A New Framework for Distributed Submodular Maximization

TL;DR

This paper introduces a framework that adapts sequential algorithms for submodular maximization to distributed settings, achieving near-optimal solutions efficiently with fewer rounds.

Contribution

It presents a novel framework that converts existing sequential algorithms into distributed algorithms with improved approximation ratios and fewer communication rounds.

Findings

Achieves near-optimal approximation ratios in a constant number of rounds

Provides a fast sequential algorithm for non-monotone maximization under matroid constraints

Reduces the number of rounds compared to previous distributed algorithms

Abstract

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing distributed algorithms for these problems. However, these results suffer from high number of rounds, suboptimal approximation ratios, or both. We develop a framework for bringing existing algorithms in the sequential setting to the distributed setting, achieving near optimal approximation ratios for many settings in only a constant number of MapReduce rounds. Our techniques also give a fast sequential algorithm for non-monotone maximization subject to a matroid constraint.