可移除在线背包问题与建议
Removable Online Knapsack and Advice
AI总结：
本文研究可移除在线背包问题的建议复杂度，证明仅需常数比特建议即可使竞争比从无界提升至接近最优，并改进了多个相关模型的下界。
摘要：
在背包问题中，给定一个具有一定容量的背包和一组物品，每个物品都有大小和价值。目标是从这些物品中选出一部分装入背包，使得总价值最大化。该问题的在线版本逐个揭示物品。对于每个物品，算法必须立即决定是否将其装入。我们考虑该问题的一个自然变体，称为可移除在线背包问题。它与经典变体的不同之处在于允许移除已装入的物品。但重新装入是不可能的：一旦物品被移除，就永久消失。我们分析了该问题的建议复杂度。它衡量一个全知预言机需要提供多少建议比特，才能使在线算法达到任意给定的竞争比，严格意义上竞争比就是近似因子。我们证明，在没有建议时竞争比是无界的，而仅需常数数量的建议比特就能达到接近最优，这一行为在迄今研究的所有问题中是独一无二的。我们还研究了几乎没有任何建议的算法，例如仅一个比特，并分析了比例背包问题的特殊情况，其中物品的大小始终等于其价值。我们证明建议算法具有多种具体应用，并且任何问题的建议复杂度下界都异常强。我们的结果改进了随机算法甚至确定性算法在一些成熟模型中已知的最佳竞争比下界，例如带资源缓冲的背包问题和各种多背包问题。引入可移除背包的开创性论文提出了这样一个问题，我们甚至可以为该问题建立与建议模型的一一对应关系；因此，本文也为这个被忽视的问题提供了全面的分析。
英文摘要：
In the knapsack problem, we are given a knapsack of some capacity and a set of items, each with a size and a value. The goal is to pack a selection of these items fitting the knapsack that maximizes the total value. The online version of this problem reveals the items one by one. For each item, the algorithm must decide immediately whether to pack it or not. We consider a natural variant of this problem, coined removable online knapsack. It differs from the classical variant by allowing the removal of packed items. Repacking is impossible, however: Once an item is removed, it is gone for good. We analyze the advice complexity of this problem. It measures how many advice bits an omniscient oracle needs to provide for an online algorithm to reach any given competitive ratio, which is, understood in its strict sense, just the approximation factor. We show that the competitive ratio jumps from unbounded without advice to near-optimal with just constantly many advice bits, a behavior unique among all problems examined so far. We also examine algorithms with barely any advice, for example just a single bit, and analyze the special case of the proportional knapsack problem, where an item's size always equals its value. We show that advice algorithms have various concrete applications and that lower bounds on the advice complexity of any problem are exceptionally strong. Our results improve some of the best known lower bounds on the competitive ratio for randomized algorithms and even for deterministic deterministic algorithms in established models such as knapsack with a resource buffer and various problems with multiple knapsacks. The seminal paper introducing knapsack with removability proposed such a problem for which we can even establish a one-to-one correspondence with the advice model; this paper therefore also provides a comprehensive analysis for this neglected problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
