IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v49y2025i4d10.1007_s10878-025-01292-5.html
   My bibliography  Save this article

The two-center problem of uncertain points on cactus graphs

Author

Listed:
  • Haitao Xu

    (Cleveland State University)

  • Jingru Zhang

    (Cleveland State University)

Abstract

We study the two-center problem on cactus graphs in facility locations, which aims to place two facilities on the graph network to serve customers in order to minimize the maximum transportation cost. In our problem, the location of each customer is uncertain and may appear at O(m) points on the network with probabilities. More specifically, given are a cactus graph G and a set $$\mathcal {P}$$ P of n (weighted) uncertain points where every uncertain point has O(m) possible locations on G each associated with a probability and is of a non-negative weight. The problem aims to compute two centers (points) on G so that the maximum (weighted) expected distance of the n uncertain points to their own expected closest center is minimized. No previous algorithms are known for this problem. In this paper, we present the first algorithm for this problem and it solves the problem in $$O(|G|+ m^{2}n^{2}\log mn)$$ O ( | G | + m 2 n 2 log m n ) time.

Suggested Citation

  • Haitao Xu & Jingru Zhang, 2025. "The two-center problem of uncertain points on cactus graphs," Journal of Combinatorial Optimization, Springer, vol. 49(4), pages 1-17, May.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:4:d:10.1007_s10878-025-01292-5
    DOI: 10.1007/s10878-025-01292-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-025-01292-5
    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/s10878-025-01292-5?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. Haitao Xu & Jingru Zhang, 2023. "The two-center problem of uncertain points on a real line," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-22, March.
    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.

      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:49:y:2025:i:4:d:10.1007_s10878-025-01292-5. 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.