IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v34y2017i4d10.1007_s10878-017-0132-2.html
   My bibliography  Save this article

On the Langberg–Médard multiple unicast conjecture

Author

Listed:
  • Kai Cai

    (The University of Hong Kong)

  • Guangyue Han

    (The University of Hong Kong)

Abstract

A version of the multiple unicast conjecture, proposed by Langberg and Médard (in: Proceedings of 47th annual Allerton, 2009), says that, there exists an undirected fractional multi-commodity flow, or simply, multi-flow, with rate $$(1,1,\ldots ,1)$$ ( 1 , 1 , … , 1 ) for strongly reachable networks. In this paper, we propose a nonsmooth matrix optimization problem to attack this conjecture: By giving upper and lower bounds on the objective value, we prove that there exists a multi-flow with rate at least $$(\frac{8}{9}, \frac{8}{9}, \ldots , \frac{8}{9})$$ ( 8 9 , 8 9 , … , 8 9 ) for such networks; on the other hand though, we show that the rate of any multi-flow constructed using this framework cannot exceed $$(1,1,\ldots ,1)$$ ( 1 , 1 , … , 1 ) .

Suggested Citation

  • Kai Cai & Guangyue Han, 2017. "On the Langberg–Médard multiple unicast conjecture," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1114-1132, November.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:4:d:10.1007_s10878-017-0132-2
    DOI: 10.1007/s10878-017-0132-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-017-0132-2
    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/s10878-017-0132-2?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:34:y:2017:i:4:d:10.1007_s10878-017-0132-2. 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.