  In the submodular ranking (SR) problem, the input consists of a set of
submodular functions defined on a ground set of elements. The goal is to order
elements for all the functions to have value above a certain threshold as soon
on average as possible, assuming we choose one element per time. The problem is
flexible enough to capture various applications in machine learning, including
decision trees.
  This paper considers the min-max version of SR where multiple instances share
the ground set. With the view of each instance being associated with an agent,
the min-max problem is to order the common elements to minimize the maximum
objective of all agents -- thus, finding a fair solution for all agents. We
give approximation algorithms for this problem and demonstrate their
effectiveness in the application of finding a decision tree for multiple
agents.
