IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v28y2014i1d10.1007_s10878-013-9638-4.html
   My bibliography  Save this article

A greedy algorithm for the fault-tolerant connected dominating set in a general graph

Author

Listed:
  • Jiao Zhou

    (Xinjiang University)

  • Zhao Zhang

    (Xinjiang University)

  • Weili Wu

    (University of Texas at Dallas)

  • Kai Xing

    (University of Texas at Dallas)

Abstract

Using a connected dominating set (CDS) to serve as the virtual backbone of a wireless network is an effective way to save energy and alleviate broadcasting storm. Since nodes may fail due to an accidental damage or energy depletion, it is desirable that the virtual backbone is fault tolerant. A node set $$C$$ C is an $$m$$ m -fold connected dominating set ( $$m$$ m -fold CDS) of graph $$G$$ G if every node in $$V(G)\setminus C$$ V ( G ) ∖ C has at least $$m$$ m neighbors in $$C$$ C and the subgraph of $$G$$ G induced by $$C$$ C is connected. In this paper, we will present a greedy algorithm to compute an $$m$$ m -fold CDS in a general graph, which has size at most $$2+\ln (\Delta +m-2)$$ 2 + ln ( Δ + m − 2 ) times that of a minimum $$m$$ m -fold CDS, where $$\Delta $$ Δ is the maximum degree of the graph. This result improves on the previous best known performance ratio of $$2H(\Delta +m-1)$$ 2 H ( Δ + m − 1 ) for this problem, where $$H(\cdot )$$ H ( · ) is the Harmonic number.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:1:d:10.1007_s10878-013-9638-4
    DOI: 10.1007/s10878-013-9638-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-013-9638-4
    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/s10878-013-9638-4?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. Yingshu Li & Yiwei Wu & Chunyu Ai & Raheem Beyah, 2012. "On the construction of k-connected m-dominating sets in wireless networks," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 118-139, January.
    2. 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.
    3. Ding-Zhu Du & Ker-I Ko & Xiaodong Hu, 2012. "Design and Analysis of Approximation Algorithms," Springer Optimization and Its Applications, Springer, number 978-1-4614-1701-9, September.
    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. Xiaozhi Wang & Xianyue Li & Bo Hou & Wen Liu & Lidong Wu & Suogang Gao, 2021. "A greedy algorithm for the fault-tolerant outer-connected dominating set problem," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 118-127, January.
    2. Yanhong Gao & Ping Li & Xueliang Li, 2022. "Further results on the total monochromatic connectivity of graphs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 603-616, August.
    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. Austin Buchanan & Je Sang Sung & Sergiy Butenko & Eduardo L. Pasiliao, 2015. "An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 178-188, February.
    6. 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.
    7. Kejia Zhang & Qilong Han & Guisheng Yin & Haiwei Pan, 2016. "OFDP: a distributed algorithm for finding disjoint paths with minimum total length in wireless sensor networks," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1623-1641, May.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Zhao Zhang & Wen Xu & Weili Wu & Ding-Zhu Du, 2017. "A novel approach for detecting multiple rumor sources in networks with partial observations," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 132-146, January.
    8. Majun Shi & Zishen Yang & Wei Wang, 2023. "Greedy guarantees for minimum submodular cost submodular/non-submodular cover problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-16, January.
    9. 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.
    10. Kübra Tanınmış & Markus Sinnl, 2022. "A Branch-and-Cut Algorithm for Submodular Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2634-2657, September.
    11. Hejiao Huang & Feng Shang & Jinling Liu & Hongwei Du, 2015. "Handling least privilege problem and role mining in RBAC," Journal of Combinatorial Optimization, Springer, vol. 30(1), pages 63-86, July.
    12. Zhao Zhang & Wei Liang & Hongmin W. Du & Siwen Liu, 2022. "Constant Approximation for the Lifetime Scheduling Problem of p -Percent Coverage," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2675-2685, September.
    13. Xiaozhi Wang & Xianyue Li & Bo Hou & Wen Liu & Lidong Wu & Suogang Gao, 2021. "A greedy algorithm for the fault-tolerant outer-connected dominating set problem," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 118-127, January.
    14. Xiang Li & H. George Du & Panos M. Pardalos, 2020. "A variation of DS decomposition in set function optimization," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 36-44, July.
    15. Xiang Li & H. George Du, 2020. "A short proof for stronger version of DS decomposition in set function optimization," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 901-906, November.
    16. Chuanwen Luo & Yongcai Wang & Yi Hong & Wenping Chen & Xingjian Ding & Yuqing Zhu & Deying Li, 2019. "Minimizing data collection latency with unmanned aerial vehicle in wireless sensor networks," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1019-1042, November.
    17. Shi, Majun & Yang, Zishen & Wang, Wei, 2021. "Minimum non-submodular cover problem with applications," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    18. Limin Wang & Wenxue Du & Zhao Zhang & Xiaoyan Zhang, 2017. "A PTAS for minimum weighted connected vertex cover $$P_3$$ P 3 problem in 3-dimensional wireless sensor networks," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 106-122, January.
    19. Austin Buchanan & Je Sang Sung & Sergiy Butenko & Eduardo L. Pasiliao, 2015. "An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 178-188, February.
    20. Yichao He & Xinlu Zhang & Wenbin Li & Xiang Li & Weili Wu & Suogang Gao, 2016. "Algorithms for randomized time-varying knapsack problems," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 95-117, 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:28:y:2014:i:1:d:10.1007_s10878-013-9638-4. 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.