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

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 $\mathcal{N}\mathcal{P}$-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 $\mathcal{P} = \mathcal{N}\mathcal{P}$. 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.

This work has been partially supported by the APPOL II (IST-2001-32007) thematic network of the European Union and the GRID project of the French Ministry of Research.

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