Popular matching in roommates setting is NP-hard

Sushmita Gupta; Pranabendu Misra; Saket Saurabh; Meirav Zehavi

doi:https://doi.org/10.1137/1.9781611975482.174

Popular matching in roommates setting is NP-hard

Sushmita Gupta, Pranabendu Misra, Saket Saurabh, Meirav Zehavi

Department of Computer Science

Ben-Gurion University of the Negev

Research output: Contribution to conference › Paper › peer-review

Abstract

An input to the Popular Matching problem, in the roommates setting, consists of a graph G where each vertex ranks its neighbors in strict order, known as its preference. In the Popular Matching problem the objective is to test whether there exists a matching M^?such that there is no matching M where more people (vertices) are happier (in terms of the preferences) with M than with M^?. In this paper we settle the computational complexity of the Popular Matching problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly and explicitly asked over the last decade.

Original language	American English
Pages	2810-2822
Number of pages	13
DOIs	https://doi.org/10.1137/1.9781611975482.174
State	Published - 1 Jan 2019
Event	30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States Duration: 6 Jan 2019 → 9 Jan 2019

Conference

Conference	30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
Country/Territory	United States
City	San Diego
Period	6/01/19 → 9/01/19

All Science Journal Classification (ASJC) codes

Software
General Mathematics

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https://doi.org/10.1137/1.9781611975482.174

Cite this

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AB - An input to the Popular Matching problem, in the roommates setting, consists of a graph G where each vertex ranks its neighbors in strict order, known as its preference. In the Popular Matching problem the objective is to test whether there exists a matching M?such that there is no matching M where more people (vertices) are happier (in terms of the preferences) with M than with M?. In this paper we settle the computational complexity of the Popular Matching problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly and explicitly asked over the last decade.

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Popular matching in roommates setting is NP-hard

Abstract

Conference

All Science Journal Classification (ASJC) codes

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