Popularity on the Roommate Diversity Problem

A recently introduced restricted variant of the multidimensional stable roommates problem is the roommate diversity problem. We study the roommate diversity problem with the notion of popularity. We show that for the roommate diversity problem with the room size fixed to 2, a popular partitioning of agents is guaranteed to exist and can be computed in polynomial time. By contrast, when there are no restrictions on the room size of a roommate diversity game, a popular partitioning may fail to exist and the problem becomes intractable.