# Scheduling stretched coupled-tasks with compatibilities constraints : model, complexity and approximation results for some class of graphs

* Corresponding author
2 MAORE - Méthodes Algorithmes pour l'Ordonnancement et les Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We tackle the makespan minimization coupled-tasks problem in presence of compatibility constraints. In particular, we focus on stretched coupled-tasks, {\it i.e.}coupled-tasks having the same sub-tasks execution time and idle time duration. We study severals problems in frame works of classic complexity and approximation for which the compatibility graph $G_c$ is bipartite (star, chain, $\ldots$) In such context, we design some efficient polynomial-time approximation algorithms according to difference parameters of the scheduling problem. When $G_c$ is a $k$-stage bipartite graph, we propose, among other, a $\frac{7}{6}$-approximation algorithm when $k=1$, and a $\frac{13}{9}$-approximation algorithm when $k=2$.\\
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https://hal.archives-ouvertes.fr/hal-00947519
Contributor : Benoît Darties <>
Submitted on : Sunday, February 16, 2014 - 7:24:18 PM
Last modification on : Monday, February 11, 2019 - 11:50:15 AM
Document(s) archivé(s) le : Friday, May 16, 2014 - 10:40:11 AM

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Benoit Darties, Rodolphe Giroudeau, Jean-Claude König, Gilles Simonin. Scheduling stretched coupled-tasks with compatibilities constraints : model, complexity and approximation results for some class of graphs. 2014. ⟨hal-00947519⟩

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