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

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China

    Chenxia Zhao & Xianyue Li

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  1. Chenxia Zhao
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  2. Xianyue Li
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Correspondence to Xianyue Li.

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Zhao, C., Li, X. Approximation algorithms on 0–1 linear knapsack problem with a single continuous variable. J Comb Optim 28, 910–916 (2014). https://doi.org/10.1007/s10878-012-9579-3

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  • DOI: https://doi.org/10.1007/s10878-012-9579-3

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