Popular Matching in Roommates Setting is NP-hard

Sushmita Gupta; Pranabendu Misra; Saket Saurabh; Meirav Zehavi

Popular Matching in Roommates Setting is NP-hard

Data Structures and Algorithms 2018-03-28 v1 Computational Complexity Computer Science and Game Theory

Authors: Sushmita Gupta , Pranabendu Misra , Saket Saurabh , Meirav Zehavi

Abstract

An input to the Popular Matching problem, in the roommates setting, consists of a graph $G$ and 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 $M^\star$ such that there is no matching $M$ where more people are happier with $M$ than with $M^\star$ . 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, explicitly asked over the last decade.

Keywords

stable matching computational complexity

Cite

@article{arxiv.1803.09370,
  title  = {Popular Matching in Roommates Setting is NP-hard},
  author = {Sushmita Gupta and Pranabendu Misra and Saket Saurabh and Meirav Zehavi},
  journal= {arXiv preprint arXiv:1803.09370},
  year   = {2018}
}

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20 pages, 7 figures

Popular Matching in Roommates Setting is NP-hard

Abstract

Keywords

Cite

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