Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M ′ with the property that more applicants prefer their allocation in M ′ to their allocation in M . In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases.
Biró et al. REF developed an algorithm to test popularity of a matching in these two settings and proved that determining whether a popular matching exists in these settings is an NP-hard problem when ties are allowed.
Popular matchings in the marriage and roommates problems
CIAC
Computer Science