  We study minimum entropy submodular optimization, a common generalization of
the minimum entropy set cover problem, studied earlier by Cardinal et al., and
the submodular set cover problem.
  We give a general bound of the approximation performance of the greedy
algorithm using an approach that can be interpreted in terms of a particular
type of biased network flows. As an application we rederive known results for
the Minimum Entropy Set Cover and Minimum Entropy Orientation problems, and
obtain a nontrivial bound for a new problem called the Minimum Entropy Spanning
Tree problem.
  The problem can be applied to (and is partly motivated by) the definition of
worst-case approaches to fairness in concave cooperative games, similar to the
notion of price of anarchy in noncooperative settings.
