IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v18y2009i2d10.1007_s10878-008-9143-3.html
   My bibliography  Save this article

The bandpass problem: combinatorial optimization and library of problems

Author

Listed:
  • Djangir A. Babayev

    (Cox Associates)

  • George I. Bell

    (Tech-X Corporation)

  • Urfat G. Nuriyev

    (Ege University)

Abstract

A combinatorial optimization problem, called the Bandpass Problem, is introduced. Given a rectangular matrix A of binary elements {0,1} and a positive integer B called the Bandpass Number, a set of B consecutive non-zero elements in any column is called a Bandpass. No two bandpasses in the same column can have common rows. The Bandpass problem consists of finding an optimal permutation of rows of the matrix, which produces the maximum total number of bandpasses having the same given bandpass number in all columns. This combinatorial problem arises in considering the optimal packing of information flows on different wavelengths into groups to obtain the highest available cost reduction in design and operating the optical communication networks using wavelength division multiplexing technology. Integer programming models of two versions of the bandpass problems are developed. For a matrix A with three or more columns the Bandpass problem is proved to be NP-hard. For matrices with two or one column a polynomial algorithm solving the problem to optimality is presented. For the general case fast performing heuristic polynomial algorithms are presented, which provide near optimal solutions, acceptable for applications. High quality of the generated heuristic solutions has been confirmed in the extensive computational experiments. As an NP-hard combinatorial optimization problem with important applications the Bandpass problem offers a challenge for researchers to develop efficient computational solution methods. To encourage the further research a Library of Bandpass Problems has been developed. The Library is open to public and consists of 90 problems of different sizes (numbers of rows, columns and density of non-zero elements of matrix A and bandpass number B), half of them with known optimal solutions and the second half, without.

Suggested Citation

  • Djangir A. Babayev & George I. Bell & Urfat G. Nuriyev, 2009. "The bandpass problem: combinatorial optimization and library of problems," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 151-172, August.
  • Handle: RePEc:spr:jcomop:v:18:y:2009:i:2:d:10.1007_s10878-008-9143-3
    DOI: 10.1007/s10878-008-9143-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-008-9143-3
    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/s10878-008-9143-3?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.

    Citations

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


    Cited by:

    1. Liqin Huang & Weitian Tong & Randy Goebel & Tian Liu & Guohui Lin, 2015. "A 0.5358-approximation for Bandpass-2," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 612-626, October.
    2. Jesús Sánchez-Oro & Manuel Laguna & Rafael Martí & Abraham Duarte, 2016. "Scatter search for the bandpass problem," Journal of Global Optimization, Springer, vol. 66(4), pages 769-790, December.
    3. Guohui Lin, 2011. "On the Bandpass problem," Journal of Combinatorial Optimization, Springer, vol. 22(1), pages 71-77, July.
    4. Hakan Kutucu & Arif Gursoy & Mehmet Kurt & Urfat Nuriyev, 0. "The band collocation problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-28.
    5. Hakan Kutucu & Arif Gursoy & Mehmet Kurt & Urfat Nuriyev, 2020. "The band collocation problem," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 454-481, August.

    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:18:y:2009:i:2:d:10.1007_s10878-008-9143-3. 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.