Parameterized complexity of a coupled-task scheduling problem

S. Bessy () and R. Giroudeau ()
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S. Bessy: LIRMM UMR 5506
R. Giroudeau: LIRMM UMR 5506

Journal of Scheduling, 2019, vol. 22, issue 3, No 4, 305-313

Abstract: Abstract In this article, we investigate the parameterized complexity of coupled-task scheduling in the presence of compatibility constraints given by a compatibility graph. In this model, each task contains two sub-tasks delayed by an idle time. Moreover, a sub-task can be performed during the idle time of another task if the two tasks are compatible. We consider a parameterized version of the scheduling problem: is there a schedule in which at least k coupled-tasks have a completion time before a fixed due date? It is known that this problem is $$\mathsf { NP}$$ NP -complete. We prove that it is fixed-parameter tractable ( $$\mathsf {FPT}$$ FPT ) parameterized by k the standard parameter if the total duration of each task is bounded by a constant, whereas the problem becomes $${\mathsf {W}}[1]$$ W [ 1 ] -hard otherwise. We also show that in the former case, the problem does not admit a polynomial kernel under some standard complexity assumptions. Moreover, we obtain an $$\mathsf {FPT}$$ FPT algorithm when the problem is parameterized by the size of a vertex cover of the compatibility graph.

Keywords: Coupled-task scheduling model; $$\mathsf {FPT}$$ FPT algorithms; $${\mathsf {W}}[1]$$ W [ 1 ] -hardness; Kernel lower bound (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10951-018-0581-1

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