On Preemptive Resource Constrained Scheduling: Polynomial-Time Approximation Schemes

  • Klaus Jansen
  • Lorant Porkolab
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2337)


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.


Approximation Algorithm Knapsack Problem Chromatic Number Unit Disk Graph Preemptive Schedule 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Klaus Jansen
    • 1
  • Lorant Porkolab
    • 2
  1. 1.Institut für Informatik und praktische MathematikChristian-Albrechts-Universität zu KielKielGermany
  2. 2.Applied Decision AnalysisPricewaterhouseCoopersLondonUK

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