Integrality Property in Preemptive Parallel Machine Scheduling

Authors:
Philippe Baptiste;Jacques Carlier;Alexander Kononov;Maurice Queyranne;Sergey Sevastyanov;Maxim Sviridenko
Affiliations:
CNRS, École Polytechnique, Paris, France;CNRS, Heudiasyc, Univ. de Tech. de Compiègne, France;Sobolev Institute of Mathematics, Novosibirsk, Russia and Novosibirsk State University, Novosibirsk, Russia;Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, Canada;Sobolev Institute of Mathematics, Novosibirsk, Russia and Novosibirsk State University, Novosibirsk, Russia;IBM T.J. Watson Research Center, Yorktown Heights, USA
Venue:
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Year:
2009

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Abstract

We consider parallel machine scheduling problems with identical machines and preemption allowed. It is shown that every such problem with chain precedence constraints and release dates and an integer-concave objective function satisfies the following integrality property : for any problem instance with integral data there exists an optimal schedule where all interruptions occur at integral dates. As a straightforward consequence of this result, for a wide class of scheduling problems with unit processing times a so-called preemption redundancy property is valid. This means that every such preemptive scheduling problem is equivalent to its non-preemptive counterpart from the viewpoint of both its optimum value and the problem complexity. The equivalence provides new and simpler proofs for some known complexity results and closes a few open questions.