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Approximation Algorithm for the Minimum Connected \(k\)-Path Vertex Cover Problem

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Combinatorial Optimization and Applications (COCOA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8881))

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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 Xingjiang Talent Youth Project (2013711011).

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, Xinjiang, People’s Republic of China

    Xiaosong Li

  2. College of Mathematics Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, Zhejiang, People’s Republic of China

    Zhao Zhang & Xiaohui Huang

Authors
  1. Xiaosong Li
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  2. Zhao Zhang
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  3. Xiaohui Huang
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Corresponding author

Correspondence to Zhao Zhang .

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Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, Zhejiang, China

    Zhao Zhang

  2. University of Texas, Tyler, Texas, USA

    Lidong Wu

  3. University of Texas, Dallas, Texas, USA

    Wen Xu

  4. University of Texas, Dallas, USA

    Ding-Zhu Du

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© 2014 Springer International Publishing Switzerland

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

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