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A greedy algorithm for the fault-tolerant outer-connected dominating set problem

Author

Listed:
  • Xiaozhi Wang

    (Hebei Normal University)

  • Xianyue Li

    (Lanzhou University)

  • Bo Hou

    (Hebei Normal University)

  • Wen Liu

    (Hebei Normal University)

  • Lidong Wu

    (University of Texas at Tyler)

  • Suogang Gao

    (Hebei Normal University)

Abstract

For a graph $$G=(V,E)$$ G = ( V , E ) , a vertex set $$C\subseteq V$$ C ⊆ V is an m-fold outer-connected dominating set (m-fold OCDS) of G if every vertex in $$V\backslash C$$ V \ C has at least m neighbors in C and the subgraph of G induced by $$V\backslash C$$ V \ C is connected. In this paper, we present a greedy algorithm to compute an m-fold OCDS in general graphs, which returns a solution of size at most $$\alpha +1+\ln (\Delta +m+1)$$ α + 1 + ln ( Δ + m + 1 ) times that of a minimum m-fold OCDS, where $$\Delta $$ Δ is the maximum degree of the graph and $$\alpha $$ α is a positive number at most $$\Delta $$ Δ +m+1.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:41:y:2021:i:1:d:10.1007_s10878-020-00668-z
    DOI: 10.1007/s10878-020-00668-z
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    References listed on IDEAS

    as
    1. D. Pradhan, 2016. "On the complexity of the minimum outer-connected dominating set problem in graphs," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 1-12, January.
    2. 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.
    3. 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.
    4. 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.
    5. M. H. Akhbari & R. Hasni & O. Favaron & H. Karami & S. M. Sheikholeslami, 2013. "On the outer-connected domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 10-18, July.
    6. 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, August.
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