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

  • Tianyu WangEmail author
  • Odile Bellenguez-Morineau


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.


Parallel machine scheduling Level-order Precedence constraints 



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


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut Mines-Télécom Atlantique, LS2N, UMR CNRS 6004Nantes Cedex 3France

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