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Constant-Time Approximation Algorithms for the Knapsack Problem

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Theory and Applications of Models of Computation (TAMC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7287))

Abstract

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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Author information

Authors and Affiliations

  1. School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Hiro Ito, Susumu Kiyoshima & Yuichi Yoshida

  2. Preferred Infrastructure, Inc., Tokyo, 113-0033, Japan

    Yuichi Yoshida

Authors
  1. Hiro Ito
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  2. Susumu Kiyoshima
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  3. Yuichi Yoshida
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Resource Planning and Generation, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Manindra Agrawal

  2. Department of Pure Mathematics, Leeds, University of Leeds, LS2 9JT, UK

    S. Barry Cooper

  3. Institute of Software, Chinese Academy of Sciences, P.O. Box 8718, 100190, Beijing, P.R. China

    Angsheng Li

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© 2012 Springer-Verlag Berlin Heidelberg

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Ito, H., Kiyoshima, S., Yoshida, Y. (2012). Constant-Time Approximation Algorithms for the Knapsack Problem. In: Agrawal, M., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2012. Lecture Notes in Computer Science, vol 7287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29952-0_17

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  • DOI: https://doi.org/10.1007/978-3-642-29952-0_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29951-3

  • Online ISBN: 978-3-642-29952-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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