Journal of Combinatorial Optimization

, Volume 28, Issue 3, pp 529–539 | Cite as

An individual-based model of information diffusion combining friends’ influence

  • Lidan Fan
  • Zaixin Lu
  • Weili Wu
  • Yuanjun Bi
  • Ailian Wang
  • Bhavani Thuraisingham
Article

Abstract

In many real-world scenarios, an individual accepts a new piece of information based on her intrinsic interest as well as friends’ influence. However, in most of the previous works, the factor of individual’s interest does not receive great attention from researchers. Here, we propose a new model which attaches importance to individual’s interest including friends’ influence. We formulate the problem of maximizing the acceptance of information (MAI) as: launch a seed set of acceptors to trigger a cascade such that the number of final acceptors under a time constraint T in a social network is maximized. We then prove that MAI is NP-hard, and for time \(T = 1,2\), the objective function for information acceptance is sub-modular when the function for friends’ influence is sub-linear in the number of friends who have accepted the information (referred to as active friends). Therefore, an approximation ratio \((1-\frac{1}{e})\) for MAI problem is guaranteed by the greedy algorithm. Moreover, we also prove that when the function for friends’ influence is not sub-linear in the number of active friends, the objective function is not sub-modular.

Keywords

Influence diffusion Information acceptance Individual’s interest Friends’ influence Social networks 

References

  1. Bhagat S, Goyal A, Lakshmanan LVS (2012) Maximizing product adoption in social networks. In: Web search and data mining, WSDM. ACMGoogle Scholar
  2. Bharathi S, Kempe D, Salek M (2007) Competitive influence maximization in social networks. Internet Netw Econ Lect Notes Comput Sci 4858:306–311CrossRefGoogle Scholar
  3. Borodin A, Filmus Y, Oren J (2010) Threshold models for competitive inuence in social networks. WINE. Springer, Berlin, pp 539–550Google Scholar
  4. Brown J, Reinegen P (1987) Social ties and word-of-mouth referral behavior. J Consum Res 14:350–362CrossRefGoogle Scholar
  5. Budak C, Agrawal D, Abbadi A E(2011) Limiting the spread of misinformation in social networks. In: WWW. ACM, pp 665–674Google Scholar
  6. Chen W, Wang Y, Yang S (2009) Efficient influence maximization in social networks. In: Proceedings of the 15th ACM SIGKDD international conference on knowledge discovery and data mining in KDD. ACMGoogle Scholar
  7. Chen W, Wang C, Wang Y (2010a) Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: Proceedings of the 16th ACM SIGKDD international conference on knowledge discovery and data mining In KDD. ACM, pp 1029–1038Google Scholar
  8. Chen W, Yuan Y, Zhang L (2010b) Scalable influence maximization in social networks under the linear threshold model. In: Proceedings of the 10th IEEE international conference on data mining (ICDM). IEEE, pp 88–97Google Scholar
  9. Domingos P, Richardson M (2001) Mining the network value of customers. In: KDD. ACM, pp 57–66Google Scholar
  10. Fan L, Lu Z, Wu W, Thuraisingham B, Ma H, Bi Y (2013) Least cost rumor blocking in social networks. In: Proceedings of the 33rd internaltional conference on distributed computing systems (ICDCS)Google Scholar
  11. Goldenberg J, Libai B, Muller E (2001a) Talk of the network: a complex systems look at the underlying process of word-of-mouth. Mark Lett 12:211–223CrossRefGoogle Scholar
  12. Goldenberg J, Libai B, Muller E (2001b) Using complex systems analysis to advance marketing theory development: modeling heterogeneity effects on new product growth through stochastic cellular automata. Acad Mark Sci Rev 9:1–18Google Scholar
  13. Goyal A, Lu W, Lakshmanan LVS (2011a) CELF++: optimizing the greedy algorithm for influence maximization in social networks. In: Proceedings of the international World wide web conference. ACM, pp 47–48Google Scholar
  14. Goyal A, Lu W, Lakshmanan LVS (2011b) SIMPATH: an efficient algorithm for influence maximization under the linear threshold model. In: Proceedings of the IEEE international conference on data mining. IEEE, pp 211–220Google Scholar
  15. He X, Song G, Chen W, Jiang Q (2012) Inuence blocking maximization in social networks under the competitive linear threshold model. In: SDMGoogle Scholar
  16. Kempe D, Kleinberg JM, Kleinberg É (2003) Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD international conference on knowledge discovery and data mining in KDD. ACM, pp 137–146Google Scholar
  17. Kempe D, Kleinberg JM, Tardos É (2005) Influential nodes in a diffusion model for social networks. ICALP. Springer, Berlin, pp 1127–1138Google Scholar
  18. Kimura M, Saito K (2006) Tractable models for information diffusion in social networks. PKDD. Springer, Berlin, pp 259–271Google Scholar
  19. Kimura M, Saito K, Nakano R (2007) Extracting influential nodes for information diffusion on a social network. In: AAAI. pp 1371–1376Google Scholar
  20. Kimura M, Saito K, Motoda H (2009) Efficient estimation of influence functions for SIS model on social networks. In: Proceedings of the 21st international joint conference on artificial intelligence. pp 2046–2051Google Scholar
  21. Leskovec J, Krause A, Guestrin C, Faloutsos C, VanBriesen J, Glance N (2007) Coste effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD international conference on knowledge discovery and data mining (KDD). ACM, pp 420–429Google Scholar
  22. Lu Z, Fan L, Wu W, Thuraisingham B, Yang K(2014) Efficient influence spread estimation for influence maximization under the linear threshold model. To appear in computational, social networksGoogle Scholar
  23. Nemhauser G, Wolsey L, Fisher M (1978) An analysis of the approximations for maximizing submodular set functions. Math Program 14:265–294CrossRefMATHMathSciNetGoogle Scholar
  24. Richardson M, Domingos V (2002) Mining knowledge-sharing sites for viral marketing. In: KDD. ACM, pp 61–70Google Scholar
  25. Valente TW (2005) Network models and methods for studying the diffusion of innovations. In: carrington Peter J, Scott John, Wasserman Stanley (eds) Models and methods in social network analysis. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Lidan Fan
    • 1
  • Zaixin Lu
    • 1
  • Weili Wu
    • 1
  • Yuanjun Bi
    • 1
  • Ailian Wang
    • 2
  • Bhavani Thuraisingham
    • 1
  1. 1.Department of Computer ScienceThe University of Texas at DallasRichardsonUSA
  2. 2.Taiyuan Institute of TechnologyTaiyuanPeople’s Republic of China

Personalised recommendations