IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v16y2008i2d10.1007_s10878-007-9124-y.html
   My bibliography  Save this article

On minimum m-connected k-dominating set problem in unit disc graphs

Author

Listed:
  • Weiping Shang

    (Chinese Academy of Sciences
    City University of Hong Kong)

  • Frances Yao

    (City University of Hong Kong)

  • Pengjun Wan

    (Illinois Institute of Technology)

  • Xiaodong Hu

    (Chinese Academy of Sciences)

Abstract

Minimum m-connected k-dominating set problem is as follows: Given a graph G=(V,E) and two natural numbers m and k, find a subset S⊆V of minimal size such that every vertex in V∖S is adjacent to at least k vertices in S and the induced graph of S is m-connected. In this paper we study this problem with unit disc graphs and small m, which is motivated by the design of fault-tolerant virtual backbone for wireless sensor networks. We propose two approximation algorithms with constant performance ratios for m≤2. We also discuss how to design approximation algorithms for the problem with arbitrarily large m.

Suggested Citation

  • Weiping Shang & Frances Yao & Pengjun Wan & Xiaodong Hu, 2008. "On minimum m-connected k-dominating set problem in unit disc graphs," Journal of Combinatorial Optimization, Springer, vol. 16(2), pages 99-106, August.
    • Handle: RePEc:spr:jcomop:v:16:y:2008:i:2:d:10.1007_s10878-007-9124-y
    DOI: 10.1007/s10878-007-9124-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-007-9124-y
    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/s10878-007-9124-y?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. Korsnes, Reinert, 2010. "Rapid self-organised initiation of ad hoc sensor networks close above the percolation threshold," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2841-2848.
    2. Jing Gao & Jianzhong Li & Yingshu Li, 2016. "Approximate event detection over multi-modal sensing data," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1002-1016, 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.
    4. Yaoyao Zhang & Zhao Zhang & Ding-Zhu Du, 2023. "Construction of minimum edge-fault tolerant connected dominating set in a general graph," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-12, March.
    5. Yishuo Shi & Yaping Zhang & Zhao Zhang & Weili Wu, 2016. "A greedy algorithm for the minimum $$2$$ 2 -connected $$m$$ m -fold dominating set problem," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 136-151, January.
    6. Chen Liao & Shiyan Hu, 2010. "Polynomial time approximation schemes for minimum disk cover problems," Journal of Combinatorial Optimization, Springer, vol. 20(4), pages 399-412, November.
    7. Jiao Zhou & Zhao Zhang & Weili Wu & Kai Xing, 2014. "A greedy algorithm for the fault-tolerant connected dominating set in a general graph," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 310-319, July.
    8. Zhao Zhang & Jiao Zhou & Shaojie Tang & Xiaohui Huang & Ding-Zhu Du, 2018. "Computing Minimum k -Connected m -Fold Dominating Set in General Graphs," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 217-224, May.
    9. Tian Liu & Zhao Lu & Ke Xu, 2015. "Tractable connected domination for restricted bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 247-256, 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:16:y:2008:i:2:d:10.1007_s10878-007-9124-y. 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.