Comparing Apples and Oranges: Query Trade-off in Submodular Maximization

Fast algorithms for submodular maximization problems have a vast potential use in applicative settings, such as machine learning, social networks, and economics. Though fast algorithms were known for some special cases, only recently such algorithms were considered in the general case of maximizing a monotone submodular function subject to a matroid independence constraint. The known fast algorithm matches the best possible approximation guarantee, while trying to reduce the number of value oracle queries the algorithm performs. Our main result is a new algorithm for this general case that establishes a surprising trade-off between two seemingly unrelated quantities: the number of value oracle queries and the number of matroid independence queries performed by the algorithm. Specifically, one can decrease the former by increasing the latter, and vice versa, while maintaining the best possible approximation guarantee. Such a trade-off is very useful since various applications might incur significantly diff...

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