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Approximation algorithm for partial positive influence problem in social network

Author

Listed:
  • Yingli Ran

    (Xinjiang University)

  • Zhao Zhang

    (Zhejiang Normal University)

  • Hongwei Du

    (Harbin Institute of Technology)

  • Yuqing Zhu

    (California State University)

Abstract

Influence problem is one of the central problems in the study of online social networks, the goal of which is to influence all nodes with the minimum number of seeds. However, in the real world, it might be too expensive to influence all nodes. In many cases, it is satisfactory to influence nodes only up to some percent p. In this paper, we study the minimum partial positive influence dominating set (MPPIDS) problem. In fact, we presented an approximation algorithm for a more general problem called minimum partial set multicover problem. As a consequence, the MPPIDS problem admits an approximation with performance ratio $$\gamma H(\Delta )$$ γ H ( Δ ) , where $$H(\cdot )$$ H ( · ) is the Harmonic number, $$\gamma =1/(1-(1-p)\eta ),\eta \approx \Delta ^2/\delta $$ γ = 1 / ( 1 - ( 1 - p ) η ) , η ≈ Δ 2 / δ , and $$\Delta ,\delta $$ Δ , δ are the maximum degree and the minimum degree of the graph, respectively. For power-law graphs, we show that our algorithm has a constant performance ratio.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:2:d:10.1007_s10878-016-0005-0
    DOI: 10.1007/s10878-016-0005-0
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    References listed on IDEAS

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    1. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    2. 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.
    3. FISHER, Marshall L. & WOLSEY, Laurence A., 1982. "On the greedy heuristic for continuous covering and packing problems," LIDAM Reprints CORE 505, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Gregory Dobson, 1982. "Worst-Case Analysis of Greedy Heuristics for Integer Programming with Nonnegative Data," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 515-531, November.
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    Cited by:

    1. Lin, Geng & Guan, Jian & Feng, Huibin, 2018. "An ILP based memetic algorithm for finding minimum positive influence dominating sets in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 199-209.
    2. Yishuo Shi & Yingli Ran & Zhao Zhang & James Willson & Guangmo Tong & Ding-Zhu Du, 2019. "Approximation algorithm for the partial set multi-cover problem," Journal of Global Optimization, Springer, vol. 75(4), pages 1133-1146, December.

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