Parallel Seed Selection for Influence Maximization Based on k-shell Decomposition

  • Hong Wu
  • Kun YueEmail author
  • Xiaodong Fu
  • Yujie Wang
  • Weiyi Liu
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 201)


Influence maximization is the problem of selecting a set of seeds in a social network to maximize the influence under certain diffusion model. Prior solutions, the greedy and its improvements are time-consuming. In this paper, we propose candidate shells influence maximization (CSIM) algorithm under heat diffusion model to select seeds in parallel. We employ CSIM algorithm (a modified algorithm of greedy) to coarsely estimate the influence spread to avoid massive estimation of heat diffusion process, thus can effectively improve the speed of selecting seeds. Moreover, we can select seeds from candidate shells in parallel. Specifically, First, we employ the k-shell decomposition method to divide a social network and generate the candidate shells. Further, we use the heat diffusion model to model the influence spread. Finally, we select seeds of candidate shells in parallel by using the CSIM algorithm. Experimental results show the effectiveness and feasibility of the proposed algorithm.


Parallel Social networks Influence maximization K-shell decomposition 



This work was supported by the National Natural Science Foundation of China (Nos. 61472345, 61462056, 61402398), Natural Science Foundation of Yunnan Province (Nos. 2014FA023, 2014FA028), Program for Excellent Young Talents of Yunnan University (No. XT412003), Research Foundation of the Education Department of Yunnan Province (Nos. 2014C134Y, 2016YJS005, 2016ZZX013).


