IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v30y2015i2d10.1007_s10878-014-9772-7.html
   My bibliography  Save this article

On the clustered Steiner tree problem

Author

Listed:
  • Bang Ye Wu

    (National Chung Cheng University)

  • Chen-Wan Lin

    (National Chung Cheng University)

Abstract

We investigate the Clustered Steiner tree problem on metric graphs, which is a variant of the Steiner minimum tree problem. In this problem, the required vertices are partitioned into clusters, and the subtrees spanning different clusters must be disjoint in a feasible clustered Steiner tree. In this paper, it is shown that the problem is NP-hard even if the inter-cluster tree and all the local topologies are given, where a local topology specifies the tree structure of required vertices in the same cluster. We show that the Steiner ratio of this problem is lower and upper bounded by three and four, respectively. We also propose a $$(\rho +2)$$ ( ρ + 2 ) -approximation algorithm, where $$\rho $$ ρ is the approximation ratio for the Steiner minimum tree problem, and the approximation ratio can be improved to $$\rho +1$$ ρ + 1 if the local topologies are given. Two variants of this problem are also studied. When the goal is to minimize the inter-cluster cost and ignore the cost of local trees, the problem can be solved in polynomial time. But it is NP-hard if we ask for the minimum cost of local trees among all solutions with minimum inter-cluster cost.

Suggested Citation

  • Bang Ye Wu & Chen-Wan Lin, 2015. "On the clustered Steiner tree problem," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 370-386, August.
  • Handle: RePEc:spr:jcomop:v:30:y:2015:i:2:d:10.1007_s10878-014-9772-7
    DOI: 10.1007/s10878-014-9772-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-014-9772-7
    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/s10878-014-9772-7?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. Wei Ding & Guoliang Xue, 2014. "Minimum diameter cost-constrained Steiner trees," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 32-48, January.
    2. Tsan-Sheng Hsu & Kuo-Hui Tsai & Da-Wei Wang & D. T. Lee, 2005. "Two Variations of the Minimum Steiner Problem," Journal of Combinatorial Optimization, Springer, vol. 9(1), pages 101-120, February.
    3. Feng Zou & Xianyue Li & Suogang Gao & Weili Wu, 2009. "Node-weighted Steiner tree approximation in unit disk graphs," Journal of Combinatorial Optimization, Springer, vol. 18(4), pages 342-349, November.
    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. Mattia D’Emidio & Luca Forlizzi & Daniele Frigioni & Stefano Leucci & Guido Proietti, 2019. "Hardness, approximability, and fixed-parameter tractability of the clustered shortest-path tree problem," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 165-184, July.
    2. Chen-Wan Lin & Bang Ye Wu, 2017. "On the minimum routing cost clustered tree problem," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 1106-1121, 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. Hongwei Du & Panos Pardalos & Weili Wu & Lidong Wu, 2013. "Maximum lifetime connected coverage with two active-phase sensors," Journal of Global Optimization, Springer, vol. 56(2), pages 559-568, June.
    2. Lidan Fan & Zhao Zhang & Wei Wang, 2011. "PTAS for minimum weighted connected vertex cover problem with c-local condition in unit disk graphs," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 663-673, November.
    3. Jiao Zhou & Zhao Zhang & Shaojie Tang & Xiaohui Huang & Ding-Zhu Du, 2018. "Breaking the O (ln n ) Barrier: An Enhanced Approximation Algorithm for Fault-Tolerant Minimum Weight Connected Dominating Set," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 225-235, 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:30:y:2015:i:2:d:10.1007_s10878-014-9772-7. 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.