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

Authors:
Eric Angel;Evripidis Bampis;Rodolphe Giroudeau
Affiliations:
-;-;-
Venue:
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Year:
2002

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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-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). 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.