Bounding the Running Time of Algorithms for Scheduling and Packing Problems

  • Klaus Jansen
  • Felix Land
  • Kati Land
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)

Abstract

We investigate the implications of the exponential time hypothesis on algorithms for scheduling and packing problems. Our main focus is to show tight lower bounds on the running time of these algorithms. For exact algorithms we investigate the dependence of the running time on the number n of items (for packing) or jobs (for scheduling). We show that many of these problems, including SubsetSum, Knapsack, BinPacking, 〈P2 | | C max 〉, and 〈P2 | | ∑ wjCj〉, have a lower bound of 2o(n) × ∥ I ∥ O(1). We also develop an algorithmic framework that is able to solve a large number of scheduling and packing problems in time 2O(n) × ∥ I ∥ O(1). Finally, we show that there is no PTAS for MultipleKnapsack and 2d-Knapsack with running time \(2^{o}({\frac{1}{\epsilon }}) \times \parallel I \parallel^{O(1)}\) and \(n^{o({\frac{1}{\epsilon }})} \times \parallel{I}\parallel^{O(1)}\).

Keywords

scheduling packing exponential time hypothesis exact algorithms lower bounds 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Klaus Jansen
    • 1
  • Felix Land
    • 1
  • Kati Land
    • 1
  1. 1.Institute of Computer ScienceUniversity of KielKielGermany

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