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Submodular Maximization with Bounded Marginal Values

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Parallel and Distributed Computing, Applications and Technologies (PDCAT 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12606))

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Abstract

We study the problem of maximizing non-monotone submodular functions subject to a p-independence system constraint. Although the submodularity ratio has been well-studied in maximizing set functions under monotonic scenario, the defined parameter may bring hardness of approximation for the maximization of set functions in the non-monotonic case. In this work, utilizing a lower bound for the marginal values, we investigate the Repeated Greedy introduced by (Feldman et al. 2017) and obtain a parameterized performance guarantee for the above constrained submodular maximization problem.

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Acknowledgements

The third author is supported by Scientific Research Project of Beijing Municipal Education Commission (No. KM201910005012) and the National Natural Science Foundation of China (No. 11971046). The fourth author is supported by the National Natural Science Foundation of China (No. 11871081).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy Sciences, Beijing, 100049, People’s Republic of China

    Ruiqi Yang & Suixiang Gao

  2. Department of Operations Research and Information Engineering, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Changjun Wang

  3. School of Computer Science and Technology, Shandong Jianzhu University, Jinan, 250101, People’s Republic of China

    Dongmei Zhang

Authors
  1. Ruiqi Yang
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  2. Suixiang Gao
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  3. Changjun Wang
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  4. Dongmei Zhang
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Corresponding author

Correspondence to Changjun Wang .

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Editors and Affiliations

  1. Shenzhen Institutes of Advanced Technology, Shenzhen, China

    Yong Zhang

  2. Shenzhen Institutes of Advanced Technology, Shenzhen, China

    Yicheng Xu

  3. Griffith University, Gold Coast, QLD, Australia

    Hui Tian

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Yang, R., Gao, S., Wang, C., Zhang, D. (2021). Submodular Maximization with Bounded Marginal Values. In: Zhang, Y., Xu, Y., Tian, H. (eds) Parallel and Distributed Computing, Applications and Technologies. PDCAT 2020. Lecture Notes in Computer Science(), vol 12606. Springer, Cham. https://doi.org/10.1007/978-3-030-69244-5_31

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  • DOI: https://doi.org/10.1007/978-3-030-69244-5_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-69243-8

  • Online ISBN: 978-3-030-69244-5

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