New algorithms for distributed submodular maximization.

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as submodular maximization problems. In many of these applications, the amount of data collected is quite large and it is growing at a very fast pace. For example, the wide deployment of sensors has led to the collection of large amounts of measurements of the physical world. Similarly, medical data and human activity data are being captured and stored at an ever increasing rate and level of detail. This data is often high-dimensional and complex, and it needs to be stored and/or processed in a distributed fashion. Following a recent line of work, we present here parallel algorithms for these problems, and analyze the compromise between quality of the solutions obtained and the amount of computational overhead. On the one hand, we develop strategies for bringing existing algorithms for constrained submodular maximization in the sequential setting to the distributed setting. The algorithms presented achieve constant approximation factors in two rounds, and near optimal approximation ratios in only a constant number of rounds. Our techniques also give a fast sequential algorithm for non-monotone maximization subject to a matroid constraint. On the other hand, for unconstrained submodular maximization, we devise parallel algorithms combining naive random sampling and Double Greedy steps, and investigate how much the quality of the solutions degrades with less coordination