IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v40y2023i05ns0217595923400122.html
   My bibliography  Save this article

Minimization Problems with Non-Submodular Cover Constraint

Author

Listed:
  • Wenqi Wang

    (School of Mathematical Science & Institute of Mathematics, Nanjing Normal University, Nanjing 210023, P. R. China)

  • Zhicheng Liu

    (Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, P. R. China)

  • Donglei Du

    (Faculty of Management, University of New Brunswick, Fredericton, New Brunswick, Canada E3B9Y2, Canada)

  • Peihao Shi

    (Nanjing Kinghua Operations Research and Artificial Intelligence, Industrial Technology Research Institute Co., Ltd., Nanjing 210035, P. R. China)

  • Xiaoyan Zhang

    (School of Mathematical Science & Institute of Mathematics, Nanjing Normal University, Nanjing 210023, P. R. China)

Abstract

The set cover problem has been studied extensively for many years. Submodular function plays a key role in combinatorial optimization. Extending the set cover problem, we consider three submodular cover problems. The first two problems minimize linear and submodular functions, respectively, subject to the same non-submodular cover constraint. The third problem minimizes a submodular function subject to non-submodular cover and precedence constraints. Based on the concepts of submodular ratio and gap, and Lovász extension, we devise greedy and primal–dual approximation algorithms for these problems.

Suggested Citation

  • Wenqi Wang & Zhicheng Liu & Donglei Du & Peihao Shi & Xiaoyan Zhang, 2023. "Minimization Problems with Non-Submodular Cover Constraint," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(05), pages 1-19, October.
    • Handle: RePEc:wsi:apjorx:v:40:y:2023:i:05:n:s0217595923400122
    DOI: 10.1142/S0217595923400122
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595923400122
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595923400122?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.

    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:wsi:apjorx:v:40:y:2023:i:05:n:s0217595923400122. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.