  We analyze different re-ranking algorithms for diversification and show that
majority of them are based on maximizing submodular/modular functions from the
class of parameterized concave/linear over modular functions. We study the
optimality of such algorithms in terms of the `total curvature'. We also show
that by adjusting the hyperparameter of the concave/linear composition to
trade-off relevance and diversity, if any, one is in fact tuning the `total
curvature' of the function for relevance-diversity trade-off.
