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

Chenxia Zhao () and Xianyue Li ()
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Chenxia Zhao: Lanzhou University
Xianyue Li: Lanzhou University

Journal of Combinatorial Optimization, 2014, vol. 28, issue 4, No 14, 910-916

Abstract: 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.

Keywords: Knapsack; Single continuous variable; Approximation algorithm (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-012-9579-3

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