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An Efficient Algorithm for the k-Dominating Set Problem on Very Large-Scale Networks (Extended Abstract)

  • Minh Hai Nguyen
  • Minh Hoàng HàEmail author
  • Dinh Thai Hoang
  • Diep N. Nguyen
  • Eryk Dutkiewicz
  • The Trung Tran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11917)

Abstract

The minimum dominating set problem (MDSP) aims to construct the minimum-size subset \(D \subset V\) of a graph \(G = (V, E)\) such that every vertex has at least one neighbor in D. The problem is proved to be NP-hard [5]. In a recent industrial application, we encountered a more general variant of MDSP that extends the neighborhood relationship as follows: a vertex is a k-neighbor of another if there exists a linking path through no more than k edges between them. This problem is called the minimum k-dominating set problem (MkDSP) and the dominating set is denoted as \(D_k\). The MkDSP can be used to model applications in social networks [2] and design of wireless sensor networks [3]. In our case, a telecommunication company uses the problem model to supervise a large social network up to 17 millions nodes via a dominating subset in which k is set to 3.

References

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Minh Hai Nguyen
    • 1
    • 2
  • Minh Hoàng Hà
    • 1
    Email author
  • Dinh Thai Hoang
    • 2
  • Diep N. Nguyen
    • 2
  • Eryk Dutkiewicz
    • 2
  • The Trung Tran
    • 3
  1. 1.ORLabVNU University of Engineering and TechnologyHanoiVietnam
  2. 2.Faculty of Engineering and Information TechnologyUniversity of TechnologySydneyAustralia
  3. 3.FPT Technology Research InstituteHanoiVietnam

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