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The average behaviour of greedy algorithms for the knapsack problem: General distributions

Author

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  • Gennady Diubin
  • Alexander Korbut

Abstract

The paper is a generalization of [4], [5] for arbitrary distributions of coefficients. It is supposed that the coefficients of the objective function and the constraint of the knapsack problem are independent identically distributed random variables having a density with support [0, 1], and the right-hand side of the constraint is proportional to the number of variables, i. e. b=λn. We establish a bound on λ (in terms of the given density and a parameter t > 0) ensuring that both the primal and the dual greedy algorithms have an asymptotic tolerance t. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Gennady Diubin & Alexander Korbut, 2003. "The average behaviour of greedy algorithms for the knapsack problem: General distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 449-479, August.
    • Handle: RePEc:spr:mathme:v:57:y:2003:i:3:p:449-479
    DOI: 10.1007/s001860200270
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    Cited by:

    1. del Castillo, Enrique & Beretta, Alessia & Semeraro, Quirico, 2017. "Optimal setup of a multihead weighing machine," European Journal of Operational Research, Elsevier, vol. 259(1), pages 384-393.
    2. Andrew Mastin & Patrick Jaillet, 2015. "Average-Case Performance of Rollout Algorithms for Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 964-984, June.

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