In the online simple knapsack problem items are presented in an iterative fashion and an algorithm has to decide for each item whether to reject or permanently include it into the knapsack without any knowledge about the rest of the instance. The goal is to pack the knapsack as full as possible. In this work, we introduce the option of reserving items for the cost of a fixed fraction $\alpha$ of their size. An algorithm may pay this fraction in order to postpone its decision on whether to include or reject these items until after the last item of the instance was presented. While the classical online simple knapsack problem does not admit any constantly bounded competitive ratio in the deterministic setting, we find that adding the possibility of reservation makes the problem constantly competitive. We give tight bounds for the whole range of $\alpha$ from $0$ to $1$.

翻译：在网上简单的背包问题项目中,以迭接方式提出,算法必须就每个项目决定是否拒绝或永久将其包括在背包中,而不了解其他实例。目标是尽可能完整地包装背包。在这项工作中,我们引入了将物品保留在固定部分(美元/阿尔法元)费用上的选择。算法可以支付这一部分,以便推迟到上次提出时才决定是否列入或拒绝这些物品。传统的在线简单背包问题并不承认在确定性环境下存在任何持续受约束的竞争比率,但我们发现,增加保留的可能性会使问题不断具有竞争力。我们给整个阿尔法元的严格界限从0美元到1美元。