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Optimization Letters

, Volume 11, Issue 2, pp 419–427 | Cite as

On positive-influence target-domination

  • Guangmo Tong
  • Weili Wu
  • Panos M. Pardalos
  • Ding-Zhu DuEmail author
Original Paper
  • 188 Downloads

Abstract

Consider a graph \(G=(V,E)\) and a vertex subset \(A \subseteq V\). A vertex v is positive-influence dominated by A if either v is in A or at least half the number of neighbors of v belong to A. For a target vertex subset \(S \subseteq V\), a vertex subset A is a positive-influence target-dominating set for target set S if every vertex in S is positive-influence dominated by A. Given a graph G and a target vertex subset S, the positive-influence target-dominating set (PITD) problem is to find the minimum positive-influence dominating set for target S. In this paper, we show two results: (1) The PITD problem has a polynomial-time \((1 + \log \lceil \frac{3}{2} \Delta \rceil )\)-approximation in general graphs where \(\Delta \) is the maximum vertex-degree of the input graph. (2) For target set S with \(|S|=\Omega (|V|)\), the PITD problem has a polynomial-time O(1)-approximation in power-law graphs.

Keywords

Positive-influence Target-dominating Social networks 

Notes

Acknowledgments

Authors wish to thank referees for their insightful comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Guangmo Tong
    • 1
  • Weili Wu
    • 1
  • Panos M. Pardalos
    • 2
    • 3
  • Ding-Zhu Du
    • 1
    • 4
    Email author
  1. 1.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA
  2. 2.Center for Applied Optimization, Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Laboratory of Algorithms and Technologies for Networks Analysis (LATNA)National Research University, Higher School of EconomicsMoscowRussia
  4. 4.Division of Algorithms and Technologies for Networks Analysis, Faculty of Information TechnologyTon Duc Thang UniversityHo Chi Minh CityVietnam

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