Finding strongly popular b-matchings in bipartite graphs

The computational complexity of the bipartite popular matching problem depends on how indifference appears in the preference lists. If one side has strict preferences while nodes on the other side are all indifferent (but prefer to be matched), then a popular matching can be found in polynomial time [Cseh, Huang, Kavitha, 2015]. However, as the same paper points out, the problem becomes NP-complete if nodes with strict preferences are allowed on both sides and indifferent nodes are allowed on one side. We show that the problem of finding a strongly popular matching is polynomial-time solvable even in the latter case. Our result also extends to the many-to-many version, i.e. the strongly popular b-matching problem.