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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
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    References listed on IDEAS

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    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, June.
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    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. Yaoyao Zhang & Chaojie Zhu & Shaojie Tang & Yingli Ran & Ding-Zhu Du & Zhao Zhang, 2024. "Evolutionary Algorithm on General Cover with Theoretically Guaranteed Approximation Ratio," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 510-525, March.
    8. 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.

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