Diverse fair allocations: Complexity and algorithms

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-08-24 DOI:10.1016/j.dam.2024.07.045

Harshil Mittal, Saraswati Nanoti, Aditi Sethia

引用次数: 0

Abstract

In this work, we initiate the study of diversity of solutions in the context of fair division of indivisible goods. In particular, we explore the notions of disjoint, distinct and symmetric allocations and study their complexity in terms of the fairness notions of envy-freeness and equitability up to one item. We show that for binary valuations, the above problems are polynomial time solvable. In contrast we show NP-hardness of disjoint and symmetric case, when the valuations are additive.

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多样化的公平分配：复杂性与算法

在这项工作中，我们开始研究不可分割物品公平分配中解决方案的多样性。特别是，我们探讨了不相交、不同和对称分配的概念，并从无嫉妒和公平性概念的角度研究了它们的复杂性。我们证明，对于二进制估值，上述问题都可以在多项式时间内解决。相反，当估值为加法时，我们证明了不相交和对称情况下的 NP 难度。

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.