Welfare loss in connected resource allocation

IF 1.1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2026-05-31 Epub Date: 2026-01-19 DOI:10.1016/j.dam.2026.01.007

Xiaohui Bei , Alexander Lam , Xinhang Lu , Warut Suksompong

引用次数: 0

Abstract

We study the allocation of indivisible items that form an undirected graph and investigate the worst-case welfare loss when requiring that each agent must receive a connected subgraph. Our focus is on both egalitarian and utilitarian welfare. Specifically, we introduce the concept of egalitarian (resp., utilitarian) price of connectivity, which captures the worst-case ratio between the optimal egalitarian (resp., utilitarian) welfare among all allocations and that among connected allocations. We provide tight or asymptotically tight bounds on the price of connectivity for several large classes of graphs in the case of two agents—including graphs with vertex connectivity 1 or 2 and complete bipartite graphs—as well as for paths, stars, and cycles in the general case where the number of agents can be arbitrary.

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关联资源配置中的福利损失

我们研究了组成无向图的不可分割项目的分配，并研究了当要求每个智能体必须接收一个连通子图时的最坏情况下的福利损失。我们的重点是平等主义和功利主义的福利。具体来说，我们引入了平等主义（平等主义）的概念。（如功利主义）的连接价格，它捕捉了最优平均主义（如功利主义）与最坏情况之间的比率。所有分配中的福利和相关分配中的福利。我们为几个大型图类在两个智能体的情况下的连通性价格提供了紧密或渐进的紧密边界——包括顶点连通性为1或2的图和完全二部图——以及在智能体数量可以任意的一般情况下的路径、星形和循环。

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

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.