IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/vyid10.1007_s10878-020-00620-1.html
   My bibliography  Save this article

Maximizing a monotone non-submodular function under a knapsack constraint

Author

Listed:
  • Zhenning Zhang

    (Beijing University of Technology)

  • Bin Liu

    (Ocean University of China)

  • Yishui Wang

    (Chinese Academy of Sciences)

  • Dachuan Xu

    (Beijing University of Technology)

  • Dongmei Zhang

    (Shandong Jianzhu University)

Abstract

Submodular optimization has been well studied in combinatorial optimization. However, there are few works considering about non-submodular optimization problems which also have many applications, such as experimental design, some optimization problems in social networks, etc. In this paper, we consider the maximization of non-submodular function under a knapsack constraint, and explore the performance of the greedy algorithm, which is characterized by the submodularity ratio $$\beta $$ β and curvature $$\alpha $$ α . In particular, we prove that the greedy algorithm enjoys a tight approximation guarantee of $$ (1-e^{-\alpha \beta })/{\alpha }$$ ( 1 - e - α β ) / α for the above problem. To our knowledge, it is the first tight constant factor for this problem. We further utilize illustrative examples to demonstrate the performance of our algorithm.

Suggested Citation

  • Zhenning Zhang & Bin Liu & Yishui Wang & Dachuan Xu & Dongmei Zhang, 0. "Maximizing a monotone non-submodular function under a knapsack constraint," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-24.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00620-1
    DOI: 10.1007/s10878-020-00620-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00620-1
    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/s10878-020-00620-1?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. 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. Akiyoshi Shioura & Natalia V. Shakhlevich & Vitaly A. Strusevich, 2016. "Application of Submodular Optimization to Single Machine Scheduling with Controllable Processing Times Subject to Release Dates and Deadlines," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 148-161, February.
    3. 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).
    Full references (including those not matched with items on IDEAS)

    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. Zhenning Zhang & Bin Liu & Yishui Wang & Dachuan Xu & Dongmei Zhang, 2022. "Maximizing a monotone non-submodular function under a knapsack constraint," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1125-1148, July.
    2. Mohit Singh & Weijun Xie, 2020. "Approximation Algorithms for D -optimal Design," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1512-1534, November.
    3. Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2018. "Multi-level facility location problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 791-805.
    4. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2022. "Submodularity and local search approaches for maximum capture problems under generalized extreme value models," European Journal of Operational Research, Elsevier, vol. 300(3), pages 953-965.
    5. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    6. Guanyi Wang, 2024. "Robust Network Targeting with Multiple Nash Equilibria," Papers 2410.20860, arXiv.org, revised Nov 2024.
    7. Majun Shi & Zishen Yang & Wei Wang, 2023. "Greedy Guarantees for Non-submodular Function Maximization Under Independent System Constraint with Applications," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 516-543, February.
    8. Rad Niazadeh & Negin Golrezaei & Joshua Wang & Fransisca Susan & Ashwinkumar Badanidiyuru, 2023. "Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization," Management Science, INFORMS, vol. 69(7), pages 3797-3817, July.
    9. Mohammad Abouei Mehrizi & Federico Corò & Emilio Cruciani & Gianlorenzo D’Angelo, 2022. "Election control through social influence with voters’ uncertainty," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 635-669, August.
    10. Eli Towle & James Luedtke, 2018. "New solution approaches for the maximum-reliability stochastic network interdiction problem," Computational Management Science, Springer, vol. 15(3), pages 455-477, October.
    11. 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.
    12. Emily M. Craparo & Mumtaz Karatas & Tobias U. Kuhn, 2017. "Sensor placement in active multistatic sonar networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 287-304, June.
    13. Alexandre D. Jesus & Luís Paquete & Arnaud Liefooghe, 2021. "A model of anytime algorithm performance for bi-objective optimization," Journal of Global Optimization, Springer, vol. 79(2), pages 329-350, February.
    14. Oded Berman & Dmitry Krass & Mozart B. C. Menezes, 2007. "Facility Reliability Issues in Network p -Median Problems: Strategic Centralization and Co-Location Effects," Operations Research, INFORMS, vol. 55(2), pages 332-350, April.
    15. Hongjie Guo & Jianzhong Li & Hong Gao, 2022. "Data source selection for approximate query," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2443-2459, November.
    16. Bin Liu & Miaomiao Hu, 2022. "Fast algorithms for maximizing monotone nonsubmodular functions," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1655-1670, July.
    17. repec:dgr:rugsom:99a17 is not listed on IDEAS
    18. Klages-Mundt, Ariah & Minca, Andreea, 2022. "Optimal intervention in economic networks using influence maximization methods," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1136-1148.
    19. Xin Chen & Qingqin Nong & Yan Feng & Yongchang Cao & Suning Gong & Qizhi Fang & Ker-I Ko, 2017. "Centralized and decentralized rumor blocking problems," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 314-329, July.
    20. Lehmann, Daniel, 2020. "Quality of local equilibria in discrete exchange economies," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 141-152.
    21. 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.

    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:jcomop:v::y::i::d:10.1007_s10878-020-00620-1. 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.