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Bounding the Running Time of Algorithms for Scheduling and Packing Problems

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Algorithms and Data Structures (WADS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8037))

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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 | | ∑ w j C j 〉, 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 \(n^{o({\frac{1}{\epsilon }})} \times \parallel{I}\parallel^{O(1)}\).

A full version of this work is available as technical report [18]. Research supported by German Research Foundation (DFG) projects JA 612/16-1 and JA 612/12-1.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Kiel, 24118, Kiel, Germany

    Klaus Jansen, Felix Land & Kati Land

Authors
  1. Klaus Jansen
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  2. Felix Land
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  3. Kati Land
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Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, ON, Canada

    Roberto Solis-Oba

  3. School of Computer Science, Carleton University, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

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Jansen, K., Land, F., Land, K. (2013). Bounding the Running Time of Algorithms for Scheduling and Packing Problems. In: Dehne, F., Solis-Oba, R., Sack, JR. (eds) Algorithms and Data Structures. WADS 2013. Lecture Notes in Computer Science, vol 8037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40104-6_38

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  • DOI: https://doi.org/10.1007/978-3-642-40104-6_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40103-9

  • Online ISBN: 978-3-642-40104-6

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