IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v36y2018i1d10.1007_s10878-018-0283-9.html
   My bibliography  Save this article

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

Author

Listed:
  • Lina Chen

    (Zhejiang Normal University)

  • Xiaohui Huang

    (Zhejiang Normal University)

  • Zhao Zhang

    (Zhejiang Normal University)

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.

Suggested Citation

  • Lina Chen & Xiaohui Huang & Zhao Zhang, 2018. "A simpler PTAS for connected k-path vertex cover in homogeneous wireless sensor network," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 35-43, July.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:1:d:10.1007_s10878-018-0283-9
    DOI: 10.1007/s10878-018-0283-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-018-0283-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-018-0283-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Limin Wang & Wenxue Du & Zhao Zhang & Xiaoyan Zhang, 2017. "A PTAS for minimum weighted connected vertex cover $$P_3$$ P 3 problem in 3-dimensional wireless sensor networks," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 106-122, January.
    2. Xianliang Liu & Hongliang Lu & Wei Wang & Weili Wu, 2013. "PTAS for the minimum k-path connected vertex cover problem in unit disk graphs," Journal of Global Optimization, Springer, vol. 56(2), pages 449-458, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ran, Yingli & Zhang, Zhao & Huang, Xiaohui & Li, Xiaosong & Du, Ding-Zhu, 2019. "Approximation algorithms for minimum weight connected 3-path vertex cover," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 723-733.
    2. Ou Sun & Neng Fan, 2019. "Solving the multistage PMU placement problem by integer programming and equivalent network design model," Journal of Global Optimization, Springer, vol. 74(3), pages 477-493, July.
    3. Raka Jovanovic & Antonio P. Sanfilippo & Stefan Voß, 2022. "Fixed set search applied to the multi-objective minimum weighted vertex cover problem," Journal of Heuristics, Springer, vol. 28(4), pages 481-508, August.
    4. Shuli Hu & Xiaoli Wu & Huan Liu & Yiyuan Wang & Ruizhi Li & Minghao Yin, 2019. "Multi-Objective Neighborhood Search Algorithm Based on Decomposition for Multi-Objective Minimum Weighted Vertex Cover Problem," Sustainability, MDPI, vol. 11(13), pages 1-21, July.
    5. Limin Wang & Wenxue Du & Zhao Zhang & Xiaoyan Zhang, 2017. "A PTAS for minimum weighted connected vertex cover $$P_3$$ P 3 problem in 3-dimensional wireless sensor networks," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 106-122, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:36:y:2018:i:1:d:10.1007_s10878-018-0283-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.