A New Framework for Distributed Submodular Maximization
This work addresses efficiency and performance issues in distributed optimization for machine learning tasks like clustering and summarization, offering a significant improvement over existing methods.
The paper tackles the problem of high round complexity and suboptimal approximation ratios in distributed submodular maximization by developing a framework that adapts sequential algorithms to distributed settings, achieving near-optimal approximation ratios in a constant number of MapReduce rounds and providing a fast sequential algorithm for non-monotone maximization under matroid constraints.
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.