Three, four, five, six, or the complexity of scheduling with communication delays

Authors:
J. A. Hoogeveen;J. K. Lenstra;B. Veltman
Affiliations:
Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands;Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands;ORTEC Consultants BV, Groningenweg 6-02, 2803 PV Gouda, Netherlands
Venue:
Operations Research Letters
Year:
1994

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Abstract

A set of unit-time tasks has to be processed on identical parallel processors subject to precedence constraints and unit-time communication delays; does there exist a schedule of length at most d? The problem has two variants, depending on whether the number of processors is restrictively small or not. For the first variant the question can be answered in polynomial time for d = 3 and is NP-complete for d = 4. The second variant is solvable in polynomial time for d = 5 and NP-complete for d = 6. As a consequence, neither of the corresponding optimization problems has a polynomial approximation scheme, unless P = NP.