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Unbounded knapsack problems with arithmetic weight sequences

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  • Deineko, Vladimir G.
  • Woeginger, Gerhard J.

Abstract

We investigate a special case of the unbounded knapsack problem in which the item weights form an arithmetic sequence. We derive a polynomial time algorithm for this special case with running time O(n8), where n denotes the number of distinct items in the instance. Furthermore, we extend our approach to a slightly more general class of knapsack instances.

Suggested Citation

  • Deineko, Vladimir G. & Woeginger, Gerhard J., 2011. "Unbounded knapsack problems with arithmetic weight sequences," European Journal of Operational Research, Elsevier, vol. 213(2), pages 384-387, September.
    • Handle: RePEc:eee:ejores:v:213:y:2011:i:2:p:384-387
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    References listed on IDEAS

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    1. Mathur, Kamlesh & Venkateshan, Prahalad, 2007. "A new lower bound for the linear knapsack problem with general integer variables," European Journal of Operational Research, Elsevier, vol. 178(3), pages 738-754, May.
    2. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    3. M. J. Magazine & G. L. Nemhauser & L. E. Trotter, 1975. "When the Greedy Solution Solves a Class of Knapsack Problems," Operations Research, INFORMS, vol. 23(2), pages 207-217, April.
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    Cited by:

    1. Yang Yang, 2024. "An Improved Unbounded-DP Algorithm for the Unbounded Knapsack Problem with Bounded Coefficients," Mathematics, MDPI, vol. 12(12), pages 1-12, June.

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