Improved Deterministic Algorithms for Non-monotone Submodular Maximization

Xiaoming Sun; Jialin Zhang; Shuo Zhang; Zhijie Zhang

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arXiv · 2208.14388

Improved Deterministic Algorithms for Non-monotone Submodular Maximization

Xiaoming Sun·Jialin Zhang·Shuo Zhang·Zhijie Zhang

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Abstract

Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the state-of-the-art algorithms are randomized. There remain non-negligible gaps with respect to approximation ratios between deterministic and randomized algorithms in submodular maximization. In this paper, we propose deterministic algorithms with improved approximation ratios for non-monotone submodular maximization. Specifically, for the matroid constraint, we provide a deterministic $0.283-o(1)$ approximation algorithm, while the previous best deterministic algorithm only achieves a $1/4$ approximation ratio. For the knapsack constraint, we provide a deterministic $1/4$ approximation algorithm, while the previous best deterministic algorithm only achieves a $1/6$ approximation ratio. For the linear packing constraints with large widths, we provide a deterministic $1/6-\epsilon$ approximation algorithm. To the best of our knowledge, there is currently no deterministic approximation algorithm for the constraints.

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BibTeX RIS

Xiaoming Sun, Jialin Zhang, Shuo Zhang, Zhijie Zhang. 2022-08-30. Improved Deterministic Algorithms for Non-monotone Submodular Maximization. https://arxiv.org/abs/2208.14388

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