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Scheduling and Packing Malleable Tasks with Precedence Constraints of Bounded Width

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Approximation and Online Algorithms (WAOA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5893))

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Abstract

We study two related problems in non-preemptive scheduling and packing of malleable tasks with precedence constraints to minimize the makespan. We distinguish the scheduling variant, in which we allow the free choice of processors, and the packing variant, in which a task must be assigned to a contiguous subset of processors.

For precedence constraints of bounded width, we completely resolve the complexity status for any particular problem setting concerning width bound and number of processors, and give polynomial-time algorithms with best possible performance. For both, scheduling and packing malleable tasks, we present an FPTAS for the NP-hard problem variants and exact algorithms for all remaining special cases. To obtain the positive results, we do not require the common monotonous penalty assumption on processing times, whereas our hardness results hold even when assuming this restriction.

With the close relation between contiguous scheduling and strip packing, our FPTAS is the first (and best possible) constant factor approximation for (malleable) strip packing under special precedence constraints.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Germany

    Elisabeth Günther & Felix G. König

  2. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Nicole Megow

Authors
  1. Elisabeth Günther
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  2. Felix G. König
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  3. Nicole Megow
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Editors and Affiliations

  1. IBISC, CNRS FRE 3190, Université d’Evry Val d’Essonne, Place des Terasses, Tour Evry 2, 91000, Evry Cedex, France

    Evripidis Bampis

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

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Günther, E., König, F.G., Megow, N. (2010). Scheduling and Packing Malleable Tasks with Precedence Constraints of Bounded Width. In: Bampis, E., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2009. Lecture Notes in Computer Science, vol 5893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12450-1_16

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  • DOI: https://doi.org/10.1007/978-3-642-12450-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12449-5

  • Online ISBN: 978-3-642-12450-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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