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A successive approximation algorithm for the multiple knapsack problem

Author

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  • Zhenbo Wang

    (Tsinghua University)

  • Wenxun Xing

    (Tsinghua University)

Abstract

It is well-known that the multiple knapsack problem is NP-hard, and does not admit an FPTAS even for the case of two identical knapsacks. Whereas the 0-1 knapsack problem with only one knapsack has been intensively studied, and some effective exact or approximation algorithms exist. A natural approach for the multiple knapsack problem is to pack the knapsacks successively by using an effective algorithm for the 0-1 knapsack problem. This paper considers such an approximation algorithm that packs the knapsacks in the nondecreasing order of their capacities. We analyze this algorithm for 2 and 3 knapsack problems by the worst-case analysis method and give all their error bounds.

Suggested Citation

  • Zhenbo Wang & Wenxun Xing, 2009. "A successive approximation algorithm for the multiple knapsack problem," Journal of Combinatorial Optimization, Springer, vol. 17(4), pages 347-366, May.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:4:d:10.1007_s10878-007-9116-y
    DOI: 10.1007/s10878-007-9116-y
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    References listed on IDEAS

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    1. Martello, Silvano & Toth, Paolo, 1977. "An upper bound for the zero-one knapsack problem and a branch and bound algorithm," European Journal of Operational Research, Elsevier, vol. 1(3), pages 169-175, May.
    2. Hans Kellerer & Ulrich Pferschy, 1999. "A New Fully Polynomial Time Approximation Scheme for the Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 59-71, July.
    3. Martello, Silvano & Pisinger, David & Toth, Paolo, 2000. "New trends in exact algorithms for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 325-332, June.
    4. Robert M. Nauss, 1976. "An Efficient Algorithm for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 23(1), pages 27-31, September.
    5. Eugene L. Lawler, 1979. "Fast Approximation Algorithms for Knapsack Problems," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 339-356, November.
    6. Pisinger, David, 1999. "An exact algorithm for large multiple knapsack problems," European Journal of Operational Research, Elsevier, vol. 114(3), pages 528-541, May.
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    Cited by:

    1. Kameng Nip & Zhenbo Wang & Zizhuo Wang, 2017. "Knapsack with variable weights satisfying linear constraints," Journal of Global Optimization, Springer, vol. 69(3), pages 713-725, November.

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