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Approximation algorithms on 0–1 linear knapsack problem with a single continuous variable

Author

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  • Chenxia Zhao

    (Lanzhou University)

  • Xianyue Li

    (Lanzhou University)

Abstract

The 0–1 linear knapsack problem with a single continuous variable (KPC) is a natural generalization of the standard 0–1 linear knapsack problem (KP). In KPC, the capacity of the knapsack is not fixed, but can be adjusted by a continuous variable. This paper studies the approximation algorithm on KPC. Firstly, assuming that the weight of each item is at most the original capacity of the knapsack, we give a 2-approximation algorithm on KPC by generalizing the 2-approximation algorithm on KP. Then, without the above assumption, we give another 2-approximation algorithm on KPC for general cases by extending the first algorithm.

Suggested Citation

  • Chenxia Zhao & Xianyue Li, 2014. "Approximation algorithms on 0–1 linear knapsack problem with a single continuous variable," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 910-916, November.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:4:d:10.1007_s10878-012-9579-3
    DOI: 10.1007/s10878-012-9579-3
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    References listed on IDEAS

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    1. MARCHAND, Hugues & WOLSEY, Laurence A., 1999. "The 0-1 Knapsack problem with a single continuous variable," LIDAM Reprints CORE 1390, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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