IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/313868.html
   My bibliography  Save this article

The Inverse 1-Median Problem on Tree Networks with Variable Real Edge Lengths

Author

Listed:
  • Longshu Wu
  • Joonwhoan Lee
  • Jianhua Zhang
  • Qin Wang

Abstract

Location problems exist in the real world and they mainly deal with finding optimal locations for facilities in a network, such as net servers, hospitals, and shopping centers. The inverse location problem is also often met in practice and has been intensively investigated in the literature. As a typical inverse location problem, the inverse 1-median problem on tree networks with variable real edge lengths is discussed in this paper, which is to modify the edge lengths at minimum total cost such that a given vertex becomes a 1-median of the tree network with respect to the new edge lengths. First, this problem is shown to be solvable in linear time with variable nonnegative edge lengths. For the case when negative edge lengths are allowable, the NP-hardness is proved under Hamming distance, and strongly polynomial time algorithms are presented under and norms, respectively.

Suggested Citation

  • Longshu Wu & Joonwhoan Lee & Jianhua Zhang & Qin Wang, 2013. "The Inverse 1-Median Problem on Tree Networks with Variable Real Edge Lengths," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-6, April.
    • Handle: RePEc:hin:jnlmpe:313868
    DOI: 10.1155/2013/313868
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2013/313868.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2013/313868.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/313868?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
    ---><---

    Citations

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


    Cited by:

    1. Baldomero-Naranjo, Marta & Kalcsics, Jörg & Marín, Alfredo & Rodríguez-Chía, Antonio M., 2022. "Upgrading edges in the maximal covering location problem," European Journal of Operational Research, Elsevier, vol. 303(1), pages 14-36.

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnlmpe:313868. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.