Journal of Global Optimization

, Volume 48, Issue 4, pp 633–642 | Cite as

New dominating sets in social networks

  • Xu Zhu
  • Jieun Yu
  • Wonjun Lee
  • Donghyun KimEmail author
  • Shan Shan
  • Ding-Zhu Du


Motivated by applications in social networks, a new type of dominating set has been studied in the literature. In this paper, we present results regarding the complexity and approximation in general graphs.


Dominating set Greedy approximation Social network 


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  1. 1.
    Calinescu, G., Chekuri, C., Pal, M., Vondrak, J.: Maximizing a submodular set function subject to a matroid constraint. In: Proceedings of the 12th International Conference on Integer Programming and Combinatorial Optimization (IPCO 2007), pp. 182–196 (2007)Google Scholar
  2. 2.
    Du, D.-Z., Graham, R.L., Pardalos, P.M., Wan, P.-J., Wu, W., Zhao, W.: Analysis of greedy approximations with nonsubmodular potential functions. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Dicrete Algorithms (SODA). San Francisco, USA, Jan 20–22, pp. 167–175 (2008)Google Scholar
  3. 3.
    Du D.-Z., Gao B., Wu W.: A special case for subset interconnection designs. Discret. Appl. Math. 78, 51–60 (1997)CrossRefGoogle Scholar
  4. 4.
    Du, D.-Z., Ko, K.-I., Hu, X.: Design and Analysis of Approximation Algorithms, Lecture Notes (2008)Google Scholar
  5. 5.
    Du D.-Z., Ko K.-I.: Theory of Computational Complexity. Wiley, New York (2000)Google Scholar
  6. 6.
    Feige U.: A threshold of ln n for approximating set cover. J. ACM 45(4), 634–652 (1998)CrossRefGoogle Scholar
  7. 7.
    Gao X., Wang Y., Li X., Wu W.: Analysis on theoretical bonds for approximating dominating set problems. Discret. Math. Algorithms Appl. 1(1), 71–84 (2009)CrossRefGoogle Scholar
  8. 8.
    Li D., Liu L., Yang H.: Minimum connected r-hop k-dominating set in wireless networks. Discret. Math. Algorithms Appl. 1(1), 45–57 (2009)CrossRefGoogle Scholar
  9. 9.
    Ruan L., Du H., Jia X., Wu W., Li Y., Ko K.: A greedy approximation for minimum connected dominating sets. Theor. Comput. Sci. 329, 325–330 (2004)CrossRefGoogle Scholar
  10. 10.
    Shioura A.: On the pipage rounding algorithm for submodular function maximization: a view from discrete convex analysis. Discret. Math. Algorithms Appl. 1(1), 1–13 (2009)CrossRefGoogle Scholar
  11. 11.
    Wang W., Kim D., Sohaee N., Ma C., Wu W.: A PTAS for minimum d-hop underwater sink placement problem in 2-D underwater sensor networks. Discret. Math. Algorithms Appl. 1(2), 283–289 (2009)CrossRefGoogle Scholar
  12. 12.
    Wang W., Kim D., Willson J., Thuraisingham B., Wu W.: A better approximation for minimum average routing path clustering problem in 2-D underwater sensor networks. Discret. Math. Algorithms Appl. 1(2), 175–191 (2009)CrossRefGoogle Scholar
  13. 13.
    Wolsey L.A.: An analysis of the greedy algorithm for submodular set covering problem. Combinatorica 2(4), 385–393 (1982)CrossRefGoogle Scholar
  14. 14.
    Zou, F., Zhang, Z., Wu, W.: Latency-bounded minimum influential node selection in social networks. In: Proceedings of Workshop on Social Networks, Applications, and Systems. Boston, Aug 16 (2009)Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  • Xu Zhu
    • 1
  • Jieun Yu
    • 2
  • Wonjun Lee
    • 2
  • Donghyun Kim
    • 3
    Email author
  • Shan Shan
    • 3
  • Ding-Zhu Du
    • 3
  1. 1.Department of MathematicsXi’an Jiaotong UniversityXi’anChina
  2. 2.Department of Computer Science and EngineeringKorea UniversitySeoulRepublic of Korea
  3. 3.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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