The is a strongly -hard combinatorial optimisation problem, with several applications. We show that an for the problem, due to Kataoka and Yamada, can be computed in linear time. We then show that some bounds due to Martello and Monaci dominate the Kataoka-Yamada bound. Finally, we define an even stronger bound, which turns out to be particularly effective when the number of knapsacks is not a multiple of the number of item classes.

中文翻译：

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多背包分配问题的上限

这是一个非常困难的组合优化问题，有多种应用。我们证明，由于 Kataoka 和 Yamada 的贡献，该问题的 an 可以在线性时间内计算。然后我们表明，由于 Martello 和 Monaci 造成的一些边界主导了 Kataoka-Yamada 边界。最后，我们定义了一个更强的界限，当背包的数量不是物品类别数量的倍数时，该界限特别有效。