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

Eric Angel (1) , Evripidis Bampis (1) , Rodolphe Giroudeau (2)

1 LaMI - Laboratoire de Méthodes Informatiques
2 APR - Algorithmes et Performance des Réseaux

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.

Domaines: Informatique [cs]

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⟩