IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v36y2018i2d10.1007_s10878-018-0306-6.html
   My bibliography  Save this article

Minimizing the total cost of barrier coverage in a linear domain

Author

Listed:
  • Xiao Zhang

    (City University of Hong Kong)

  • Haosheng Fan

    (Hong Kong University of Science and Technology)

  • Victor C. S. Lee

    (City University of Hong Kong)

  • Minming Li

    (City University of Hong Kong)

  • Yingchao Zhao

    (Caritas Institute of Higher Education)

  • Chuang Liu

    (Shenzhen Key Laboratory of Internet Information Collaboration)

Abstract

Barrier coverage, as one of the most important applications of wireless sensor network (WSNs), is to provide coverage for the boundary of a target region. We study the barrier coverage problem by using a set of n sensors with adjustable coverage radii deployed along a line interval or circle. Our goal is to determine a range assignment $$\mathbf {R}=({r_{1}},{r_{2}}, \ldots , {r_{n}})$$ R = ( r 1 , r 2 , … , r n ) of sensors such that the line interval or circle is fully covered and its total cost $$C(\mathbf {R})=\sum _{i=1}^n {r_{i}}^\alpha $$ C ( R ) = ∑ i = 1 n r i α is minimized. For the line interval case, we formulate the barrier coverage problem of line-based offsets deployment, and present two approximation algorithms to solve it. One is an approximation algorithm of ratio 4 / 3 runs in $$O(n^{2})$$ O ( n 2 ) time, while the other is a fully polynomial time approximation scheme (FPTAS) of computational complexity $$O(\frac{n^{2}}{\epsilon })$$ O ( n 2 ϵ ) . For the circle case, we optimally solve it when $$\alpha = 1$$ α = 1 and present a $$2(\frac{\pi }{2})^\alpha $$ 2 ( π 2 ) α -approximation algorithm when $$\alpha > 1$$ α > 1 . Besides, we propose an integer linear programming (ILP) to minimize the total cost of the barrier coverage problem such that each point of the line interval is covered by at least k sensors.

Suggested Citation

  • Xiao Zhang & Haosheng Fan & Victor C. S. Lee & Minming Li & Yingchao Zhao & Chuang Liu, 2018. "Minimizing the total cost of barrier coverage in a linear domain," Journal of Combinatorial Optimization, Springer, vol. 36(2), pages 434-457, August.
  • Handle: RePEc:spr:jcomop:v:36:y:2018:i:2:d:10.1007_s10878-018-0306-6
    DOI: 10.1007/s10878-018-0306-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-018-0306-6
    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/s10878-018-0306-6?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. Yaochun Huang & Xiaofeng Gao & Zhao Zhang & Weili Wu, 2009. "A better constant-factor approximation for weighted dominating set in unit disk graph," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 179-194, August.
    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. Feng Zou & Xianyue Li & Suogang Gao & Weili Wu, 2009. "Node-weighted Steiner tree approximation in unit disk graphs," Journal of Combinatorial Optimization, Springer, vol. 18(4), pages 342-349, November.
    2. Hongwei Du & Panos Pardalos & Weili Wu & Lidong Wu, 2013. "Maximum lifetime connected coverage with two active-phase sensors," Journal of Global Optimization, Springer, vol. 56(2), pages 559-568, June.
    3. Jiao Zhou & Zhao Zhang & Shaojie Tang & Xiaohui Huang & Ding-Zhu Du, 2018. "Breaking the O (ln n ) Barrier: An Enhanced Approximation Algorithm for Fault-Tolerant Minimum Weight Connected Dominating Set," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 225-235, May.
    4. Zhao Zhang & Wei Liang & Hongmin W. Du & Siwen Liu, 2022. "Constant Approximation for the Lifetime Scheduling Problem of p -Percent Coverage," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2675-2685, September.

    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:2:d:10.1007_s10878-018-0306-6. 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.