Constant-Time Approximation Algorithms for the Knapsack Problem

  • Hiro Ito
  • Susumu Kiyoshima
  • Yuichi Yoshida
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7287)


In this paper, we give a constant-time approximation algorithm for the knapsack problem. Using weighted sampling, with which we can sample items with probability proportional to their profits, our algorithm runs with query complexity O(ε − 4 logε − 1), and it approximates the optimal profit with probability at least 2/3 up to error at most an ε-fraction of the total profit. For the subset sum problem, which is a special case of the knapsack problem, we can improve the query complexity to O(ε − 1 logε − 1).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hiro Ito
    • 1
  • Susumu Kiyoshima
    • 1
  • Yuichi Yoshida
    • 1
    • 2
  1. 1.School of InformaticsKyoto UniversityKyotoJapan
  2. 2.Preferred InfrastructureInc.TokyoJapan

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