通过斯宾纳引理连接公平蛋糕分割

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2024-12-27 DOI:10.1016/j.ipl.2024.106554

Umang Bhaskar , A.R. Sricharan , Rohit Vaish

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引用次数: 0

摘要

我们研究了公平切蛋糕的问题，其中每个智能体接收到一块相连的蛋糕。如果蛋糕的分配是公平的，那就被认为是公平的，这意味着所有的代理都从分配给他们的那块蛋糕中获得了相同的价值。先前的工作已经利用各种技术建立了具有非负估值的代理的连接公平分配的存在。我们利用Sperner引理给出了这个结果的一个简单证明。我们的证明将已知的关联公平划分的存在性结果扩展到更一般的估值类别，包括具有外部性的非负估值，以及几个有趣的一般（可能是负的）估值子类。

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Connected equitable cake division via Sperner's lemma

We study the problem of fair cake-cutting where each agent receives a connected piece of the cake. A division of the cake is deemed fair if it is equitable, which means that all agents derive the same value from their assigned piece. Prior work has established the existence of a connected equitable division for agents with nonnegative valuations using various techniques. We provide a simple proof of this result using Sperner's lemma. Our proof extends known existence results for connected equitable divisions to significantly more general classes of valuations, including nonnegative valuations with externalities, as well as several interesting subclasses of general (possibly negative) valuations.

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来源期刊

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.