Submodular Optimization in the MapReduce Model

TL;DR

This paper introduces two efficient distributed algorithms for submodular optimization within the MapReduce framework, achieving near-optimal solutions with minimal rounds, suitable for large-scale data processing.

Contribution

It presents the first simple algorithms for cardinality constrained submodular optimization in MapReduce with provable approximation guarantees.

Findings

Achieves a (1/2-o(1))-approximation in 2 rounds

Achieves a (1-1/e-ε)-approximation in (1+o(1))/ε rounds

Algorithms are simple and practical for large-scale distributed data

Abstract

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.