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Two-stage submodular maximization under curvature

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Abstract

The concept of submodularity has wide applications in data science, artificial intelligence, and machine learning, providing a boost to the investigation of new ideas, innovative techniques, and creative algorithms to solve different submodular optimization problems arising from a diversity of applications. However pure submodular problems only represent a small portion of the problems we are facing in real life applications. In this paper, we further discuss the two-stage submodular maximization problem under a \(\ell \)-matroid constraint. We design an approximation algorithm with constant approximation ratio with respect to the curvature, which improves the previous bound. In addition, we generalize our algorithm to the two-stage submodular maximization problem under a \(\ell \)-exchange system constraint.

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Acknowledgements

The authors would like to thank the referees for giving this paper a careful reading and many valuable comments and useful suggestions.

Funding

The research is supported by NSFC (Nos.12271259, 11971349, 12101314, 12131003), Qinglan Project, Natural Science Foundation of Jiangsu Province (No. BK20200723), and Jiangsu Province Higher Education Foundation (No.20KJB110022).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, People’s Republic of China

    Yanzhi Li

  2. Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Zhicheng Liu

  3. School of Mathematical Science & Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Chuchu Xu, Xiaoyan Zhang & Hong Chang

  4. Huawei Technologies Co. Ltd. Theory Lab, Central Research Institute, 2012 Labs, Hongkong, 9990777, People’s Republic of China

    Ping Li

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  1. Yanzhi Li
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  2. Zhicheng Liu
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  3. Chuchu Xu
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  4. Ping Li
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  5. Xiaoyan Zhang
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  6. Hong Chang
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Correspondence to Hong Chang.

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A preliminary version of this paper appeared in Proceedings of the 15th Annual International Conference on Combinatorial Optimization and Applications (COCOA).

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Li, Y., Liu, Z., Xu, C. et al. Two-stage submodular maximization under curvature. J Comb Optim 45, 77 (2023). https://doi.org/10.1007/s10878-023-01001-0

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  • DOI: https://doi.org/10.1007/s10878-023-01001-0

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