Simple but efficient approaches for the collapsing knapsack problem

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Abstract

The collapsing knapsack problem is a generalization of the ordinary knapsack problem, where the knapsack capacity is a non-increasing function of the number of items included. Whereas previous papers on the topic have applied quite involved techniques, the current paper presents and analyzes two rather simple approaches: One approach that is based on the reduction to a standard knapsack problem, and another approach that is based on a simple dynamic programming recursion. Both algorithms have pseudo-polynomial solution times, guaranteeing reasonable solution times for moderate coefficient sizes. Computational experiments are provided to expose the efficiency of the two approaches compared to previous algorithms.

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APA

Pferschy, U., Pisinger, D., & Woeginger, G. J. (1997). Simple but efficient approaches for the collapsing knapsack problem. Discrete Applied Mathematics, 77(3), 271–280. https://doi.org/10.1016/S0166-218X(96)00134-5

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