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Note: On the set‐union knapsack problem

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  • Olivier Goldschmidt
  • David Nehme
  • Gang Yu

Abstract

We consider a generalization of the 0‐1 knapsack problem called the set‐union knapsack problem (SKP). In the SKP, each item is a set of elements, each item has a nonnegative value, and each element has a nonnegative weight. The total weight of a collection of items is given by the total weight of the elements in the union of the items' sets. This problem has applications to data‐base partitioning and to machine loading in flexible manufacturing systems. We show that the SKP remains NP‐hard, even in very restricted cases. We present an exact, dynamic programming algorithm for the SKP and show sufficient conditions for it to run in polynomial time. © 1994 John Wiley & Sons, Inc.

Suggested Citation

  • Olivier Goldschmidt & David Nehme & Gang Yu, 1994. "Note: On the set‐union knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 833-842, October.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:6:p:833-842
    DOI: 10.1002/1520-6750(199410)41:63.0.CO;2-Q
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    References listed on IDEAS

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    1. Christopher S. Tang & Eric V. Denardo, 1988. "Models Arising from a Flexible Manufacturing Machine, Part II: Minimization of the Number of Switching Instants," Operations Research, INFORMS, vol. 36(5), pages 778-784, October.
    2. Crama, Yves & Oerlemans, Alwin G., 1994. "A column generation approach to job grouping for flexible manufacturing systems," European Journal of Operational Research, Elsevier, vol. 78(1), pages 58-80, October.
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    Cited by:

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    2. Adil Baykasoğlu & Fehmi Burcin Ozsoydan & M. Emre Senol, 2020. "Weighted superposition attraction algorithm for binary optimization problems," Operational Research, Springer, vol. 20(4), pages 2555-2581, December.
    3. Zishen Yang & Wei Wang & Majun Shi, 2021. "Algorithms and Complexity for a Class of Combinatorial Optimization Problems with Labelling," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 673-695, March.

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