On a parallel machine scheduling problem with precedence constraints

Authors:
Isto Aho;Erkki Mäkinen
Affiliations:
Department of Computer Sciences, University of Tampere, Finland FIN-33014;Department of Computer Sciences, University of Tampere, Finland FIN-33014
Venue:
Journal of Scheduling
Year:
2006

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Abstract

We characterize a nontrivial special case with a polynomial-time algorithm for a well-known parallel machine scheduling problem with precedence constraints, with a fixed number of machines, and with tasks of unit length. The special case is related to instances with given maximum path length and maximum degree of the task precedence graph. The method is based on the observation that the number of tasks is either small and bounded by a constant depending on the maximum path length and maximum degree, or alternatively, the number of tasks is large, giving a "dense" schedule.