IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v30y2015i3d10.1007_s10878-013-9656-2.html
   My bibliography  Save this article

A 0.5358-approximation for Bandpass-2

Author

Listed:
  • Liqin Huang

    (Fuzhou University)

  • Weitian Tong

    (University of Alberta)

  • Randy Goebel

    (University of Alberta)

  • Tian Liu

    (Peking University)

  • Guohui Lin

    (University of Alberta)

Abstract

The Bandpass-2 problem is a variant of the maximum traveling salesman problem arising from optical communication networks using wavelength-division multiplexing technology, in which the edge weights are dynamic rather than fixed. The previously best approximation algorithm for this NP-hard problem has a worst-case performance ratio of $$\frac{227}{426}.$$ 227 426 . Here we present a novel scheme to partition the edge set of a 4-matching into a number of subsets, such that the union of each of them and a given matching is an acyclic 2-matching. Such a partition result takes advantage of a known structural property of the optimal solution, leading to a $$\frac{70-\sqrt{2}}{128}\approx 0.5358$$ 70 - 2 128 ≈ 0.5358 -approximation algorithm for the Bandpass-2 problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:3:d:10.1007_s10878-013-9656-2
    DOI: 10.1007/s10878-013-9656-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-013-9656-2
    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/s10878-013-9656-2?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.

    References listed on IDEAS

    as
    1. Esther M. Arkin & Refael Hassin, 1998. "On Local Search for Weighted k -Set Packing," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 640-648, August.
    2. Donald L. Miller & Joseph F. Pekny, 1995. "A Staged Primal-Dual Algorithm for Perfect b-Matching with Edge Capacities," INFORMS Journal on Computing, INFORMS, vol. 7(3), pages 298-320, August.
    3. Guohui Lin, 2011. "On the Bandpass problem," Journal of Combinatorial Optimization, Springer, vol. 22(1), pages 71-77, July.
    4. 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.
    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. William Cook & André Rohe, 1999. "Computing Minimum-Weight Perfect Matchings," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 138-148, May.
    2. Karthekeyan Chandrasekaran & László A. Végh & Santosh S. Vempala, 2016. "The Cutting Plane Method is Polynomial for Perfect Matchings," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 23-48, February.
    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, 2020. "The band collocation problem," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 454-481, August.
    5. Hakan Kutucu & Arif Gursoy & Mehmet Kurt & Urfat Nuriyev, 0. "The band collocation problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-28.
    6. 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.
    7. David Applegate & William Cook & André Rohe, 2003. "Chained Lin-Kernighan for Large Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 82-92, February.
    8. Boštjan Gabrovšek & Tina Novak & Janez Povh & Darja Rupnik Poklukar & Janez Žerovnik, 2020. "Multiple Hungarian Method for k -Assignment Problem," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    9. Dimitris Bertsimas & Dan A. Iancu & Dmitriy Katz, 2013. "A New Local Search Algorithm for Binary Optimization," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 208-221, May.
    10. Jon Lee & Maxim Sviridenko & Jan Vondrák, 2010. "Submodular Maximization over Multiple Matroids via Generalized Exchange Properties," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 795-806, November.
    11. Fan Xue & C. Chan & W. Ip & C. Cheung, 2011. "A learning-based variable assignment weighting scheme for heuristic and exact searching in Euclidean traveling salesman problems," Netnomics, Springer, vol. 12(3), pages 183-207, October.
    12. Petra Schuurman & Tjark Vredeveld, 2007. "Performance Guarantees of Local Search for Multiprocessor Scheduling," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 52-63, February.
    13. Lennart Baardman & Maxime C. Cohen & Kiran Panchamgam & Georgia Perakis & Danny Segev, 2019. "Scheduling Promotion Vehicles to Boost Profits," Management Science, INFORMS, vol. 65(1), pages 50-70, January.
    14. Medaglia, Andres L. & Fang, Shu-Cherng, 2003. "A genetic-based framework for solving (multi-criteria) weighted matching problems," European Journal of Operational Research, Elsevier, vol. 149(1), pages 77-101, August.
    15. Yong Chen & Zhi-Zhong Chen & Guohui Lin & Lusheng Wang & An Zhang, 2021. "A randomized approximation algorithm for metric triangle packing," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 12-27, January.

    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:30:y:2015:i:3:d:10.1007_s10878-013-9656-2. 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.

    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.