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PTAS for the minimum k-path connected vertex cover problem in unit disk graphs

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Abstract

In the Minimum k-Path Connected Vertex Cover Problem (MkPCVCP), we are given a connected graph G and an integer k ≥ 2, and are required to find a subset C of vertices with minimum cardinality such that each path with length k − 1 has a vertex in C, and moreover, the induced subgraph G[C] is connected. MkPCVCP is a generalization of the minimum connected vertex cover problem and has applications in many areas such as security communications in wireless sensor networks. MkPCVCP is proved to be NP-complete. In this paper, we give the first polynomial time approximation scheme (PTAS) for MkPCVCP in unit disk graphs, for every fixed k ≥ 2.

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Authors and Affiliations

  1. School of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Xianliang Liu, Hongliang Lu & Wei Wang

  2. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75083, USA

    Weili Wu

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  1. Xianliang Liu
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  2. Hongliang Lu
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  3. Wei Wang
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  4. Weili Wu
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Corresponding author

Correspondence to Wei Wang.

Additional information

This work was supported in part by the Fundamental Research Funds for the Central Universities, the National Natural Science Foundation of China No. 11071191 and 11101329.

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Liu, X., Lu, H., Wang, W. et al. PTAS for the minimum k-path connected vertex cover problem in unit disk graphs. J Glob Optim 56, 449–458 (2013). https://doi.org/10.1007/s10898-011-9831-x

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  • DOI: https://doi.org/10.1007/s10898-011-9831-x

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