Maximizing Social Influence for the Awareness Threshold Model

  • Haiqi Sun
  • Reynold Cheng
  • Xiaokui Xiao
  • Jing Yan
  • Yudian Zheng
  • Yuqiu Qian
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10827)


Given a social network G, the Influence Maximization (IM) problem aims to find a seed set \(S \subseteq G\) of k users. These users are advertised, or activated, through marketing campaigns, with the hope that they will continue to influence others in G (e.g., by spreading messages about a new book). The goal of IM is to find the set S that achieves an optimal advertising effect or expected spread (e.g., make the largest number of users in G know about the book).

Existing IM solutions make extensive use of propagation models, such as Linear Threshold (LT) or the Independent Cascade (IC). These models define the activation probability, or the chance that a user successfully gets activated by his/her neighbors in G. Although these models are well-studied, they overlook the fact that a user’s influence on others decreases with time. This can lead to an over-estimation of activation probabilities, as well as the expected spread.

To address the drawbacks of LT and IC, we develop a new propagation model, called Awareness Threshold (or AT), which considers the fact that a user’s influence decays with time. We further study the Scheduled Influence Maximization (or SIM), to find out the set S of users to activate, as well as when they should be activated. The SIM problem considers the time-decaying nature of influence based on the AT model. We show that the problem is NP-hard, and we develop three approximation solutions with accuracy guarantees. Extensive experiments on real social networks show that (1) AT yields a more accurate estimation of activation probability; and (2) Solutions to the SIM gives a better expected spread than IM algorithms on the AT model.



We would like to thank the reviewers for the insightful comments. Haiqi Sun, Jing Yan, Yudian zheng, and Reynold Cheng were supported by the Research Grants Council of Hong Kong (RGC Projects HKU 17229116 and 17205115) and the University of Hong Kong (Projects 104004572, 102009508, 104004129).


