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arXiv · 2204.11149

Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond $1/2$-Approximation

Aviad Rubinstein·Junyao Zhao
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Abstract

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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Aviad Rubinstein, Junyao Zhao. 2022-04-23. Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond $1/2$-Approximation. https://arxiv.org/abs/2204.11149

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