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

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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.

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Acknowledgements

This work was supported by the China Scholarship Council (Grant No. 201404490037).

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Authors and Affiliations

  1. Institut Mines-Télécom Atlantique, LS2N, UMR CNRS 6004, 4 rue Alfred Kastler, B.P. 20722, 44307, Nantes Cedex 3, France

    Tianyu Wang & Odile Bellenguez-Morineau

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  1. Tianyu Wang
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  2. Odile Bellenguez-Morineau
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Correspondence to Tianyu Wang.

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Wang, T., Bellenguez-Morineau, O. The Complexity of Parallel Machine Scheduling of Unit-Processing-Time Jobs under Level-Order Precedence Constraints. J Sched 22, 263–269 (2019). https://doi.org/10.1007/s10951-018-0596-7

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  • DOI: https://doi.org/10.1007/s10951-018-0596-7

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