  1. 1.
    Granovetter, M.: Threshold models of collective behavior. Am. J. Soc. 83, 1420–1443 (1978)CrossRefGoogle Scholar
  2. 2.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998)CrossRefGoogle Scholar
  3. 3.
    Chen, W., Wang, C., Wang, Y.: Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: SIGKDD, pp. 1029–1038 (2010)Google Scholar
  4. 4.
    Domingos, P., Richardson, M.: Mining the network value of customers. In: KDD, pp. 57–66 (2001)Google Scholar
  5. 5.
    Richardson, M., Domingos, P.: Mining knowledge-sharing sites for viral marketing. In: KDD, pp. 61–70 (2002)Google Scholar
  6. 6.
    Kempe, D., Kleinberg, J., Tardos É.: Maximizing the spread of influence through a social network. In: KDD, pp. 137–146 (2003)Google Scholar
  7. 7.
    Nemhauser, G.L., Wolsey, L.A., Fisher, M.L.: An analysis of approximations for maximizing submodular set functions—I. Math. Program. 14(1), 265–294 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Leskovec, J., Krause, A., Guestrin, C., et al.: Cost-effective outbreak detection in networks. In: KDD, pp. 420–429 (2007)Google Scholar
  9. 9.
    Wang, C., Chen, W., Wang, Y.: Scalable influence maximization for independent cascade model in large-scale social networks. Data Min. Knowl. Disc. 25(3), 545–576 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Cheng, S., Shen, H., Huang, J., Zhang, G., Cheng, X.: Staticgreedy: solving the scalability-accuracy dilemma in influence maximization. In: CIKM, pp. 509–518 (2013)Google Scholar
  11. 11.
    Chen, W., Wang, Y., Yang, S.: Efficient influence maximization in social networks. In: KDD, pp. 199–208 (2009)Google Scholar
  12. 12.
    Chen, Y.C., Zhu, W.Y., Peng, W.C., Lee, W.C., Lee, S.Y.: CIM: community-based influence maximization in social networks. ACM Trans. Intell. Syst. Technol. 5(2), 25 (2014)CrossRefGoogle Scholar
  13. 13.
    Horel, T., Singer, Y.: Scalable methods for adaptively seeding a social network. In: WWW, pp. 441–451 (2015)Google Scholar
  14. 14.
    Chen, Y.C., Peng, W.C., Lee, S.Y.: Efficient algorithms for influence maximization in social networks. Knowl. Inf. Syst. 33(3), 577–601 (2012)CrossRefGoogle Scholar
  15. 15.
    Ma, H., Yang, H., Lyu, M.R., King, I.: Mining social networks using heat diffusion processes for marketing candidates selection. In: CIKM, pp. 233–242 (2008)Google Scholar
  16. 16.
    Bollobás, B.: Graph theory and combinatorics. In: Proceedings of the Cambridge Combinatorial Conference in honor of Paul Erdös, Academic, p. 35 (1984)Google Scholar
  17. 17.
    Carmi, S., Havlin, S., Kirkpatrick, S., Shavitt, Y., Shir, E.: A model of Internet topology using k-shell decomposition. In: PNAS, pp. 11150–11154 (2007)Google Scholar
  18. 18.
    Kitsak, M., Gallos, L.K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H.E., Makse, H.A.: Identification of influential spreaders in complex networks. Nat. Phys. 6(11), 888–893 (2010)CrossRefGoogle Scholar
  19. 19.
    Ren, Z.M., Liu, J.G., Shao, F., Hu, Z.L.: Guo, Q: Analysis of the spreading influence of the nodes with minimum K-shell value in complex networks. Acta. Phys. Sin 62(10), 108902-1–108902-6 (2013)Google Scholar
  20. 20.
  21. 21.
    Cao, J.X., Dong, D., Xu, S., Zheng, X., Liu, B., Luo, J.Z.: A k-core based algorithm for influence maximization in social networks. Chin. J. Comput. 38(2), 238–248 (2015)MathSciNetGoogle Scholar
  22. 22.
    Song, G., Zhou, X., Wang, Y., Xie, K.: Influence maximization on large-scale mobile social network: a divide-and-conquer method. IEEE Trans. Parallel Distrib. Syst. 26(5), 1379–1392 (2015)CrossRefGoogle Scholar
  23. 23.
    Kim, J., Kim, S.K., Yu, H.: Scalable and parallelizable processing of influence maximization for large-scale social networks. In: ICDE, pp. 266–277 (2013)Google Scholar
  24. 24.
    Bello-Orgaz, G., Jung, J.J., Camacho, D.: Social big data: recent achievements and new challenges. Inf. Fusion 28, 45–59 (2016)CrossRefGoogle Scholar
  25. 25.
    Seo, S., Yoon, E.J., Kim, J., Jin, S., Kim, J.S., Maeng, S.: Hama: an efficient matrix computation with the mapreduce framework. In: CloudCom, pp. 721–726 (2010)Google Scholar
  26. 26.
    Avery, C.: Giraph: Large-scale graph processing infrastruction on hadoop. In: Hadoop Summit (2011)Google Scholar
  27. 27.
    Low, Y., Gonzalez, J.E., Kyrola, A., Bickson, D., Guestrin, C.E., Hellerstein, J.: Graphlab: a new framework for parallel machine learning. In: UAI, p. 10, (2014)Google Scholar
  28. 28.
    Xin, R.S., Gonzalez, J.E., Franklin, M.J., Stoica, I.: GraphX: a resilient distributed graph system on spark. In: GRADES, pp. 2:1–2:6 (2013)Google Scholar
  29. 29.
    Yang, J., Leskovec, J.: Defining and evaluating network communities based on ground-truth. In: ICDM, pp. 745–754 (2012)Google Scholar

Copyright information

© ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2017

Authors and Affiliations

  • Hong Wu
    • 1
    • 2
  • Kun Yue
    • 1
    Email author
  • Xiaodong Fu
    • 3
  • Yujie Wang
    • 1
  • Weiyi Liu
    • 1
  1. 1.School of Information Science and EngineeringYunnan UniversityKunmingChina
  2. 2.School of Information EngineeringQujing Normal UniversityQujingChina
  3. 3.Faculty of Information Engineering and AutomationKunming University of Science and TechnologyKunmingChina

Personalised recommendations