Popular matching in roommates setting is NP-hard

Sushmita Gupta, Pranabendu Misra, Saket Saurabh, Meirav Zehavi

Research output: Contribution to conferencePaperpeer-review


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 languageAmerican English
Number of pages13
StatePublished - 1 Jan 2019
Event30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States
Duration: 6 Jan 20199 Jan 2019


Conference30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
Country/TerritoryUnited States
CitySan Diego

All Science Journal Classification (ASJC) codes

  • Software
  • General Mathematics


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