  Submodular optimization has received significant attention in both practice
and theory, as a wide array of problems in machine learning, auction theory,
and combinatorial optimization have submodular structure. In practice, these
problems often involve large amounts of data, and must be solved in a
distributed way. One popular framework for running such distributed algorithms
is MapReduce. In this paper, we present two simple algorithms for cardinality
constrained submodular optimization in the MapReduce model: the first is a
$(1/2-o(1))$-approximation in 2 MapReduce rounds, and the second is a
$(1-1/e-\epsilon)$-approximation in $\frac{1+o(1)}{\epsilon}$ MapReduce rounds.
