IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v14y2007i2d10.1007_s10878-007-9063-7.html
   My bibliography  Save this article

The use of edge-directions and linear programming to enumerate vertices

Author

Listed:
  • Shmuel Onn

    (Technion—Israel Institute of Technology)

  • Uriel G. Rothblum

    (Technion—Israel Institute of Technology)

Abstract

Given a list of vectors that contains directions of the edges of a given polytope ℘ and the availability of an algorithm that solves linear programs over ℘, we describe a method for enumerating the vertices of ℘; in particular, the method is adaptable to polytopes which are presented as (linear) projections of polytopes having linear inequality representation. Polynomial complexity bounds under both the real and the binary computation models are derived when the dimension of the polytope is fixed and the given LP algorithm is polynomial.

Suggested Citation

  • Shmuel Onn & Uriel G. Rothblum, 2007. "The use of edge-directions and linear programming to enumerate vertices," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 153-164, October.
    • Handle: RePEc:spr:jcomop:v:14:y:2007:i:2:d:10.1007_s10878-007-9063-7
    DOI: 10.1007/s10878-007-9063-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-007-9063-7
    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/s10878-007-9063-7?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. Shmuel Onn & Leonard J. Schulman, 2001. "The Vector Partition Problem for Convex Objective Functions," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 583-590, August.
    2. Frank K. Hwang & Uriel G. Rothblum, 1996. "Directional-Quasi-Convexity, Asymmetric Schur-Convexity and Optimality of Consecutive Partitions," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 540-554, August.
    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.
    1. Le Breton, Michel & Peluso, Eugenio, 2010. "Smooth inequality measurement: Approximation theorems," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 405-415, July.
    2. Borgwardt, S. & Brieden, A. & Gritzmann, P., 2017. "An LP-based k-means algorithm for balancing weighted point sets," European Journal of Operational Research, Elsevier, vol. 263(2), pages 349-355.
    3. Frank K. Hwang & Uriel G. Rothblum, 2011. "On the number of separable partitions," Journal of Combinatorial Optimization, Springer, vol. 21(4), pages 423-433, May.
    4. Jia Shu & Chung-Piaw Teo & Zuo-Jun Max Shen, 2005. "Stochastic Transportation-Inventory Network Design Problem," Operations Research, INFORMS, vol. 53(1), pages 48-60, February.
    5. J. Haberl, 2004. "Maximization of Generalized Convex Functionals in Locally Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 327-359, May.

    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:14:y:2007:i:2:d:10.1007_s10878-007-9063-7. 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.