A Simpler Method to Obtain a PTAS for Connected k-Path Vertex Cover in Unit Disk Graph

Given a connected graph \(G=(V,E)\), a connected k-path vertex cover (CVCP\(_k\)) is a vertex set \(C\subseteq V\) which contains at least one vertex from every path of G on k vertices and the subgraph of G induced by C is connected. This paper presents a new PTAS for Min-CVCP\(_k\) on unit disk graphs. Compared with previous PTAS given by Liu et al., Our method not only simplifies the algorithm but also simplifies the analysis by a large amount.

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