Journal of Combinatorial Optimization

, Volume 36, Issue 1, pp 35–43 | Cite as

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

  • Lina Chen
  • Xiaohui Huang
  • Zhao Zhang


Because of its application in the field of security in wireless sensor networks, k-path vertex cover (\(\hbox {VCP}_k\)) has received a lot of attention in recent years. Given a graph \(G=(V,E)\), a vertex set \(C\subseteq V\) is a k-path vertex cover (\(\hbox {VCP}_k\)) 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 (\(\hbox {CVCP}_k\)) 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 \(\hbox {MinCVCP}_k\) 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.


Connected k-path vertex cover Unit disk graph PTAS Approximation algorithm 



This research is supported by NSFC (11771013, 11531011, 61502431).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics Physics and Information EngineeringZhejiang Normal UniversityJinhuaChina
  2. 2.Library and Information CenterZhejiang Normal UniversityJinhuaChina

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