Approximating a coupled-task scheduling problem in the presence of compatibility graph and additional tasks

Rodolphe Giroudeau 1 Jean-Claude König 1 Gilles Simonin 2
1 MAORE - Méthodes Algorithmes pour l'Ordonnancement et les Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This paper introduces a coupled-task scheduling problem in the presence of a compatibility graph and additional tasks on a single processor. We investigate a specific configuration, in which the coupled-tasks have an idle time of two. The complexity of these problems will be studied according to the presence or absence of triangles in the compatibility graph. Using the results given by Kelmans (1997) on an optimal packing problem of induced stars in a graph, we develop a polynomial-time algorithm which consists of minimising the number of non-covered vertices by covering vertices with edges or paths of length two in the compatibility graph. This type of covering will be called the two-cover technique. According to the compatibility graph type, the two-cover technique provides a polynomial-time ρ-approximation algorithm with ρ = 10 9 (resp. ρ = 13 ) in the presence (resp. absence) of triangles.
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Journal articles
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00952599
Contributor : Rodolphe Giroudeau <>
Submitted on : Thursday, February 27, 2014 - 10:41:14 AM
Last modification on : Friday, January 10, 2020 - 9:10:16 PM

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  • HAL Id : lirmm-00952599, version 1

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Rodolphe Giroudeau, Jean-Claude König, Gilles Simonin. Approximating a coupled-task scheduling problem in the presence of compatibility graph and additional tasks. International Journal of Planning and Scheduling, Inderscience, 2013, 1 (en cours de publication) (4), pp.285-300. ⟨lirmm-00952599⟩

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