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Non-submodular maximization on massive data streams

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Abstract

The problem of maximizing a normalized monotone non-submodular set function subject to a cardinality constraint arises in the context of extracting information from massive streaming data. In this paper, we present four streaming algorithms for this problem by utilizing the concept of diminishing-return ratio. We analyze these algorithms to obtain the corresponding approximation ratios, which generalize the previous results for the submodular case. The numerical experiments show that our algorithms have better solution quality and competitive running time when compared to an existing algorithm.

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Acknowledgements

We would like to appreciate the anonymous reviewers and editors whose valuable comments and suggestions have greatly improved the quality of this paper. The second author is supported by Natural Science Foundation of China (No. 11531014). The third author is supported by National Natural Science Foundation of China (Nos. 61433012 and U1435215). The fourth author is supported by Natural Science Foundation of China (No. 11871081).

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Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Yijing Wang & Dachuan Xu

  2. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, People’s Republic of China

    Yishui Wang

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

    Dongmei Zhang

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  1. Yijing Wang
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  2. Dachuan Xu
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  3. Yishui Wang
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  4. Dongmei Zhang
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Correspondence to Dongmei Zhang.

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Wang, Y., Xu, D., Wang, Y. et al. Non-submodular maximization on massive data streams. J Glob Optim 76, 729–743 (2020). https://doi.org/10.1007/s10898-019-00840-8

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