Online knapsack with removal and recourse

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2025-07-30 DOI:10.1016/j.jcss.2025.103697

Hans-Joachim Böckenhauer , Ralf Klasing , Tobias Mömke , Peter Rossmanith , Moritz Stocker , David Wehner

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引用次数: 0

Abstract

We analyze the competitive ratio of the proportional online knapsack problem with removal and limited recourse. In contrast to the classical online knapsack problem, packed items can be removed and a limited number of removed items can be re-inserted to the knapsack. The variant with removal only was analyzed by Iwama and Taketomi (ICALP, 2002). We show that even a single use of recourse can improve the performance of an algorithm. We give lower bounds for a constant number of

k \geq 1

uses of recourse in total, matching upper bounds for

1 \leq k \leq 3

, and a general upper bound for any value of k. For a variant where a constant number of

k \geq 1

uses of recourse can be used per step, we give tight bounds for all

k \geq 1

. We further look at a scenario where an algorithm is informed when the instance ends and give improved upper bounds in both variants for this case.

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在线背包与移除和追索权

我们分析了具有移除和有限追索权的比例在线背包问题的竞争率。与经典的在线背包问题相比，打包好的物品可以被移除，并且被移除的物品数量有限，可以重新插入背包。Iwama和Taketomi （ICALP, 2002）对仅去除的变异进行了分析。我们表明，即使是单次使用追索权也可以提高算法的性能。我们给出了总k≥1个追索权使用次数为常数的下界，1≤k≤3的匹配上界，以及任意k值的一般上界。对于每步可以使用k≥1个追索权使用次数为常数的变体，我们给出了所有k≥1的紧界。我们进一步研究这样一种场景，即在实例结束时通知算法，并在这种情况下给出两种变体的改进上界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.