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Streaming Algorithms for Cardinality-Constrained Maximization of Non-Monotone Submodular Functions in Linear Time

04/14/2021
by   Alan Kuhnle, et al.
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For the problem of maximizing a nonnegative, (not necessarily monotone) submodular function with respect to a cardinality constraint, we propose deterministic algorithms with linear time complexity; these are the first algorithms to obtain constant approximation ratio with high probability in linear time. Our first algorithm is a single-pass streaming algorithm that obtains ratio 9.298 + ϵ and makes only two queries per received element. Our second algorithm is a multi-pass streaming algorithm that obtains ratio 4 + ϵ. Empirically, the algorithms are validated to use fewer queries than and to obtain comparable objective values to state-of-the-art algorithms.

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