum Lateness," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 275-284, August.
    3. D. Prot & O. Bellenguez-Morineau, 2018. "A survey on how the structure of precedence constraints may change the complexity class of scheduling problems," Journal of Scheduling, Springer, vol. 21(1), pages 3-16, February.
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    Cited by:

    1. Klaus Heeger & Danny Hermelin & George B. Mertzios & Hendrik Molter & Rolf Niedermeier & Dvir Shabtay, 2023. "Equitable scheduling on a single machine," Journal of Scheduling, Springer, vol. 26(2), pages 209-225, April.
    2. Tianyu Wang & Odile Bellenguez, 2021. "Three notes on scheduling unit-length jobs with precedence constraints to minimize the total completion time," Journal of Scheduling, Springer, vol. 24(6), pages 649-662, December.

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