  1. 1.
  2. 2.
  3. 3.
  4. 4.
    Almon, S.: The distributed lag between capital appropriations and expenditures. Econom.: J. Econom. Soc. 33, 178–196 (1965)CrossRefGoogle Scholar
  5. 5.
    Bharathi, S., Kempe, D., Salek, M.: Competitive influence maximization in social networks. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 306–311. Springer, Heidelberg (2007). Scholar
  6. 6.
    Borgs, C., Brautbar, M., Chayes, J., Lucier, B.: Maximizing social influence in nearly optimal time. In: SODA (2014)Google Scholar
  7. 7.
    Broadbent, S.: Accountable Advertising: A Handbook for Managers and Analysts. Admap Publications, Henley-on-Thames (1997)Google Scholar
  8. 8.
    Brown, G.: Modelling advertising awareness. Statistician 35, 289–299 (1986)CrossRefGoogle Scholar
  9. 9.
    Chen, S., Fan, J., Li, G., Feng, J., Tan, K.-L., Tang, J.: Online topic-aware influence maximization. PVLDB 8, 666–677 (2015)Google Scholar
  10. 10.
    Chen, W., Lu, W., Zhang, N.: Time-critical influence maximization in social networks with time-delayed diffusion process. In: AAAI (2012)Google Scholar
  11. 11.
    Chen, W., Wang, C., Wang, Y.: Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: KDD (2010)Google Scholar
  12. 12.
    Chen, W., Wang, Y., Yang, S.: Efficient influence maximization in social networks. In: KDD (2009)Google Scholar
  13. 13.
    Dubé, J.-P., Hitsch, G.J., Manchanda, P.: An empirical model of advertising dynamics. Quant. Mark. Econ. 3, 107–144 (2005)CrossRefGoogle Scholar
  14. 14.
    Feng, S., Chen, X., Cong, G., Zeng, Y., Chee, Y.M., Xiang, Y.: Influence maximization with novelty decay in social networks. In: AAAI (2014)Google Scholar
  15. 15.
    Ferguson, R.: Word of mouth and viral marketing: taking the temperature of the hottest trends in marketing. J. Consum. Mark. 25, 179–182 (2008)CrossRefGoogle Scholar
  16. 16.
    Fry, T.R., Broadbent, S., Dixon, J.M., et al.: Estimating advertising half-life and the data interval bias. Technical report, Monash University, Department of Econometrics and Business Statistics (1999)Google Scholar
  17. 17.
    Goyal, A., Bonchi, F., Lakshmanan, L.V.: Learning influence probabilities in social networks. In: WSDM (2010)Google Scholar
  18. 18.
    Goyal, A., Bonchi, F., Lakshmanan, L.V.: A data-based approach to social influence maximization. PVLDB 5, 73–84 (2011)Google Scholar
  19. 19.
    Goyal, A., Lu, W., Lakshmanan, L.V.: CELF++: optimizing the greedy algorithm for influence maximization in social networks. In: WWW (2011)Google Scholar
  20. 20.
    Goyal, A., Lu, W., Lakshmanan, L.V.: Simpath: an efficient algorithm for influence maximization under the linear threshold model. In: ICDM (2011)Google Scholar
  21. 21.
    He, X., Song, G., Chen, W., Jiang, Q.: Influence blocking maximization in social networks under the competitive linear threshold model. In: Proceedings of the 2012 SIAM International Conference on Data Mining, pp. 463–474. SIAM (2012)CrossRefGoogle Scholar
  22. 22.
    Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: KDD (2003)Google Scholar
  23. 23.
    Kempe, D., Kleinberg, J., Tardos, É.: Influential nodes in a diffusion model for social networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1127–1138. Springer, Heidelberg (2005). Scholar
  24. 24.
    Kim, J., Kim, S.-K., Yu, H.: Scalable and parallelizable processing of influence maximization for large-scale social networks? In: ICDE (2013)Google Scholar
  25. 25.
    Kirby, J.: Viral marketing. In: Connected marketing (2012)Google Scholar
  26. 26.
    Lei, S., Maniu, S., Mo, L., Cheng, R., Senellart, P.: Online influence maximization. In: KDD (2015)Google Scholar
  27. 27.
    Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J., Glance, N.: Cost-effective outbreak detection in networks. In: KDD (2007)Google Scholar
  28. 28.
    Li, G., Chen, S., Feng, J., Tan, K.-L., Li, W.: Efficient location-aware influence maximization. In: SIGMOD (2014)Google Scholar
  29. 29.
    Lin, S.-C., Lin, S.-D., Chen, M.-S.: A learning-based framework to handle multi-round multi-party influence maximization on social networks. In: KDD (2015)Google Scholar
  30. 30.
    Liu, B., Cong, G., Xu, D., Zeng, Y.: Time constrained influence maximization in social networks. In: ICDM (2012)Google Scholar
  31. 31.
    Lu, W., Chen, W., Lakshmanan, L.V.: From competition to complementarity: comparative influence diffusion and maximization. PVLDB 9, 60–71 (2015)Google Scholar
  32. 32.
    Mohammadi, A., Saraee, M., Mirzaei, A.: Time-sensitive influence maximization in social networks. J. Inf. Sci. 41, 765–778 (2015)CrossRefGoogle Scholar
  33. 33.
    Nemhauser, G.L., Wolsey, L.A., Fisher, M.L.: An analysis of approximations for maximizing submodular set functions. Math. Program. 14, 265–294 (1978)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Ohsaka, N., Yamaguchi, Y., Kakimura, N., Kawarabayashi, K.: Maximizing time-decaying influence in social networks. In: Frasconi, P., Landwehr, N., Manco, G., Vreeken, J. (eds.) ECML PKDD 2016. LNCS (LNAI), vol. 9851, pp. 132–147. Springer, Cham (2016). Scholar
  35. 35.
    Steeg, G.V., Ghosh, R., Lerman, K.: What stops social epidemics? In: ICWSM (2011)Google Scholar
  36. 36.
    Tang, Y., Shi, Y., Xiao, X.: Influence maximization in near-linear time: a martingale approach. In: SIGMOD (2015)Google Scholar
  37. 37.
    Tang, Y., Xiao, X., Shi, Y.: Influence maximization: near-optimal time complexity meets practical efficiency. In: SIGMOD (2014)Google Scholar
  38. 38.
    Zhang, Z., Wu, H., Yue, K., Li, J., Liu, W.: Influence maximization for cascade model with diffusion decay in social networks. In: Che, W., et al. (eds.) ICYCSEE 2016. CCIS, vol. 623, pp. 418–427. Springer, Singapore (2016). Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Haiqi Sun
    • 1
  • Reynold Cheng
    • 1
  • Xiaokui Xiao
    • 2
  • Jing Yan
    • 1
  • Yudian Zheng
    • 1
  • Yuqiu Qian
    • 1
  1. 1.The University of Hong KongPok Fu LamHong Kong
  2. 2.Nanyang Technological UniversitySingaporeSingapore

Personalised recommendations