对自私的垃圾箱包装的无政府状态的价格的新限制和部分惩罚

IF 0.9 4区数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Combinatorial Optimization Pub Date : 2024-12-04 DOI:10.1007/s10878-024-01239-2

Xiaowei Li, Peihai Liu, Xiwen Lu

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引用次数: 0

摘要

研究了具有部分惩罚的自私装箱问题。在这个问题中，一个物品的效用被定义为它所在的箱子的装载量。每个项目都扮演一个自私的代理人的角色，并希望最大化自己的效用。如果大小为\(s_i\)的物品移动到另一个垃圾箱，它必须支付\(\alpha s_{i}\)的部分惩罚，其中\(0<\alpha <1\)。我们证明了这个游戏的无政府状态的价格（PoA）至少是1.6424对于任何\(\alpha \in (0,1)\)。特别是，对于任何\(\alpha \in (\frac{2}{5},1)\)，这款游戏的PoA至少是\(5/3 \approx 1.6667\)。进一步，我们得到了PoA上\(h(\alpha ) \le 31/18 \approx 1.7222\)的一个新的上界。

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New bounds on the price of anarchy of selfish bin packing with partial punishment

The selfish bin packing with partial punishment is studied in this paper. In this problem, the utility of an item is defined as the load of the bin it is in. Each item plays the role of a selfish agent and wants to maximize its own utility. If an item with size \(s_i\) moves to another bin, it has to pay the partial punishment of \(\alpha s_{i}\), where \(0<\alpha <1\). We prove that the price of anarchy (PoA) of this game is at least 1.6424 for any \(\alpha \in (0,1)\). In particular, the PoA of this game is at least \(5/3 \approx 1.6667\) for any \(\alpha \in (\frac{2}{5},1)\). Furthermore, we obtain a new upper bound of \(h(\alpha ) \le 31/18 \approx 1.7222\) on the PoA.

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来源期刊

Journal of Combinatorial Optimization 数学-计算机：跨学科应用

CiteScore

2.00

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering. The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.