Limiting the Influence to Vulnerable Users in Social Networks: A Ratio Perspective

  • Huiping Chen
  • Grigorios LoukidesEmail author
  • Jiashi Fan
  • Hau Chan
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 926)


Influence maximization is a key problem in social networks, seeking to find users who will diffuse information to influence a large number of users. A drawback of the standard influence maximization is that it is unethical to influence users many of whom would be harmed, due to their demographics, health conditions, or socioeconomic characteristics (e.g., predominantly overweight people influenced to buy junk food). Motivated by this drawback and by the fact that some of these vulnerable users will be influenced inadvertently, we introduce the problem of finding a set of users (seeds) that limits the influence to vulnerable users while maximizing the influence to the non-vulnerable users. We define a measure that captures the quality of a set of seeds, as an additively smoothed ratio between the expected number of influenced non-vulnerable users and the expected number of influenced vulnerable users. Then, we develop greedy heuristics and an approximation algorithm called ISS for our problem, which aim to find a set of seeds that maximizes the measure. We evaluate our methods on synthetic and real-world datasets and demonstrate that ISS substantially outperforms a heuristic competitor in terms of both effectiveness and efficiency while being more effective and/or efficient than the greedy heuristics.


  1. 1.
  2. 2.
    Abebe, R., Adamic, L., Kleinberg, J.: Mitigating overexposure in viral marketing (2018)Google Scholar
  3. 3.
    Bai, W., Iyer, R., Wei, K., Bilmes, J.: Algorithms for optimizing the ratio of submodular functions. In: ICML, pp. 2751–2759 (2016)Google Scholar
  4. 4.
    Buchbinder, N., Feldman, M., Naor, J., Schwartz, R.: Submodular maximization with cardinality constraints. In: SODA, pp. 1433–1452 (2014)Google Scholar
  5. 5.
    Chen, W., et al.: Influence maximization in social networks when negative opinions may emerge and propagate. In: SDM, pp. 379–390 (2011)Google Scholar
  6. 6.
    Goyal, A., Lu, W., Lakshmanan, L.V.S.: SIMPATH: an efficient algorithm for influence maximization under the linear threshold model. In: ICDM, pp. 211–220 (2011)Google Scholar
  7. 7.
    Gupta, S.: A conceptual framework that identifies antecedents and consequences of building socially responsible international brands. Thunderbird Int. Bus. Rev. 58(3), 225–237 (2016)CrossRefGoogle Scholar
  8. 8.
    Gwadera, R., Loukides, G.: Cost-effective viral marketing in the latency aware independent cascade model. In: PAKDD, pp. 251–265 (2017)Google Scholar
  9. 9.
    Iyer, R., Bilmes, J.: Algorithms for approximate minimization of the difference between submodular functions, with applications. In: UAI, pp. 407–417 (2012)Google Scholar
  10. 10.
    Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: KDD, pp. 137–146 (2003)Google Scholar
  11. 11.
    Khan, A., Zehnder, B., Kossmann, D.: Revenue maximization by viral marketing: a social network host’s perspective. In: ICDE, pp. 37–48 (2016)Google Scholar
  12. 12.
    Krause, A., Golovin, D.: Submodular function maximization. In: Tractability (2013)Google Scholar
  13. 13.
    Li, F., Li, C., Shan, M.: Labeled influence maximization in social networks for target marketing. In: PASSAT/SocialCom 2011, pp. 560–563 (2011)Google Scholar
  14. 14.
    Li, Y., Fan, J., Wang, Y., Tan, K.: Influence maximization on social graphs: a survey. TKDE 30(10), 1852–1872 (2018)Google Scholar
  15. 15.
    Loukides, G., Gwadera, R.: Preventing the diffusion of information to vulnerable users while preserving pagerank. Int. J. Data Sci. Anal. 5(1), 19–39 (2018)CrossRefGoogle Scholar
  16. 16.
    Manning, C., Raghavan, P., Schütze, M.: Introduction to Information Retrieval (2008)Google Scholar
  17. 17.
    Mitrovic, M., Bun, M., Krause, A., Karbasi, A.: Differentially private submodular maximization: data summarization in disguise. In: ICML, pp. 2478–2487 (2017)Google Scholar
  18. 18.
    Nemhauser, G.L., Wolsey, L.A., Fisher, M.L.: An analysis of approximations for maximizing submodular set functions. Math. Program. 14(1), 265–294 (1978)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Nielsen: Sustainable selections: how socially responsible companies are turning a profit.
  20. 20.
    Pasumarthi, R., Narayanam, R., Ravindran, B.: Near optimal strategies for targeted marketing in social networks. In: AAMAS, pp. 1679–1680 (2015)Google Scholar
  21. 21.
    Shaw, G., Karami, A.: Computational content analysis of negative tweets for obesity, diet, diabetes, and exercise. Proc. Assoc. Inf. Sci. Technol. 54(1), 357–365 (2017)CrossRefGoogle Scholar
  22. 22.
    Song, C., Hsu, W., Lee, M.L.: Targeted influence maximization in social networks. In: CIKM, pp. 1683–1692 (2016)Google Scholar
  23. 23.
    Svitkina, Z., Fleischer, L.: Submodular approximation: sampling-based algorithms and lower bounds. SIAM J. Comput. 40(6), 1715–1737 (2011)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Wang, C., Chen, W., Wang, Y.: Scalable influence maximization for independent cascade model in large-scale social networks. DMKD 25(3), 545–576 (2012)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Wen, Y.T., Peng, W., Shuai, H.: Maximizing social influence on target users. In: PAKDD, pp. 701–712 (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Huiping Chen
    • 1
  • Grigorios Loukides
    • 1
    Email author
  • Jiashi Fan
    • 1
  • Hau Chan
    • 2
  1. 1.King’s College LondonLondonUK
  2. 2.University of Nebraska-LincolnLincolnUSA

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