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On the approximability of positive influence dominating set in social networks

Author

Listed:
  • Thang N. Dinh

    (University of Florida)

  • Yilin Shen

    (University of Florida)

  • Dung T. Nguyen

    (University of Florida)

  • My T. Thai

    (University of Florida)

Abstract

In social networks, there is a tendency for connected users to match each other’s behaviors. Moreover, a user likely adopts a behavior, if a certain fraction of his family and friends follows that behavior. Identifying people who have the most influential effect to the others is of great advantages, especially in politics, marketing, behavior correction, and so on. Under a graph-theoretical framework, we study the positive influence dominating set (PIDS) problem that seeks for a minimal set of nodes $\mathcal{P}$ such that all other nodes in the network have at least a fraction ρ>0 of their neighbors in $\mathcal{P}$ . We also study a different formulation, called total positive influence dominating set (TPIDS), in which even nodes in $\mathcal{P}$ are required to have a fraction ρ of neighbors inside $\mathcal{P}$ . We show that neither of these problems can be approximated within a factor of (1−ϵ)lnmax{Δ,|V|1/2}, where Δ is the maximum degree. Moreover, we provide a simple proof that both problems can be approximated within a factor lnΔ+O(1). In power-law networks, where the degree sequence follows a power-law distribution, both problems admit constant factor approximation algorithms. Finally, we present a linear-time exact algorithms for trees.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jcomop:v:27:y:2014:i:3:d:10.1007_s10878-012-9530-7
    DOI: 10.1007/s10878-012-9530-7
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    References listed on IDEAS

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    1. Xu Zhu & Jieun Yu & Wonjun Lee & Donghyun Kim & Shan Shan & Ding-Zhu Du, 2010. "New dominating sets in social networks," Journal of Global Optimization, Springer, vol. 48(4), pages 633-642, December.
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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    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.

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