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

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

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Acknowledgements

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

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Authors and Affiliations

  1. LS2N, UMR CNRS 6004, Institut Mines-Télécom Atlantique, 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. A complexity analysis of parallel scheduling unit-time jobs with in-tree precedence constraints while minimizing the mean flow time. J Sched 22, 709–714 (2019). https://doi.org/10.1007/s10951-019-00602-0

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