Popular Matching in Roommates Setting Is NP-hard

Sushmita Gupta; Pranabendu Misra; Saket Saurabh; Meirav Zehavi

doi:https://doi.org/10.1145/3442354

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 journal › Article › peer-review

Abstract

An input to the POPULAR MATCHING problem, in the roommates setting (as opposed to the marriage setting), consists of a graph G (not necessarily bipartite) 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 vertices prefer their matched status in M (in terms of their preferences) over their matched status in M∗. In this article, 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
Article number	9
Journal	ACM Transactions on Computation Theory
Volume	13
Issue number	2
DOIs	https://doi.org/10.1145/3442354
State	Published - 1 Jun 2021

Keywords

NP-hard
Popular matching

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computational Theory and Mathematics

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https://doi.org/10.1145/3442354

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AB - An input to the POPULAR MATCHING problem, in the roommates setting (as opposed to the marriage setting), consists of a graph G (not necessarily bipartite) 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 vertices prefer their matched status in M (in terms of their preferences) over their matched status in M∗. In this article, 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

Keywords

All Science Journal Classification (ASJC) codes

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