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European Symposium on Algorithms

ESA 2004: Algorithms – ESA 2004 pp 616–627Cite as

An Experimental Study of Random Knapsack Problems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3221))

Abstract

The size of the Pareto curve for the bicriteria version of the knapsack problem is polynomial on average. This has been shown for various random input distributions. We experimentally investigate the number of Pareto optimal knapsack fillings. Our experiments suggests that the theoretically proven upper bound of O(n 3) for uniform instances and O(φμ n 4) for general probability distributions is not tight. Instead we conjecture an upper bound of O(φμ n 2) matching a lower bound for adversarial weights.

In the second part we study advanced algorithmic techniques for the knapsack problem. We combine several ideas that have been used in theoretical studies to bound the average-case complexity of the knapsack problem. The concepts used are simple and have been known since at least 20 years, but apparently have not been used together. The result is a very competitive code that outperforms the best known implementation Combo by orders of magnitude also for harder random knapsack instances.

This work was supported in part by DFG grant Vo889/1-1.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Rene Beier

  2. Fachbereich Informatik, Universität Dortmund, Germany

    Berthold Vöcking

Authors
  1. Rene Beier
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  2. Berthold Vöcking
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Editor information

Editors and Affiliations

  1. University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer Science, King’s College, WC2R 2LS, London, UK

    Tomasz Radzik

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© 2004 Springer-Verlag Berlin Heidelberg

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Beier, R., Vöcking, B. (2004). An Experimental Study of Random Knapsack Problems. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_55

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  • DOI: https://doi.org/10.1007/978-3-540-30140-0_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23025-0

  • Online ISBN: 978-3-540-30140-0

  • eBook Packages: Springer Book Archive

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