# Theoretical Aspects of Scheduling Coupled-Tasks in the Presence of Compatibility Graph

1 MAORE - Méthodes Algorithmes pour l'Ordonnancement et les Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : This paper presents a generalization of the coupled-task sche-duling problem introduced by Shapiro \cite{Shapiro}, where considered tasks are subject to incompatibility constraints depicted by an undirected graph. The motivation of this problem comes from data acquisition and processing in a mono-processor torpedo used for underwater exploration. As we add the compatibility graph, we focus on complexity of the problem, and more precisely on the boundary between $\mathcal{P}$ and $\mathcal{NP}$-completeness when some other input parameters are restricted (e.g. the ratio between the durations of the two sub-tasks composing a task): we adapt the global visualization of the complexity of scheduling problems with coupled-task given by Orman and Potts \cite{op1997} to our model, determine new complexity results, and thus propose a new visualization including incompatibility constraints. In the end, we give a new polynomial-time approximation algorithm result which completes previous works.
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Article dans une revue
Algorithmic Operations Research, Preeminent Academic Facets, 2012, 7 (1), pp.1-12

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00715828
Contributeur : Rodolphe Giroudeau <>
Soumis le : lundi 9 juillet 2012 - 12:45:44
Dernière modification le : vendredi 26 octobre 2018 - 10:27:23

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• HAL Id : lirmm-00715828, version 1

### Citation

Rodolphe Giroudeau, Benoit Darties, Jean-Claude König, Gilles Simonin. Theoretical Aspects of Scheduling Coupled-Tasks in the Presence of Compatibility Graph. Algorithmic Operations Research, Preeminent Academic Facets, 2012, 7 (1), pp.1-12. 〈lirmm-00715828〉

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