Journal of Global Optimization

, Volume 56, Issue 2, pp 449–458 | Cite as

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

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


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.


PTAS k-Path connected vertex cover Unit disk graph 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Xianliang Liu
    • 1
  • Hongliang Lu
    • 1
  • Wei Wang
    • 1
  • Weili Wu
    • 2
  1. 1.School of ScienceXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  2. 2.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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