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Streaming algorithm for maximizing a monotone non-submodular function under d-knapsack constraint

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Abstract

Maximizing constrained submodular functions lies at the core of substantial machine learning and data mining. Specially, the case that the data come in a streaming fashion receives more attention in recent decades. In this work, we study the approximation algorithm for maximizing a non-decreasing set function under d-knapsack constraint. Based on the diminishing-return ratio for set functions, a non-trivial algorithm is devised for maximizing the set function without submodularity. Our results cover some known results and provide an effective method for the maximization on set functions no matter they are submodular or not. We also run the algorithm to handle the application of support selection for sparse linear regression. Numerical results show that the output quality of the algorithm is good.

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Acknowledgements

The research of the first author is supported by NSFC (No. 11801251). The third author is supported by NSFC (Nos. 11871081 and 11531014). The fifth author is supported by NSFC (No. 61433012), Shenzhen research Grant (KQJSCX20180330170311901, JCYJ20180305180840138 and GGFW2017073114031767) and Hong Kong GRF 17210017.

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Authors and Affiliations

  1. School of Mathematics and Statistics Science, Ludong University, 186 Hongqi Middle Road, Zhifu District, Yantai, 264025, Shandong, People’s Republic of China

    Yanjun Jiang

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

    Yishui Wang & Yong Zhang

  3. Department of Operations Research and Scientific Computing, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Dachuan Xu & Ruiqi Yang

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  1. Yanjun Jiang
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  2. Yishui Wang
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  3. Dachuan Xu
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  4. Ruiqi Yang
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  5. Yong Zhang
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Correspondence to Yanjun Jiang.

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Jiang, Y., Wang, Y., Xu, D. et al. Streaming algorithm for maximizing a monotone non-submodular function under d-knapsack constraint. Optim Lett 14, 1235–1248 (2020). https://doi.org/10.1007/s11590-019-01430-z

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  • DOI: https://doi.org/10.1007/s11590-019-01430-z

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