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On Preemptive Resource Constrained Scheduling: Polynomial-Time Approximation Schemes

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Integer Programming and Combinatorial Optimization (IPCO 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2337))

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Abstract

We study resource constrained scheduling problems where the objective is to compute feasible preemptive schedules minimizing the makespan and using no more resources than what are available. We present approximation schemes along with some inapproximibility results showing how the approximability of the problem changes in terms of the number of resources. The results are based on linear programming formulations (though with exponentially many variables) and some interesting connections between resource constrained scheduling and (multi-dimensional, multiple-choice, and cardinality constrained) variants of the classical knapsack problem. In order to prove the results we generalize a method by Grigoriadis et al. for the max-min resource sharing problem to the case with weak approximate block solvers (i.e. with only constant, logarithmic, or even worse approximation ratios). Finally we present applications of the above results in fractional graph coloring and multiprocessor task scheduling.

Supported in part by EU Thematic Network APPOL I + II, Approximation and Online Algorithms, IST-1999-14084 and IST-2001-30012 and by the EU Research Training Network ARACNE, Approximation and Randomized Algorithms in Communication Networks, HPRN-CT-1999-00112.

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Author information

Authors and Affiliations

  1. Institut für Informatik und praktische Mathematik, Christian-Albrechts-Universität zu Kiel, 24 098, Kiel, Germany

    Klaus Jansen

  2. Applied Decision Analysis, PricewaterhouseCoopers, London, UK

    Lorant Porkolab

Authors
  1. Klaus Jansen
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  2. Lorant Porkolab
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Editor information

Editors and Affiliations

  1. Program in Applied and Computational Mathematics, University of Princeton, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    William J. Cook

  2. Sloan School of Management, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Andreas S. Schulz

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© 2002 Springer-Verlag Berlin Heidelberg

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Jansen, K., Porkolab, L. (2002). On Preemptive Resource Constrained Scheduling: Polynomial-Time Approximation Schemes. In: Cook, W.J., Schulz, A.S. (eds) Integer Programming and Combinatorial Optimization. IPCO 2002. Lecture Notes in Computer Science, vol 2337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47867-1_24

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  • DOI: https://doi.org/10.1007/3-540-47867-1_24

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  • Print ISBN: 978-3-540-43676-8

  • Online ISBN: 978-3-540-47867-6

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