English

The Popular Roommates problem

Data Structures and Algorithms 2018-04-10 v2

Abstract

We consider the popular matching problem in a roommates instance with strict preference lists. While popular matchings always exist in a bipartite instance, they need not exist in a roommates instance. The complexity of the popular matching problem in a roommates instance has been an open problem for several years and here we show it is NP-hard. A sub-class of max-size popular matchings called dominant matchings has been well-studied in bipartite graphs. We show that the dominant matching problem in a roommates instance is also NP-hard and this is the case even when the instance admits a stable matching.

Keywords

Cite

@article{arxiv.1804.00141,
  title  = {The Popular Roommates problem},
  author = {Telikepalli Kavitha},
  journal= {arXiv preprint arXiv:1804.00141},
  year   = {2018}
}

Comments

13 pages, 3 figures

R2 v1 2026-06-23T01:10:24.560Z