IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v24y2012i4d10.1007_s10878-011-9411-5.html
   My bibliography  Save this article

LLL-reduction for integer knapsacks

Author

Listed:
  • Iskander Aliev

    (Cardiff University)

  • Martin Henk

    (Otto-von-Guericke Universität Magdeburg)

Abstract

Given a matrix A∈ℤ m×n satisfying certain regularity assumptions, a well-known integer programming problem asks to find an integer point in the associated knapsack polytope or determine that no such point exists. We obtain an LLL-based polynomial time algorithm that solves the problem subject to a constraint on the location of the vector b.

Suggested Citation

  • Iskander Aliev & Martin Henk, 2012. "LLL-reduction for integer knapsacks," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 613-626, November.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:4:d:10.1007_s10878-011-9411-5
    DOI: 10.1007/s10878-011-9411-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-011-9411-5
    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/s10878-011-9411-5?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. Friedrich Eisenbrand & Gennady Shmonin, 2008. "Parametric Integer Programming in Fixed Dimension," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 839-850, November.
    2. Hansen, Paul & Ryan, Jennifer, 1996. "Testing integer knapsacks for feasibility," European Journal of Operational Research, Elsevier, vol. 88(3), pages 578-582, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Karen Aardal & Frederik von Heymann, 2014. "On the Structure of Reduced Kernel Lattice Bases," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 823-840, August.

    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. Y-J Seong & Y-G G & M-K Kang & C-W Kang, 2004. "An improved branch and bound algorithm for a strongly correlated unbounded knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(5), pages 547-552, May.
    2. Iskander Aliev & Martin Henk, 2009. "Integer Knapsacks: Average Behavior of the Frobenius Numbers," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 698-705, August.
    3. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    4. Pisinger, David & Saidi, Alima, 2017. "Tolerance analysis for 0–1 knapsack problems," European Journal of Operational Research, Elsevier, vol. 258(3), pages 866-876.

    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:24:y:2012:i:4:d:10.1007_s10878-011-9411-5. 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.