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Submodular optimization has received significant attention in both practiceand theory, as a wide array of problems in machine learning, auction theory,and combinatorial optimization have submodular structure. In practice, theseproblems often involve large amounts of data, and must be solved in adistributed way. One popular framework for running such distributed algorithmsis MapReduce. In this paper, we present two simple algorithms for cardinalityconstrained 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.

Submodular Optimization in the MapReduce Model