IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/883.html
   My bibliography  Save this paper

The Shapes of Polyhedra

Author

Listed:

Abstract

Let A be a real matrix of size (n+d+1)xn. We assume that all n x n submatrices of A are non-singular and define the condition number C = C(A) to be the ratio of the largest n x n subdeterminant of A to the smallest in absolute value. In addition we assume that there is a positive vector pi such that (pi)A = 0. This implies that for any b, the body K(b) = 'X such that AX 0, there exists a subset of the bodies K(b), of cardinality not larger than f(A) 1/2(log to the base 2 of (nC)/epsilon^{d}, such that every body is within epsilon of some member of the subset.

Suggested Citation

  • Herbert E. Scarf & R. Kannan & Laszlo Lovasz, 1988. "The Shapes of Polyhedra," Cowles Foundation Discussion Papers 883, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:883
    Note: CFP 753.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d08/d0883.pdf
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. I. Bárány & H. E. Scarf & D. Shallcross, 2008. "The topological structure of maximal lattice free convex bodies: The general case," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 11, pages 191-205, Palgrave Macmillan.
    2. Herbert E. Scarf & Shallcross, David F., 1991. "Shortest Integer Vectors," Cowles Foundation Discussion Papers 965, Cowles Foundation for Research in Economics, Yale University.
    3. William Cook & Thomas Rutherford & Herbert E. Scarf & David F. Shallcross, 1991. "An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming," Cowles Foundation Discussion Papers 990, Cowles Foundation for Research in Economics, Yale University.
    4. Robert Weismantel, 1998. "Test sets of integer programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 1-37, February.

    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:cwl:cwldpp:883. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    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.