Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation
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In this work we give two new algorithms that use similar techniques for (non-monotone) submodular function maximization subject to a cardinality constraint. The first is an offline fixed parameter tractable algorithm that guarantees a 0.539-approximation for all non-negative submodular functions. The second algorithm works in the random-order streaming model. It guarantees a (1/2+c)-approximation for symmetric functions, and we complement it by showing that no space-efficient algorithm can beat 1/2 for asymmetric functions. To the best of our knowledge this is the first provable separation between symmetric and asymmetric submodular function maximization.
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