Submodular Optimization in the MapReduce Model
Paul Liu, J. Vondrák · arXiv (Cornell University) · 2018
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 $(1-1/e-ε)$-approximation in $\frac{1+o(1)}ε$ MapReduce rounds.