Simultaenous Sieves: A Deterministic Streaming Algorithm for Non-Monotone Submodular Maximization

• URL: http://arxiv.org/abs/2010.14367v3
• Date: Mon, 2 Nov 2020 15:35:57 GMT
• Title: Simultaenous Sieves: A Deterministic Streaming Algorithm for Non-Monotone Submodular Maximization
• Authors: Alan Kuhnle
• Abstract summary: We present a deterministic, single-pass streaming algorithm for the problem of maximizing a submodular function, not necessarily a monotone, with respect to a cardinality constraint. For a monotone, single-pass streaming algorithm, our algorithm achieves in time an improvement of the best approximation factor from $1/9$ of previous literature to $approx 0.2689$.
• Score: 16.346069386394703
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we present a combinatorial, deterministic single-pass streaming algorithm for the problem of maximizing a submodular function, not necessarily monotone, with respect to a cardinality constraint (SMCC). In the case the function is monotone, our algorithm reduces to the optimal streaming algorithm of Badanidiyuru et al. (2014). In general, our algorithm achieves ratio $\alpha / (1 + \alpha) - \varepsilon$, for any $\varepsilon > 0$, where $\alpha$ is the ratio of an offline (deterministic) algorithm for SMCC used for post-processing. Thus, if exponential computation time is allowed, our algorithm deterministically achieves nearly the optimal $1/2$ ratio. These results nearly match those of a recently proposed, randomized streaming algorithm that achieves the same ratios in expectation. For a deterministic, single-pass streaming algorithm, our algorithm achieves in polynomial time an improvement of the best approximation factor from $1/9$ of previous literature to $\approx 0.2689$.

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