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A complexity analysis of parallel scheduling unit-time jobs with in-tree precedence constraints while minimizing the mean flow time

Author

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  • Tianyu Wang

    (Institut Mines-Télécom Atlantique)

  • Odile Bellenguez-Morineau

    (Institut Mines-Télécom Atlantique)

Abstract

This paper deals with a particular scheduling problem. We consider unit-time jobs and in-tree precedence constraints while minimizing the mean flow time. This problem is observed as $$P|p_{j}=1,\text {in-tree}|\sum C_{j}$$ P | p j = 1 , in-tree | ∑ C j with the use of the 3-filed notation. To the best of our knowledge, its complexity is still open. Through a reduction from 3-Partition, we show that this problem is strongly $$ \mathcal {NP} $$ NP -hard.

Suggested Citation

  • Tianyu Wang & Odile Bellenguez-Morineau, 2019. "A complexity analysis of parallel scheduling unit-time jobs with in-tree precedence constraints while minimizing the mean flow time," Journal of Scheduling, Springer, vol. 22(6), pages 709-714, December.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:6:d:10.1007_s10951-019-00602-0
    DOI: 10.1007/s10951-019-00602-0
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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. 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. 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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