@article{f67e6e2b82d3455f9cf8f28b5bf07911,
title = "Popular Matching in Roommates Setting Is NP-hard",
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.",
keywords = "NP-hard, Popular matching",
author = "Sushmita Gupta and Pranabendu Misra and Saket Saurabh and Meirav Zehavi",
note = "Funding Information: *A preliminary version of this paper appeared in the proceedings of SODA 2019 [13]. Saket Saurabh received funding from European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant no. 819416), and Swarnajayanti Fellowship grant DST/SJF/MSA-01/2017-18. Meirav Zehavi received funding from the Israel Science Foundation (ISF) under the Individual Research Grant program (grant no. 1176/18). Authors{\textquoteright} addresses: S. Gupta, The Institute of Mathematical Sciences, IV Cross Road, CIT Campus, Taramani, Chennai 600 113, India; email: sushmitagupta@imsc.res.in; P. Misra, Max Planck Institute for Informatics, Campus E1 4, Saarland University, 66123 Saarbrucken, Germany; email: pmisra@mpi-inf.mpg.de; S. Saurabh, The Institute of Mathematical Sciences, IV Cross Road, CIT Campus, Taramani, Chennai 600 113, India; email: saket@imsc.res.in; M. Zehavi, Department of Computer Science, Ben-Gurion University of the Negev, Beersheba, Israel; email: meiravze@bgu.ac.il. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. {\textcopyright} 2021 Association for Computing Machinery. 1942-3454/2021/03-ART9 $15.00 https://doi.org/10.1145/3442354 Funding Information: A preliminary version of this paper appeared in the proceedings of SODA 2019 [13]. Saket Saurabh received funding from European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant no. 819416), and Swarnajayanti Fellowship grant DST/SJF/MSA-01/2017-18. Meirav Zehavi received funding from the Israel Science Foundation (ISF) under the Individual Research Grant program (grant no. 1176/18) Publisher Copyright: {\textcopyright} 2021 ACM.",
year = "2021",
month = jun,
day = "1",
doi = "10.1145/3442354",
language = "English",
volume = "13",
journal = "ACM Transactions on Computation Theory",
issn = "1942-3454",
publisher = "Association for Computing Machinery (ACM)",
number = "2",
}