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

  • Tianyu WangEmail author
  • Odile Bellenguez-Morineau


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 \(P|p_{j}=1,\text {in-tree}|\sum C_{j}\) 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 \( \mathcal {NP} \)-hard.


Parallel scheduling In-tree Precedence constraints Complexity theory 



This work was supported by the China Scholarship Council [grant numbers 201404490037].


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Authors and Affiliations

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

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