  We consider the problem of computing a matching in a bipartite graph in the
presence of one-sided preferences. There are several well studied notions of
optimality which include pareto optimality, rank maximality, fairness and
popularity. In this paper, we conduct an in-depth experimental study comparing
different notions of optimality based on a variety of metrics like cardinality,
number of rank-1 edges, popularity, to name a few. Observing certain
shortcomings in the standard notions of optimality, we propose an algorithm
which maximizes an alternative metric called the Area under Profile Curve ratio
(AUPCR). To the best of our knowledge, the AUPCR metric was used earlier but
there is no known algorithm to compute an AUPCR maximizing matching. Finally,
we illustrate the superiority of the AUPCR-maximizing matching by comparing its
performance against other optimal matchings on synthetic instances modeling
real-world data.
