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arXiv · 2605.05233

Near-Tight Approximation Algorithms for Bottleneck Multiple Knapsack Problems

Lin Chen·Tingwei Hu·Yuchen Mao·Yong Chen·Lili Mei·An Zhang·Guangting Chen·Guochuan Zhang
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Abstract

In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the minimum profit received by any knapsack subject to the capacity constraint. When all knapsacks have identical capacity, we give a $(\frac{2}{3} - \varepsilon)$-approximation algorithm for any constant $\varepsilon > 0$. This result almost matches the $(\frac{2}{3} + \varepsilon)$ inapproximability bound for the bottleneck multiple subset sum problem (Caprara et al., 2000). When the knapsacks can have arbitrary capacities, we propose a $(\frac{1}{2} - \varepsilon)$-approximation algorithm for any constant $\varepsilon > 0$. We also prove a hardness bound of $(\frac{1}{2} + \varepsilon)$ for any constant $\varepsilon > 0$.

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Lin Chen, Tingwei Hu, Yuchen Mao, Yong Chen, Lili Mei, An Zhang, Guangting Chen, Guochuan Zhang. 2026-04-30. Near-Tight Approximation Algorithms for Bottleneck Multiple Knapsack Problems. https://arxiv.org/abs/2605.05233

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