具有加法三元估值的少数代理商的EF1的价格

IF 0.9 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2025-07-30 DOI:10.1016/j.orl.2025.107351

Maria Kyropoulou, Alexandros A. Voudouris

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引用次数: 0

摘要

我们考虑了一个资源分配问题，agent对一组不可分割的物品具有附加的三元估值，并将无嫉妒的价格绑定到一个物品（EF1）分配。对于大量的n个代理，我们给出了Ω(n)的下界，这意味着EF1的价格并不比代理具有一般的次加性估值时更好。然后，我们将重点放在具有少量代理的实例上，并表明当n=2时，EF1的价格为12/11，当n=3时，EF1的价格在1.2和1.256之间。

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The price of EF1 for few agents with additive ternary valuations

We consider a resource allocation problem with agents that have additive ternary valuations for a set of indivisible items, and bound the price of envy-free up to one item (EF1) allocations. For a large number n of agents, we show a lower bound of

Ω (\sqrt{n})

, implying that the price of EF1 is no better than when the agents have general subadditive valuations. We then focus on instances with few agents and show that the price of EF1 is 12/11 for

n = 2

, and between 1.2 and 1.256 for

n = 3

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.