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

Lina Chen, Xiaohui Huang and Zhao Zhang ()
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Lina Chen: Zhejiang Normal University
Xiaohui Huang: Zhejiang Normal University
Zhao Zhang: Zhejiang Normal University

Journal of Combinatorial Optimization, 2018, vol. 36, issue 1, No 4, 35-43

Abstract: 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.

Keywords: Connected k-path vertex cover; Unit disk graph; PTAS; Approximation algorithm (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-018-0283-9

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