Abstract
In this paper, we give a constant-time approximation algorithm for the knapsack problem. Using weighted sampling, with which we can sample items with probability proportional to their profits, our algorithm runs with query complexity O(ε − 4 logε − 1), and it approximates the optimal profit with probability at least 2/3 up to error at most an ε-fraction of the total profit. For the subset sum problem, which is a special case of the knapsack problem, we can improve the query complexity to O(ε − 1 logε − 1).
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Ito, H., Kiyoshima, S., Yoshida, Y. (2012). Constant-Time Approximation Algorithms for the Knapsack Problem. In: Agrawal, M., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2012. Lecture Notes in Computer Science, vol 7287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29952-0_17
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DOI: https://doi.org/10.1007/978-3-642-29952-0_17
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