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Computing Minimum k -Connected m -Fold Dominating Set in General Graphs

Author

Listed:
  • Zhao Zhang

    (College of Mathematics Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China)

  • Jiao Zhou

    (College of Mathematics Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China)

  • Shaojie Tang

    (Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080)

  • Xiaohui Huang

    (College of Mathematics Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China)

  • Ding-Zhu Du

    (Department of Computer Science, University of Texas at Dallas, Richardson, Texas 75080)

Abstract

Connected dominating set (CDS) problem has been extensively studied in the literature due to its applications in many domains, including computer science and operations research. For example, CDS has been recommended to serve as a virtual backbone in wireless sensor networks (WSNs). Since sensor nodes in WSNs are prone to failures, it is important to build a fault-tolerant virtual backbone that maintains a certain degree of redundancy. A fault-tolerant virtual backbone can be modeled as a k -connected m -fold dominating set ( k , m )-CDS. For a connected graph G = ( V , E ) and two fixed integers k and m , a node set C ⊆ V is a ( k , m )-CDS of G if every node in V \ C has at least m neighbors in C , and the subgraph of G induced by C is k -connected. Previous to this work, approximation algorithms with guaranteed performance ratio in a general graph were known only for k ≤ 3. This paper makes significant progress by presenting a (2 k − 1) α 0 approximation algorithm for general k and m with m ≥ k , where α 0 is the performance ratio for the minimum (1, m )-CDS problem. Using a currently best-known ratio for α 0 , our algorithm has performance ratio O (lnΔ), where Δ is the maximum degree of the graph. Simulation results validate the effectiveness of our algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:30:y:2018:i:2:p:217-224
    DOI: 10.1287/ijoc.2017.0776
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    References listed on IDEAS

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    1. M. Gisela Bardossy & S. Raghavan, 2010. "Dual-Based Local Search for the Connected Facility Location and Related Problems," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 584-602, November.
    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. 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.
    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.
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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. 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. 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.

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