# Approximation Algorithms for the Weight-Reducible Knapsack Problem

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### Cites background from "Approximation Algorithms for the We..."

...Disser et al [14] consider policies for packing a knapsack with unknown capacity and Goerigk et al [15] consider the knapsack problem in which there is a limited budget to decrease item weights....

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### Cites methods from "Approximation Algorithms for the We..."

...alysis for several cases of improvable knapsack problems, presenting constant factor approximation algorithms and two PTAS. Parts of this paper have been published in the extended conference abstract [GSSS14]. 1 Introduction We consider an extension of the knapsack problem which allows to use diﬀerent versions of the same item, where the weight of an item can be reduced. Each such improvement has associat...

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##### References

4,290 citations

### "Approximation Algorithms for the We..." refers result in this paper

...which is similar to the classic FPTAS for Knapsack [6]....

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999 citations

### Additional excerpts

..., [5] for the knapsack problem....

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### "Approximation Algorithms for the We..." refers background or methods in this paper

...For a constant number of knapsack constraints, as is the case here, one can apply the randomized rounding methods proposed in [4] to obtain a randomized e/(e− 1)-approximation algorithm....

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...It may be noted that, no explicit analysis is presented in [4] except for a claim that the method takes polynomial time....

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193 citations

### "Approximation Algorithms for the We..." refers background or methods in this paper

...Considering the special case of only one improvement per item and constant improvement costs, we further presented a linear-time 3-approximation based on the algorithm of [7] for the related k-CKP, and strengthened the analysis of the previous 3-approximation for the general problem, to be a 2-approximation for the special case....

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...[7] and [8] present algorithms for this kind of problem....

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...We first note that a linear-time 4-approximation algorithm can be easiliy achieved: Following [7], there is a 2-approximation algorithm for CKP, with linear runtime due to [9]....

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122 citations

### "Approximation Algorithms for the We..." refers background in this paper

...Note that we may consider this problem as a special case of a multi-dimensional knapsack problem with conflict constraints (for the one-dimensional case, we refer to [2,3])....

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