Approximation Schemes for a Class of Subset Selection Problems

  • Kirk Pruhs
  • Gerhard J. Woeginger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


In paper we develop an easily applicable algorithmic technique/tool for developing approximation schemes for certain types of combinatorial optimization problems. Special cases that are covered by our result show up in many places in the literature. For every such special case, a particular rounding trick has been implemented in a slightly different way, with slightly different arguments, and with slightly different worst case estimations. Usually, the rounding procedure depended on certain upper or lower bounds on the optimal objective value that have to be justified in a separate argument. Our easily applied result unifies many of these results, and sometimes it even leads to a simpler proof. We demonstrate how our result can be easily applied to a broad family of combinatorial optimization problems. As a special case, we derive the existence of an FPTAS for the scheduling problem of minimizing the weighted number of late jobs under release dates and preemption on a single machine. The approximability status of this problem has been open for some time.


Schedule Problem Approximation Scheme Single Machine Knapsack Problem Combinatorial Optimization Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Kirk Pruhs
    • 1
  • Gerhard J. Woeginger
    • 2
  1. 1.Department of Computer ScienceUniversity of PittsburghUSA
  2. 2.Department of MathematicsUniversity of TwenteThe Netherlands

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