IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v37y2019i4d10.1007_s10878-018-0351-1.html
   My bibliography  Save this article

Balanced tree partition problems with virtual nodes

Author

Listed:
  • Baoling Ning

    (Harbin Institute of Technology)

  • Jianzhong Li

    (Harbin Institute of Technology)

  • Shouxu Jiang

    (Harbin Institute of Technology)

Abstract

We study two variants of the Balanced Tree Partition (BTP for short) problem, whose goal is to find the minimum number of edges such that a partition of vertices into sets of equal size can be obtained after deleting those edges. We consider the BTP problem over trees with virtual nodes, which is motivated by the real applications in storing tree structured data distributively. Different from the traditional BTP problem, after deleting an edge from the tree, two virtual nodes must be added to provide the ability to recover the edge when computing, which will increase the size of some set in the partition and the set may become too large and need further splitting. Depending on whether or not to consider the partition set number k to be a parameter, to investigate the balanced tree partition methods over trees with virtual nodes, we formally defined two specific problems, $$k$$ k -VBTP and VBTP. The computational complexity and inapproximability of $$k$$ k -VBTP are analyzed, for the VBTP problem, a polynomial time algorithm is designed to find the optimal solution based on dynamic programming. Finally, the connections between $$k$$ k -VBTP and VBTP are built, and based the algorithm for VBTP, we design a heuristic algorithm for $$k$$ k -VBTP with performance guarantee.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:4:d:10.1007_s10878-018-0351-1
    DOI: 10.1007/s10878-018-0351-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-018-0351-1
    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/s10878-018-0351-1?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.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

    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:37:y:2019:i:4:d:10.1007_s10878-018-0351-1. 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.