  We investigate the performance of a deterministic GREEDY algorithm for the
problem of maximizing functions under a partition matroid constraint. We
consider non-monotone submodular functions and monotone subadditive functions.
Even though constrained maximization problems of monotone submodular functions
have been extensively studied, little is known about greedy maximization of
non-monotone submodular functions or monotone subadditive functions.
  We give approximation guarantees for GREEDY on these problems, in terms of
the curvature. We find that this simple heuristic yields a strong approximation
guarantee on a broad class of functions.
  We discuss the applicability of our results to three real-world problems:
Maximizing the determinant function of a positive semidefinite matrix, and
related problems such as the maximum entropy sampling problem, the constrained
maximum cut problem on directed graphs, and combinatorial auction games.
  We conclude that GREEDY is well-suited to approach these problems. Overall,
we present evidence to support the idea that, when dealing with constrained
maximization problems with bounded curvature, one needs not search for
approximate) monotonicity to get good approximate solutions.
