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A simpler PTAS for connected k-path vertex cover in homogeneous wireless sensor network

Author

Listed:
  • Lina Chen

    (Zhejiang Normal University)

  • Xiaohui Huang

    (Zhejiang Normal University)

  • Zhao Zhang

    (Zhejiang Normal University)

Abstract

Because of its application in the field of security in wireless sensor networks, k-path vertex cover ( $$\hbox {VCP}_k$$ VCP k ) has received a lot of attention in recent years. Given a graph $$G=(V,E)$$ G = ( V , E ) , a vertex set $$C\subseteq V$$ C ⊆ V is a k-path vertex cover ( $$\hbox {VCP}_k$$ VCP k ) of G if every path on k vertices has at least one vertex in C, and C is a connected k-path vertex cover of G ( $$\hbox {CVCP}_k$$ CVCP k ) if furthermore the subgraph of G induced by C is connected. A homogeneous wireless sensor network can be modeled as a unit disk graph. This paper presents a new PTAS for $$\hbox {MinCVCP}_k$$ MinCVCP k on unit disk graphs. Compared with previous PTAS given by Liu et al., our method not only simplifies the algorithm and reduces the time-complexity, but also simplifies the analysis by a large amount.

Suggested Citation

  • Lina Chen & Xiaohui Huang & Zhao Zhang, 2018. "A simpler PTAS for connected k-path vertex cover in homogeneous wireless sensor network," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 35-43, July.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:1:d:10.1007_s10878-018-0283-9
    DOI: 10.1007/s10878-018-0283-9
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    References listed on IDEAS

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    1. Xianliang Liu & Hongliang Lu & Wei Wang & Weili Wu, 2013. "PTAS for the minimum k-path connected vertex cover problem in unit disk graphs," Journal of Global Optimization, Springer, vol. 56(2), pages 449-458, June.
    2. 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.
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