Abstract
A vertex subset \(C\) of a connected graph \(G\) is called a connected \(k\)-path vertex cover (\(CVCP_k\)) if every path of length \(k-1\) contains at least one vertex from \(C\), and the subgraph of \(G\) induced by \(C\) is connected. This concept has its background in the field of security and supervisory control. A variation, called \(CVCC_k\), asks every connected subgraph on \(k\) vertices contains at least one vertex from \(C\). The \(MCVCP_k\) (resp. \(MCVCC_k\)) problem is to find a \(CVCP_k\) (resp. \(CVCC_k\)) with the minimum cardinality. In this paper, we give a \(k\)-approximation algorithm for \(MCVCP_k\) under the assumption that the graph has girth at least \(k\). Similar algorithm on \(MCVCC_k\) also yields approximation ratio \(k\), which is valid for any connected graph (without additional conditions).
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Acknowledgments
This research is supported by NSFC (61222201), SRFDP (20126501110001), and **ngjiang Talent Youth Project (2013711011).
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Li, X., Zhang, Z., Huang, X. (2014). Approximation Algorithm for the Minimum Connected \(k\)-Path Vertex Cover Problem. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_56
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DOI: https://doi.org/10.1007/978-3-319-12691-3_56
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