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Streaming Algorithms for Maximizing Monotone DR-Submodular Functions with a Cardinality Constraint on the Integer Lattice

Author

Listed:
  • Zhenning Zhang

    (Department of Operations Research and Information Engineering, Beijing University of Technology, Beijing 100124, P. R. China)

  • Longkun Guo

    (Shandong Key Laboratory of Computer Networks, School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan, Shandong 250353, P. R. China)

  • Yishui Wang

    (School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, P. R. China)

  • Dachuan Xu

    (Department of Operations Research and Information Engineering, Beijing University of Technology, Beijing 100124, P. R. China)

  • Dongmei Zhang

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

Abstract

Emerging applications such as optimal budget allocation and sensor placement impose problems of maximizing variants of submodular functions with constraints under a streaming setting. In this paper, we first devise a streaming algorithm based on Sieve-Streaming for maximizing a monotone diminishing return submodular (DR-submodular) function with a cardinality constraint on the integer lattice and show it is a one-pass algorithm with approximation ratio 1 2 βˆ’ πœ–. The key idea to ensure one pass for the algorithm is to combine binary search for determining the level of an element with the exponential-growth method for estimating the OPT. Inspired by Sieve-Streaming++, we then improve the memory of the algorithm to O(k πœ– ) and the query complexity to O(klog2k πœ– ).

Suggested Citation

  • Zhenning Zhang & Longkun Guo & Yishui Wang & Dachuan Xu & Dongmei Zhang, 2021. "Streaming Algorithms for Maximizing Monotone DR-Submodular Functions with a Cardinality Constraint on the Integer Lattice," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(05), pages 1-14, October.
    • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:05:n:s0217595921400042
    DOI: 10.1142/S0217595921400042
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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. Bich-Ngan T. Nguyen & Phuong N. H. Pham & Van-Vang Le & VΓ‘clav SnΓ‘Ε‘el, 2022. "Efficient Streaming Algorithms for Maximizing Monotone DR-Submodular Function on the Integer Lattice," Mathematics, MDPI, vol. 10(20), pages 1-19, October.

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