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Non-submodular maximization on massive data streams

Author

Listed:
  • Yijing Wang

    (Beijing University of Technology)

  • Dachuan Xu

    (Beijing University of Technology)

  • Yishui Wang

    (Chinese Academy of Sciences)

  • Dongmei Zhang

    (Shandong Jianzhu University)

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.

Suggested Citation

  • Yijing Wang & Dachuan Xu & Yishui Wang & Dongmei Zhang, 2020. "Non-submodular maximization on massive data streams," Journal of Global Optimization, Springer, vol. 76(4), pages 729-743, April.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-019-00840-8
    DOI: 10.1007/s10898-019-00840-8
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. K. Kampa & S. Mehta & C. Chou & W. Chaovalitwongse & T. Grabowski, 2014. "Sparse optimization in feature selection: application in neuroimaging," Journal of Global Optimization, Springer, vol. 59(2), pages 439-457, July.
    3. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Lehmann, Benny & Lehmann, Daniel & Nisan, Noam, 2006. "Combinatorial auctions with decreasing marginal utilities," Games and Economic Behavior, Elsevier, vol. 55(2), pages 270-296, May.
    5. Goldengorin, Boris & Ghosh, Diptesh, 2004. "A Multilevel Search Algorithm for the Maximization of Submodular Functions," Research Report 04A20, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    6. Xu Zhu & Jieun Yu & Wonjun Lee & Donghyun Kim & Shan Shan & Ding-Zhu Du, 2010. "New dominating sets in social networks," Journal of Global Optimization, Springer, vol. 48(4), pages 633-642, December.
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    Citations

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    Cited by:

    1. Bin Liu & Zihan Chen & Huijuan Wang & Weili Wu, 2023. "An optimal streaming algorithm for non-submodular functions maximization on the integer lattice," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-17, January.
    2. Majun Shi & Zishen Yang & Wei Wang, 2023. "Greedy Guarantees for Non-submodular Function Maximization Under Independent System Constraint with Applications," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 516-543, February.
    3. Ruiqi Yang & Dachuan Xu & Longkun Guo & Dongmei Zhang, 2021. "Sequence submodular maximization meets streaming," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 43-55, January.
    4. Yijing Wang & Dachuan Xu & Donglei Du & Yanjun Jiang, 2022. "Bicriteria streaming algorithms to balance gain and cost with cardinality constraint," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2946-2962, November.
    5. Jingjing Tan & Yicheng Xu & Dongmei Zhang & Xiaoqing Zhang, 2023. "On streaming algorithms for maximizing a supermodular function plus a MDR-submodular function on the integer lattice," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-19, March.

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