Popular matchings with weighted voters

Klaus Heeger; Ágnes Cseh

doi:10.1016/j.geb.2024.01.015

Popular matchings with weighted voters

Klaus Heeger, Ágnes Cseh

Department of Industrial Engineering and Management

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a natural generalization of the well-known POPULAR MATCHING problem where every vertex has a weight. We call a matching M more popular than matching M^′ if the weight of vertices preferring M to M^′ is larger than the weight of vertices preferring M^′ to M. For this case, we show that it is NP-hard to find a popular matching. Our main result is a polynomial-time algorithm that delivers a popular matching or a proof for its non-existence in instances where all vertices on one side have weight c for some c>3 and all vertices on the other side have weight 1.

Original language	English
Pages (from-to)	300-328
Number of pages	29
Journal	Games and Economic Behavior
Volume	144
DOIs	https://doi.org/10.1016/j.geb.2024.01.015
State	Published - 1 Mar 2024

Keywords

Algorithm
Complexity
Popular matching
Stable matching

ASJC Scopus subject areas

Finance
Economics and Econometrics

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10.1016/j.geb.2024.01.015

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title = "Popular matchings with weighted voters",

abstract = "We consider a natural generalization of the well-known POPULAR MATCHING problem where every vertex has a weight. We call a matching M more popular than matching M′ if the weight of vertices preferring M to M′ is larger than the weight of vertices preferring M′ to M. For this case, we show that it is NP-hard to find a popular matching. Our main result is a polynomial-time algorithm that delivers a popular matching or a proof for its non-existence in instances where all vertices on one side have weight c for some c>3 and all vertices on the other side have weight 1.",

keywords = "Algorithm, Complexity, Popular matching, Stable matching",

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AU - Cseh, Ágnes

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AB - We consider a natural generalization of the well-known POPULAR MATCHING problem where every vertex has a weight. We call a matching M more popular than matching M′ if the weight of vertices preferring M to M′ is larger than the weight of vertices preferring M′ to M. For this case, we show that it is NP-hard to find a popular matching. Our main result is a polynomial-time algorithm that delivers a popular matching or a proof for its non-existence in instances where all vertices on one side have weight c for some c>3 and all vertices on the other side have weight 1.

KW - Algorithm

KW - Complexity

KW - Popular matching

KW - Stable matching

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JO - Games and Economic Behavior

JF - Games and Economic Behavior

ER -

Popular matchings with weighted voters

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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