IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v44y2022i1d10.1007_s10878-021-00834-x.html
   My bibliography  Save this article

A heuristic approximation algorithm of minimum dominating set based on rough set theory

Author

Listed:
  • Lihe Guan

    (Chongqing Jiaotong University)

  • Hong Wang

    (Chongqing Jiaotong University)

Abstract

The minimum dominating set of graph has been widely used in many fields, but its solution is NP-hard. The complexity and approximation accuracy of existing algorithms need to be improved. In this paper, we introduce rough set theory to solve the dominating set of undirected graph. First, the adjacency matrix of undirected graph is used to establish an induced decision table, and the minimum dominating set of undirected graph is equivalent to the minimum attribute reduction of its induced decision table. Second, based on rough set theory, the significance of attributes (i.e., vertices) based on the approximate quality is defined in induced decision table, and a heuristic approximation algorithm of minimum dominating set is designed by using the significance of attributes (i.e., vertices) as heuristic information. This algorithm uses forward and backward search mechanism, which not only ensures to find a minimal dominating set, but also improves the approximation accuracy of minimum dominating set. In addition, a cumulative strategy is used to calculate the positive region of induced decision table, which effectively reduces the computational complexity. Finally, the experimental results on public datasets show that our algorithm has obvious advantages in running time and approximation accuracy of the minimum dominating set.

Suggested Citation

  • Lihe Guan & Hong Wang, 2022. "A heuristic approximation algorithm of minimum dominating set based on rough set theory," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 752-769, August.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-021-00834-x
    DOI: 10.1007/s10878-021-00834-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-021-00834-x
    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/s10878-021-00834-x?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. Shiping Wang & Qingxin Zhu & William Zhu & Fan Min, 2013. "Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
    2. Fuyu Yuan & Chenxi Li & Xin Gao & Minghao Yin & Yiyuan Wang, 2019. "A Novel Hybrid Algorithm for Minimum Total Dominating Set Problem," Mathematics, MDPI, vol. 7(3), pages 1-11, February.
    3. Thang N. Dinh & Yilin Shen & Dung T. Nguyen & My T. Thai, 2014. "On the approximability of positive influence dominating set in social networks," Journal of Combinatorial Optimization, Springer, vol. 27(3), pages 487-503, April.
    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. Yingli Ran & Zhao Zhang & Shaojie Tang & Ding-Zhu Du, 2021. "Breaking the r max Barrier: Enhanced Approximation Algorithms for Partial Set Multicover Problem," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 774-784, May.
    2. Weidong Chen & Hao Zhong & Lidong Wu & Ding-Zhu Du, 2022. "A general greedy approximation algorithm for finding minimum positive influence dominating sets in social networks," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 1-20, August.
    3. S. Raghavan & Rui Zhang, 2022. "Rapid Influence Maximization on Social Networks: The Positive Influence Dominating Set Problem," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1345-1365, May.
    4. Pedro Pinacho-Davidson & Christian Blum, 2020. "Barrakuda : A Hybrid Evolutionary Algorithm for Minimum Capacitated Dominating Set Problem," Mathematics, MDPI, vol. 8(11), pages 1-26, October.
    5. José Alejandro Cornejo Acosta & Jesús García Díaz & Ricardo Menchaca-Méndez & Rolando Menchaca-Méndez, 2020. "Solving the Capacitated Vertex K-Center Problem through the Minimum Capacitated Dominating Set Problem," Mathematics, MDPI, vol. 8(9), pages 1-16, September.
    6. Yingli Ran & Zhao Zhang & Hongwei Du & Yuqing Zhu, 2017. "Approximation algorithm for partial positive influence problem in social network," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 791-802, February.
    7. S. Raghavan & Rui Zhang, 2022. "Influence Maximization with Latency Requirements on Social Networks," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 710-728, March.
    8. Yingli Ran & Yishuo Shi & Changbing Tang & Zhao Zhang, 2020. "A primal-dual algorithm for the minimum partial set multi-cover problem," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 725-746, April.
    9. Yingli Ran & Yishuo Shi & Zhao Zhang, 2017. "Local ratio method on partial set multi-cover," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 302-313, July.

    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:44:y:2022:i:1:d:10.1007_s10878-021-00834-x. 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.