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PTAS for the minimum k-path connected vertex cover problem in unit disk graphs

Author

Listed:
  • Xianliang Liu
  • Hongliang Lu
  • Wei Wang
  • Weili Wu

Abstract

In the Minimum k-Path Connected Vertex Cover Problem (MkPCVCP), we are given a connected graph G and an integer k ≥ 2, and are required to find a subset C of vertices with minimum cardinality such that each path with length k − 1 has a vertex in C, and moreover, the induced subgraph G[C] is connected. MkPCVCP is a generalization of the minimum connected vertex cover problem and has applications in many areas such as security communications in wireless sensor networks. MkPCVCP is proved to be NP-complete. In this paper, we give the first polynomial time approximation scheme (PTAS) for MkPCVCP in unit disk graphs, for every fixed k ≥ 2. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:449-458
    DOI: 10.1007/s10898-011-9831-x
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    Cited by:

    1. 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.
    2. Ou Sun & Neng Fan, 2019. "Solving the multistage PMU placement problem by integer programming and equivalent network design model," Journal of Global Optimization, Springer, vol. 74(3), pages 477-493, July.
    3. Ran, Yingli & Zhang, Zhao & Huang, Xiaohui & Li, Xiaosong & Du, Ding-Zhu, 2019. "Approximation algorithms for minimum weight connected 3-path vertex cover," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 723-733.
    4. 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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