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On streaming algorithms for maximizing a supermodular function plus a MDR-submodular function on the integer lattice

Author

Listed:
  • Jingjing Tan

    (Weifang University)

  • Yicheng Xu

    (Chinese Academy of Sciences
    Guangxi Key Laboratory of Cryptography and Information Security)

  • Dongmei Zhang

    (Shandong Jianzhu University)

  • Xiaoqing Zhang

    (Beijing University of Technology)

Abstract

In this paper, we provide a streaming algorithm for the problem of maximizing the sum of a supermodular function and a nonnegative monotone diminishing return submodular (MDR-submodular) function with a knapsack constraint on the integer lattice. Inspired by the SIEVE-STREAMING algorithm, we present a two-pass streaming algorithm by using the threshold technique. Then, we improve the two-pass streaming algorithm to one-pass and further reduce its space complexity. The proposed algorithms are proved to have polynomial time and space complexity, and a performance guarantee dependent on the curvature of the supermodular function. Finally, we carry out numerical experiments to verify the performance of the algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:2:d:10.1007_s10878-023-00986-y
    DOI: 10.1007/s10878-023-00986-y
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    References listed on IDEAS

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    1. Ruiqi Yang & Dachuan Xu & Min Li & Yicheng Xu, 2019. "Thresholding Methods for Streaming Submodular Maximization with a Cardinality Constraint and Its Variants," Springer Optimization and Its Applications, in: Ding-Zhu Du & Panos M. Pardalos & Zhao Zhang (ed.), Nonlinear Combinatorial Optimization, pages 123-140, Springer.
    2. 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.
    3. Zhenning Zhang & Donglei Du & Yanjun Jiang & Chenchen Wu, 2021. "Maximizing DR-submodular+supermodular functions on the integer lattice subject to a cardinality constraint," Journal of Global Optimization, Springer, vol. 80(3), pages 595-616, July.
    4. Simai He & Jiawei Zhang & Shuzhong Zhang, 2012. "Polymatroid Optimization, Submodularity, and Joint Replenishment Games," Operations Research, INFORMS, vol. 60(1), pages 128-137, February.
    Full references (including those not matched with items on IDEAS)

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