  Bipartite b-matching, where agents on one side of a market are matched to one
or more agents or items on the other, is a classical model that is used in
myriad application areas such as healthcare, advertising, education, and
general resource allocation. Traditionally, the primary goal of such models is
to maximize a linear function of the constituent matches (e.g., linear social
welfare maximization) subject to some constraints. Recent work has studied a
new goal of balancing whole-match diversity and economic efficiency, where the
objective is instead a monotone submodular function over the matching. Basic
versions of this problem are solvable in polynomial time. In this work, we
prove that the problem of simultaneously maximizing diversity along several
features (e.g., country of citizenship, gender, skills) is NP-hard. To address
this problem, we develop the first combinatorial algorithm that constructs
provably-optimal diverse b-matchings in pseudo-polynomial time. We also provide
a Mixed-Integer Quadratic formulation for the same problem and show that our
method guarantees optimal solutions and takes less computation time for a
reviewer assignment application.
