We study a variant of the knapsack problem, where a minimum filling constraint is imposed such that the total weight of selected items cannot be less than a given threshold. We consider the case when the ratio of the threshold to the capacity equals a given constant α with 0 ≤ α < 1. For any such constant α, since finding an optimal solution is NP-hard, we develop the first FPTAS for the problem, which has a time complexity polynomial in 1/(1 - α). © 2011 Springer-Verlag.
CITATION STYLE
Xu, Z., & Lai, X. (2011). A fully polynomial approximation scheme for a knapsack problem with a minimum filling constraint (extended abstract). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6844 LNCS, pp. 704–715). https://doi.org/10.1007/978-3-642-22300-6_61
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