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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
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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.

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