Title: Parallel Double Greedy Submodular Maximization”, Pan, Jegelka, Gonzalez, Bradley, Jordan

Authors: Xinghao Pan, Stefanie Jegelka, Joseph Gonzalez, Joseph Bradley, Michael I. Jordan

Abstract

Many machine learning problems can be reduced to the maximization of sub- modular functions. Although well understood in the serial setting, the parallel maximization of submodular functions remains an open area of research with recent results [1] only addressing monotone functions. The optimal algorithm for maximizing the more general class of non-monotone submodular functions was introduced by Buchbinder et al. [2] and follows a strongly serial double-greedy logic and program analysis. In this work, we propose two methods to parallelize the double-greedy algorithm. The first, coordination-free approach emphasizes speed at the cost of a weaker approximation guarantee. The second, concurrency control approach guarantees a tight 1/2-approximation, at the quantifiable cost of additional coordination and reduced parallelism. As a consequence we explore the tradeoff space between guaranteed performance and objective optimality. We implement and evaluate both algorithms on multi-core hardware and billion edge graphs, demonstrating both the scalability and tradeoffs of each approach.

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