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Approximating Robust Parameterized Submodular Function Maximization in Large-Scales

Author

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  • Ruiqi Yang

    (Department of Operations Research and Scientific Computing, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, P. R. China)

  • Dachuan Xu

    (Department of Operations Research and Scientific Computing, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, P. R. China)

  • Yanjun Jiang

    (School of Mathematics and Statistics Science, Ludong University, 186 Hongqi Middle Road, Zhifu District, Yantai, Shandong 264025, P. R. China)

  • Yishui Wang

    (Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, P. R. China)

  • Dongmei Zhang

    (School of Computer Science and Technology, Shandong Jianzhu University, Jinan 250101, P. R. China)

Abstract

We study a robust parameterized submodular function maximization inspired by [Mitrović, S, I Bogunovic, A Norouzi-Fard and Jakub Tarnawski (2017). Streaming robust submodular maximization: A partitioned thresholding approach. In Proc. NIPS, pp. 4560–4569] and [Bogunovic, I, J Zhao and V Cevher (2018). Robust maximization of nonsubmodular objectives. In Proc. AISTATS, pp. 890–899]. In our setting, given a parameterized set function, there are two additional twists. One is that elements arrive in a streaming style, and the other is that there are at most τ items deleted from the algorithm’s memory when the stream is finished. The goal is to choose a robust set from the stream such that the robust ratio is maximized. We propose a two-phase algorithm for maximizing a normalized monotone robust parameterized submodular function with a cardinality constraint and show the robust ratio is close to a constant as k →∞. In the end, we empirically demonstrate the performance of our algorithm on deletion robust support selection problem.

Suggested Citation

  • Ruiqi Yang & Dachuan Xu & Yanjun Jiang & Yishui Wang & Dongmei Zhang, 2019. "Approximating Robust Parameterized Submodular Function Maximization in Large-Scales," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-24, August.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:04:n:s0217595919500222
    DOI: 10.1142/S0217595919500222
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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. 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).
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    Cited by:

    1. 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.

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