Solving the Maximum Popular Matching Problem with Matroid Constraints

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-07-24 DOI:10.1137/23m1579911

Gergely Csáji, Tamás Király, Yu Yokoi

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2226-2242, September 2024.
Abstract. We consider the problem of finding a maximum popular matching in a many-to-many matching setting with two-sided preferences and matroid constraints. This problem was proposed by Kamiyama [Theoret. Comput. Sci., 809 (2020), pp. 265–276] and solved in the special case where matroids are base orderable. Utilizing a newly shown matroid exchange property, we show that the problem is tractable for arbitrary matroids. We further investigate a different notion of popularity, where the agents vote with respect to lexicographic preferences, and show that both existence and verification problems become coNP-hard even in the [math]-matching case.

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利用矩阵约束解决最大热门匹配问题

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2226-2242 页，2024 年 9 月。摘要我们考虑的问题是在多对多匹配设置中寻找具有双面偏好和矩阵约束的最大流行匹配。这个问题是由 Kamiyama [Theoret.利用新显示的矩阵交换属性，我们证明了这个问题对于任意矩阵都是可行的。我们进一步研究了一种不同的流行度概念，即代理人根据词典偏好进行投票，结果表明，即使在 [math] 匹配的情况下，存在性和验证问题都变得 coNP-hard。

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

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.