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A Linear-Time Streaming Algorithm for Cardinality-Constrained Maximizing Monotone Non-submodular Set Functions

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Combinatorial Optimization and Applications (COCOA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13135))

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Abstract

Nowadays, massive amounts of data are growing at a rapid rate every moment. If data can be processed and analyzed promptly as they arrive, they can bring huge added values to the society. In this paper, we consider the problem of maximizing a monotone non-submodular function subject to a cardinality constraint under the streaming setting and present a linear-time single-pass deterministic algorithm for this problem. We analyze the algorithm using the parameter of the generic submodularity ratio \(\gamma \) to achieve an approximation ratio of \(\left[ \frac{\gamma ^4}{c(1+\gamma +\gamma ^2+\gamma ^3)}-\varepsilon \right] \) for any \(\varepsilon \ge 0\) with the query complexity \(\lceil n/c \rceil +c\), and the memory complexity is \(O(ck\log (k)\log (1/\varepsilon ))\), where c is a positive integer. When \(\gamma =1\), the algorithm achieves the same ratio for the submodular version of the problem with the matching query complexity and memory complexity.

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Acknowledgements

The first author is supported by Bei**g Natural Science Foundation Project No. Z200002 and National Natural Science Foundation of China (No. 12131003). The second author is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant 06446, and Natural Science Foundation of China (Nos. 11771386, 11728104). The third author is supported by National Natural Science Foundation of China (No. 11201333). The fourth author is supported by the Fundamental Research Funds for the Central Universities (No. E1E40108X2) and National Natural Science Foundation of China (No. 12101587).

Author information

Authors and Affiliations

  1. Department of Operations Research and Information Engineering, Bei**g University of Technology, 100 **leyuan, Chaoyang District, Bei**g, 100124, People’s Republic of China

    Min Cui

  2. Faculty of Management, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Donglei Du

  3. Glorious Sun School of Business and Management, Donghua University, Shanghai, 200051, People’s Republic of China

    Ling Gai

  4. School of Mathematical Sciences, University of Chinese Academy Sciences, Bei**g, 100049, People’s Republic of China

    Ruiqi Yang

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  1. Min Cui
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  2. Donglei Du
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  4. Ruiqi Yang
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Corresponding author

Correspondence to Ling Gai .

Editor information

Editors and Affiliations

  1. University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. University of New Brunswick, Fredericton, NB, Canada

    Donglei Du

  3. Tian** University of Technology, Tian**, China

    Chenchen Wu

  4. Bei**g University of Technology, Bei**g, China

    Dachuan Xu

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Cui, M., Du, D., Gai, L., Yang, R. (2021). A Linear-Time Streaming Algorithm for Cardinality-Constrained Maximizing Monotone Non-submodular Set Functions. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_9

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  • DOI: https://doi.org/10.1007/978-3-030-92681-6_9

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