An Optimal Streaming Algorithm for Non-monotone Submodular Maximization
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We study the problem of maximizing a non-monotone submodular function subject to a size constraint in the streaming model. Our main contribution is a single-pass streaming algorithm that uses k·poly(1/ϵ) memory, where k is the size constraint. At the end of the stream, we post-process the output of the algorithm using any offline algorithm for submodular maximization, and we obtain a solution whose approximation guarantee is α/1+α-ϵ, where α is the approximation of the offline algorithm. If we use an exact (exponential time) post-processing algorithm, we obtain a 1/2-ϵ approximation, almost matching the lower bound of [Alaluf-Feldman, 2019]. If we post-process with the algorithm of [Buchbinder-Feldman, Math of OR 2019] that achieves the currently best approximation guarantee α=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to [Alaluf-Feldman, 2019]. In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time.
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