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Maximizing DR-submodular+supermodular functions on the integer lattice subject to a cardinality constraint

Author

Listed:
  • Zhenning Zhang

    (Beijing University of Technology)

  • Donglei Du

    (University of New Brunswick)

  • Yanjun Jiang

    (School of Mathematics and Statistics Science, Ludong University)

  • Chenchen Wu

    (College of Science, Tianjin University of Technology)

Abstract

Arising from practical problems such as in sensor placement and influence maximization in social network, submodular and non-submodular maximization on the integer lattice has attracted much attention recently. In this work, we consider the problem of maximizing the sum of a monotone non-negative diminishing return submodular (DR-submodular) function and a supermodular function on the integer lattice subject to a cardinality constraint. By exploiting the special combinatorial structures in the problem, we introduce a decreasing threshold greedy algorithm with a binary search as its subroutine to solve the problem. To avoid introducing the diminishing return ratio and submodularity ratio of the objective function, we generalize the total curvatures of submodular functions and supermodular functions to the integer lattice version. We show that our algorithm has a constant approximation ratio parameterized by the new introduced total curvatures on integer lattice with a polynomial query complexity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:3:d:10.1007_s10898-021-01014-1
    DOI: 10.1007/s10898-021-01014-1
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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).
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    4. Maxim Sviridenko & Jan Vondrák & Justin Ward, 2017. "Optimal Approximation for Submodular and Supermodular Optimization with Bounded Curvature," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1197-1218, November.
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    6. 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. 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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