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Integer knapsack problems with profit functions of the same value range

Author

Listed:
  • Evgeny Gurevsky

    (LS2N, Université de Nantes)

  • Dmitry Kopelevich

    (Belarusian State University)

  • Sergey Kovalev

    (INSEEC Business School)

  • Mikhail Y. Kovalyov

    (United Institute of Informatics Problems, NASB)

Abstract

Integer knapsack problems with profit functions of the same value range are studied. Linear time algorithms are presented for the case of convex non-decreasing profit functions, and an NP-hardness proof and a fully polynomial-time approximation scheme are provided for the case of arbitrary non-negative non-decreasing profit functions. Fast solution procedures are also devised for the bottleneck counterparts of these problems. Computational complexity of the case with concave profit functions remains open.

Suggested Citation

  • Evgeny Gurevsky & Dmitry Kopelevich & Sergey Kovalev & Mikhail Y. Kovalyov, 2023. "Integer knapsack problems with profit functions of the same value range," 4OR, Springer, vol. 21(3), pages 405-419, September.
    • Handle: RePEc:spr:aqjoor:v:21:y:2023:i:3:d:10.1007_s10288-022-00514-4
    DOI: 10.1007/s10288-022-00514-4
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    References listed on IDEAS

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