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

Tianyu Wang () and Odile Bellenguez-Morineau ()
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Tianyu Wang: Institut Mines-Télécom Atlantique
Odile Bellenguez-Morineau: Institut Mines-Télécom Atlantique

Journal of Scheduling, 2019, vol. 22, issue 6, No 7, 709-714

Abstract: 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.

Keywords: Parallel scheduling; In-tree; Precedence constraints; Complexity theory (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10951-019-00602-0

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