Popular Matching in Roommates Setting Is NP-hard

Sushmita Gupta, Pranabendu Misra, Saket Saurabh, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number9
JournalACM Transactions on Computation Theory
Issue number2
StatePublished - 1 Jun 2021


  • NP-hard
  • Popular matching

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Theory and Mathematics


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