IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v32y2016i4d10.1007_s10878-015-9880-z.html
   My bibliography  Save this article

An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding

Author

Listed:
  • Chenchen Wu

    (Tianjin University of Technology)

  • Dachuan Xu

    (Beijing University of Technology)

  • Donglei Du

    (University of New Brunswick)

  • Wenqing Xu

    (Beijing University of Technology
    California State University)

Abstract

Graph partition problems have been investigated extensively in combinatorial optimization. In this work, we consider an important graph partition problem which has applications in the design of VLSI circuits, namely, the balanced Max-3-Uncut problem. We formulate the problem as a discrete linear program with complex variables and propose an approximation algorithm with an approximation ratio of 0.3456 using a semidefinite programming rounding technique along with a greedy swapping step afterwards to guarantee the balanced constraint. Our analysis utilizes a bivariate function, rather than the univariate function in previous work.

Suggested Citation

  • Chenchen Wu & Dachuan Xu & Donglei Du & Wenqing Xu, 2016. "An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1017-1035, November.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:4:d:10.1007_s10878-015-9880-z
    DOI: 10.1007/s10878-015-9880-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-015-9880-z
    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/s10878-015-9880-z?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. Thomas Feo & Olivier Goldschmidt & Mallek Khellaf, 1992. "One-Half Approximation Algorithms for the k-Partition Problem," Operations Research, INFORMS, vol. 40(1-supplem), pages 170-173, February.
    2. Chenchen Wu & Donglei Du & Dachuan Xu, 2015. "An improved semidefinite programming hierarchies rounding approximation algorithm for maximum graph bisection problems," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 53-66, January.
    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. Jiawei Chen & Suliman Al-Homidan & Qamrul Hasan Ansari & Jun Li & Yibing Lv, 2021. "Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 221-243, April.

    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. Z P Fan & Y Chen & J Ma & S Zeng, 2011. "Erratum: A hybrid genetic algorithmic approach to the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1423-1430, July.
    2. 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.
    3. Z P Fan & Y Chen & J Ma & S Zeng, 2011. "A hybrid genetic algorithmic approach to the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 92-99, January.
    4. Anna Martínez-Gavara & Vicente Campos & Micael Gallego & Manuel Laguna & Rafael Martí, 2015. "Tabu search and GRASP for the capacitated clustering problem," Computational Optimization and Applications, Springer, vol. 62(2), pages 589-607, November.
    5. Weitz, R. R. & Lakshminarayanan, S., 1997. "An empirical comparison of heuristic and graph theoretic methods for creating maximally diverse groups, VLSI design, and exam scheduling," Omega, Elsevier, vol. 25(4), pages 473-482, August.
    6. Kayse Lee Maass & Vera Mann Hey Lo & Anna Weiss & Mark S. Daskin, 2015. "Maximizing Diversity in the Engineering Global Leadership Cultural Families," Interfaces, INFORMS, vol. 45(4), pages 293-304, August.
    7. Baoling Ning & Jianzhong Li & Shouxu Jiang, 2019. "Balanced tree partition problems with virtual nodes," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1249-1265, 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:32:y:2016:i:4:d:10.1007_s10878-015-9880-z. 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.