Work

Solving the Maximum Popular Matching Problem with Matroid Constraints

Year: 2024

Type: article

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 [Formula: see text]-matching case.

Source: SIAM Journal on Discrete Mathematics

DOI: 10.1137/23m1579911

Authors: Gergely Csáji, Tamás Király, Yu Yokoi

Institutions: Eötvös Loránd University, ELTE Centre for Economic and Regional Studies, Hungarian Research Network, Tokyo Institute of Technology

Language: English

Topic: Game Theory and Voting Systems

Subfield: Economics and Econometrics

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green