  We consider many-to-one matching problems, where one side corresponds to
applicants who have preferences and the other side to houses who do not have
preferences. We consider two different types of this market: one, where the
applicants have capacities, and one where the houses do. First, we answer an
open question by Manlove and Sng (2006) (partly solved Paluch (2014) for
preferences with ties), that is, we show that deciding if a popular matching
exists in the house allocation problem, where agents have capacities is NP-hard
for previously studied versions of popularity. Then, we consider the other
version, where the houses have capacities. We study how to optimally increase
the capacities of the houses to obtain a matching satisfying multiple
optimality criteria, like popularity, Pareto-optimality and perfectness. We
consider two common optimality criteria, one aiming to minimize the sum of
capacity increases of all houses and the other aiming to minimize the maximum
capacity increase of any school. We obtain a complete picture in terms of
computational complexity and some algorithms.
