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Non-approximability Results for the Hierarchical Communication Problem with a Bounded Number of Clusters

Eric Angel 1 Evripidis Bampis 1 Rodolphe Giroudeau 2
2 APR - Algorithmes et Performance des Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We study the hierarchical multiprocessor scheduling problem with a constant number of clusters. We show that the problem of deciding whether there is a schedule of length three for the hierarchical multiprocessor scheduling problem is NP \mathcal{N}\mathcal{P} -complete even for bipartite graphs i.e. for precedence graphs of depth one. This result implies that there is no polynomial time approximation algorithm with performance guarantee smaller than 4/3 (unless P = NP \mathcal{P} = \mathcal{N}\mathcal{P}). On the positive side, we provide a polynomial time algorithm for the decision problem when the schedule length is equal to two, the number of clusters is constant and the number of processors per cluster is arbitrary.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00268636
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Eric Angel, Evripidis Bampis, Rodolphe Giroudeau. Non-approximability Results for the Hierarchical Communication Problem with a Bounded Number of Clusters. Euro-Par: European Conference on Parallel Processing, Aug 2002, Paderborn, Germany. pp.217-224, ⟨10.1007/3-540-45706-2_28⟩. ⟨lirmm-00268636⟩

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