IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v30y2015i4d10.1007_s10878-013-9697-6.html
   My bibliography  Save this article

The minimum number of hubs in networks

Author

Listed:
  • Easton Li Xu

    (The University of Hong Kong)

  • Guangyue Han

    (The University of Hong Kong)

Abstract

In this paper, a hub refers to a non-terminal vertex of degree at least three. We study the minimum number of hubs needed in a network to guarantee certain flow demand constraints imposed between multiple pairs of sources and sinks. We prove that under the constraints, regardless of the size of the network, such minimum number is always upper bounded and we derive tight upper bounds for some special parameters. In particular, for two pairs of sources and sinks, we present a novel path-searching algorithm, the analysis of which is instrumental for the derivations of the tight upper bounds. Our results are of both theoretical and practical interest: in theory, they can be viewed as generalizations of the classical Menger’s theorem to a class of undirected graphs with multiple sources and sinks; in practice, our results, roughly speaking, suggest that for some given flow demand constraints, not “too many” hubs are needed in a network.

Suggested Citation

  • Easton Li Xu & Guangyue Han, 2015. "The minimum number of hubs in networks," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 1196-1218, November.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:4:d:10.1007_s10878-013-9697-6
    DOI: 10.1007/s10878-013-9697-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-013-9697-6
    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/s10878-013-9697-6?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:spr:jcomop:v:30:y:2015:i:4:d:10.1007_s10878-013-9697-6. 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: 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.