Advertisement

Minimum cost seed set for threshold influence problem under competitive models

Article
Part of the following topical collections:
  1. Special Issue on Social Computing and Big Data Applications

Abstract

Single source influence propagation based models have been widely studied, but a key challenge remains: How does a company utilize the minimum cost to select a seed set such that its influence spread can reach a desired threshold in competitive environment. One efficient way to overcome this challenge is to design an influence spread function with monotonicity and submodularity, which can provide a nice theoretical analysis of approximation ratio. In this paper, we first propose the Threshold Influence (TI) problem, i.e., selecting a seed set with minimum cost such that the influence spread reaches a given threshold η. Then we present two influence diffusion models named One-To-Many (OTM) and One-To-One (OTO) respectively. On one hand, for One-To-Many model, we prove that the influence spread function is monotone increasing as well as submodular and develop a greedy algorithm with a \((1+\ln (\frac {\eta }{\delta }))\) approximation ratio, where \(\delta >0\). In particular, the approximation ratio is (\(1+\ln (\eta )\)) if \(\eta \) is a positive integer. On the other hand, for One-To-One model, we demonstrate that the influence spread function is non-submodular. Besides, a heuristic framework is developed to solve this problem. Finally, we evaluate our algorithms by simulations on different scale networks. Through experiments, our algorithms outperform comparative methods.

Keywords

Competitive influence Diffusion model Seed selection Submodularity 

Notes

Acknowledgment

This research was supported in part by the National Natural Science Foundation of China under grant 11671400, 61672524, the Fundamental Research Funds for the Central University, and the Research Funds of Renmin University of China 2015030273, and the Research Funds of Renmin University of China 16XNH116.

References

  1. 1.
    Bharathi, S., Kempe, D., Salek, M.: Competitive influence maximization in social networks[J]. Internet and Network Economics, pp. 306–311 (2007)Google Scholar
  2. 2.
    Budak, C., Agrawal, D., El Abbadi, A.: Limiting the spread of misinformation in social networks. In: Proceedings of the 20th international conference on World Wide Web, pp. 665–674. ACM (2011)Google Scholar
  3. 3.
    Cornuejols, G., Fisher, M., Nemhauser, G.: Location of bank accounts to optimize float: an analytic study of exact and approximate algorithms[J]. Manag. Sci. 23(8), 789–810 (1977)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Du, N., Liang, Y., Balcan, M., Manuel, G., Zha, H., Song, L: Scalable influence maximization for multiple products in continuous-time diffusion networks. J. Mach. Learn. Res. 18, 1–45 (2017)MathSciNetMATHGoogle Scholar
  5. 5.
    Fan, L., Lu, Z., Wu, W., Thuraisingham, B., Ma, H., Bi, Y.: Least cost rumor blocking in social networks. In: 33rd international conference on distributed computing systems (2013)Google Scholar
  6. 6.
    Gao, S., Ma, J., Chen, Z., Wang, G., Xing, C.: Ranking the spreading ability of nodes in complex networks based on local structure[J]. Physica A: Statistical Mechanics and its Applications 403, 130–147 (2014)CrossRefGoogle Scholar
  7. 7.
    Goyal, A., Bonchi, F., Lakshmanan, L.V.S., Venkatasubramanian, S.: On minimizing budget and time in influence propagation over social networks. Soc. Netw. Anal. Min. 3(2), 179–192 (2013)CrossRefGoogle Scholar
  8. 8.
    Han, M., Yan, M., Cai, Z., Li, Y., Cai, X., Yu, J.: Influence maximization by probing partial communities in dynamic online social networks[J]. Transactions on Emerging Telecommunications Technologies 28(4) (2017)Google Scholar
  9. 9.
    Karp, R.M.: Reducibility among combinatorial problems. In: Thatcher, R.E., Miller, J.W. (eds.) Complexity of computer computations, pp 85–103. Plenum, New York (1972)Google Scholar
  10. 10.
    Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. KDD’03, pp. 137–146 (2003)Google Scholar
  11. 11.
    Kuhnle, A., Pan, T., Alim, M., Thai, T.: Scalable bicriteria algorithms for the threshold activation problem in online social networks. In: IEEE INFOCOM 2017 - IEEE Conference on Computer Communications, pp. 1–9. Atlanta (2017)Google Scholar
  12. 12.
    Lawyer, G.: Understanding the influence of all nodes in a network[J]. Sci. Rep. 5, 8665 (2015)CrossRefGoogle Scholar
  13. 13.
    Li, S., Zhu, Y., Li, D., Kim, D., Huang, H.: Rumor restriction in online social networks. In: Performance computing and communications conference (IPCCC), 2013 IEEE 32nd International. IEEE, pp. 1–10 (2013)Google Scholar
  14. 14.
    Long, C., Wong, R.C.: Minimizing seed set for viral marketing. In: Proceedings of the 2011 IEEE 11th international conference on data mining, ICDM 11, pp. 427–436 (2011)Google Scholar
  15. 15.
    Lu, W., Bonchi, F., Goyal, A., Lakshmanan, L.V.S.: The bang for the buck: Fair competitive viral marketing from the host perspective. In: Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining (KDD ’13), pp. 928–936Google Scholar
  16. 16.
    Myers, S.A., Zhu, C., Leskovec, J.: Information diffusion and external influence in networks. In: Proceedings of the 18th ACM SIGKDD international conference on knowledge discovery and data mining, pp. 33–41. ACM (2012)Google Scholar
  17. 17.
    Nemhauser, G., Wolsey, L., Fisher, M.: An analysis of the approximations for maximizing submodular set functions. Math. Program. 14, 265–294 (1978)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Page, L., Brin, S., Motwani, R, Winograd, T.: The PageRank citation ranking: Bringing order to the Web. Stanford InfoLab (1999)Google Scholar
  19. 19.
    Tong, G., Wu, W., Tang, S., Du, D.: Adaptive influence maximization in dynamic social networks[J]. IEEE/ACM Trans. Networking (TON) 25(1), 112–125 (2017)CrossRefGoogle Scholar
  20. 20.
    Tong, G., Wu, W., Guo, L., Li, D., Liu, C., Liu, B., Du, D.: An efficient randomized algorithm for rumor blocking in online social networks. In: IEEE international conference on computer communications (2016)Google Scholar
  21. 21.
    Yan, Q., Huang, H., Gao, Y., Lu, W., He, Q.: Group-level influence maximization with budget constraint. In: Database systems for advanced applications (DASFAA), Part I, LNCS, 10177, pp. 625–641 (2017)Google Scholar
  22. 22.
    Zhang, P., Chen, W., Sun, X., Wang, Y., Zhang, J.: Minimizing seed set selection with probabilistic coverage guarantee in a social network. In: Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining (KDD14), pp. 1306–1315 (2014)Google Scholar
  23. 23.
    Zhu, Y.D.L., Zhang, Z.: Minimum cost seed set for competitive social influence. In: IEEE INFOCOM 2016-The 35th annual IEEE international conference on computer communications, pp. 1–9 (2016)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of InformationRenmin University of ChinaBeijingChina
  2. 2.Department of Computer ScienceCalifornia State University at Los AngelesLos AngelesUSA

Personalised recommendations