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

04/14/2021

∙

by   Alan Kuhnle, et al.

∙

0

∙

share

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.