IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v80y2021i3d10.1007_s10898-021-01014-1.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-021-01014-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-021-01014-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. G. L. Nemhauser & L. A. Wolsey, 1978. "Best Algorithms for Approximating the Maximum of a Submodular Set Function," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 177-188, August.
    2. Nemhauser, G.L. & Wolsey, L.A., 1978. "Best algorithms for approximating the maximum of a submodular set function," LIDAM Reprints CORE 343, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
    4. 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).
    5. 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).
    6. Goldengorin, Boris, 2009. "Maximization of submodular functions: Theory and enumeration algorithms," European Journal of Operational Research, Elsevier, vol. 198(1), pages 102-112, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cheng Lu & Wenguo Yang & Ruiqi Yang & Suixiang Gao, 2022. "Maximizing a non-decreasing non-submodular function subject to various types of constraints," Journal of Global Optimization, Springer, vol. 83(4), pages 727-751, August.
    2. Bin Liu & Miaomiao Hu, 2022. "Fast algorithms for maximizing monotone nonsubmodular functions," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1655-1670, July.
    3. Awi Federgruen & Nan Yang, 2008. "Selecting a Portfolio of Suppliers Under Demand and Supply Risks," Operations Research, INFORMS, vol. 56(4), pages 916-936, August.
    4. Simon Bruggmann & Rico Zenklusen, 2019. "Submodular Maximization Through the Lens of Linear Programming," Management Science, INFORMS, vol. 44(4), pages 1221-1244, November.
    5. Ivan Contreras & Elena Fernández, 2014. "Hub Location as the Minimization of a Supermodular Set Function," Operations Research, INFORMS, vol. 62(3), pages 557-570, June.
    6. Jon Lee & Maxim Sviridenko & Jan Vondrák, 2010. "Submodular Maximization over Multiple Matroids via Generalized Exchange Properties," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 795-806, November.
    7. 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.
    8. Niv Buchbinder & Moran Feldman & Roy Schwartz, 2017. "Comparing Apples and Oranges: Query Trade-off in Submodular Maximization," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 308-329, May.
    9. Suning Gong & Qingqin Nong & Shuyu Bao & Qizhi Fang & Ding-Zhu Du, 2023. "A fast and deterministic algorithm for Knapsack-constrained monotone DR-submodular maximization over an integer lattice," Journal of Global Optimization, Springer, vol. 85(1), pages 15-38, January.
    10. Xin Sun & Gaidi Li & Yapu Zhang & Zhenning Zhang, 2022. "Private non-monotone submodular maximization," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3212-3232, December.
    11. Kung, Ling-Chieh & Liao, Wei-Hung, 2018. "An approximation algorithm for a competitive facility location problem with network effects," European Journal of Operational Research, Elsevier, vol. 267(1), pages 176-186.
    12. Niv Buchbinder & Moran Feldman, 2019. "Constrained Submodular Maximization via a Nonsymmetric Technique," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 988-1005, August.
    13. Arash Asadpour & Hamid Nazerzadeh, 2016. "Maximizing Stochastic Monotone Submodular Functions," Management Science, INFORMS, vol. 62(8), pages 2374-2391, August.
    14. Min Cui & Dachuan Xu & Longkun Guo & Dan Wu, 2022. "Approximation guarantees for parallelized maximization of monotone non-submodular function with a cardinality constraint," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1671-1690, July.
    15. Manuel A. Nunez & Robert S. Garfinkel & Ram D. Gopal, 2007. "Stochastic Protection of Confidential Information in Databases: A Hybrid of Data Perturbation and Query Restriction," Operations Research, INFORMS, vol. 55(5), pages 890-908, October.
    16. Marek Adamczyk & Maxim Sviridenko & Justin Ward, 2016. "Submodular Stochastic Probing on Matroids," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1022-1038, August.
    17. Zengfu Wang & Bill Moran & Xuezhi Wang & Quan Pan, 2015. "An accelerated continuous greedy algorithm for maximizing strong submodular functions," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 1107-1124, November.
    18. 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.
    19. Saeed Alaei & Ali Makhdoumi & Azarakhsh Malekian, 2021. "Maximizing Sequence-Submodular Functions and Its Application to Online Advertising," Management Science, INFORMS, vol. 67(10), pages 6030-6054, October.
    20. Zengfu Wang & Bill Moran & Xuezhi Wang & Quan Pan, 2016. "Approximation for maximizing monotone non-decreasing set functions with a greedy method," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 29-43, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:80:y:2021:i:3:d:10.1007_s10898-021-01014-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.