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Cumulative activation in social networks

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Abstract

Most studies on influence maximization focus on one-shot propagation, i.e., the influence is propagated from seed users only once following a probabilistic diffusion model and users’ activation are determined via single cascade. In reality it is often the case that a user needs to be cumulatively impacted by receiving enough pieces of information propagated to her before she makes the final purchase decision. In this paper we model such cumulative activation as the following process: first multiple pieces of information are propagated independently in the social network following the classical independent cascade model, then the user will be activated (and adopt the product) if the cumulative pieces of information she received reaches her cumulative activation threshold. Two optimization problems are investigated under this framework: seed minimization with cumulative activation (SM-CA), which asks how to select a seed set with minimum size such that the number of cumulatively active nodes reaches a given requirement η; influence maximization with cumulative activation (IM-CA), which asks how to choose a seed set with fixed budget to maximize the number of cumulatively active nodes. For SM-CA problem, we design a greedy algorithm that yields a bicriteria O(ln n)-approximation when η = n, where n is the number of nodes in the network. For both SM-CA problem with η < n and IM-CA problem, we prove strong inapproximability results. Despite the hardness results, we propose two efficient heuristic algorithms for SM-CA and IM-CA respectively based on the reverse reachable set approach. Experimental results on different real-world social networks show that our algorithms significantly outperform baseline algorithms.

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References

  1. 1

    Chen W, Lakshmanan L S V, Castillo C. Information and influence propagation in social networks. In: Synthesis Lectures on Data Management. Morgan & Claypool Publishers, 2013

  2. 2

    Domingos P, Richardson M. Mining the network value of customers. In: Proceeding of KDD. New York: ACM, 2001. 57–66

  3. 3

    Kempe D, Kleinberg J, TardosÉ. Maximizing the spread of influence through a social network. In: Proceeding of KDD. New York: ACM, 2003. 137–146

  4. 4

    Centola D, Macy M. Complex contagions and the weakness of long ties. Am J Soc, 2007, 113: 702–734

  5. 5

    Borgs C, Brautbar M, Chayes J, et al. Maximizing social influence in nearly optimal time. In: Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, Portland, 2014. 946–957

  6. 6

    Nguyen H T, Thai M T, Dinh N T. Stop-and-stare: optimal sampling algorithms for viral marketing in billion-scale networks. In: Proceeding of SIGMOD. New York: ACM, 2016. 695–710

  7. 7

    Tang Y, Shi Y, Xiao X. Influence maximization in near-linear time: a martingale approach. In: Proceeding of SIGMOD. New York: ACM, 2015. 1539–1554

  8. 8

    Tang Y, Xiao X, Shi Y. Influence maximization: near-optimal time complexity meets practical efficiency. In: Proceeding of SIGMOD. New York: ACM, 2014. 946–957

  9. 9

    Richardson M, Domingos P. Mining knowledge-sharing sites for viral marketing. In: Proceeding of KDD. New York: ACM, 2002. 61–70

  10. 10

    Chen W, Wang C, Wang Y. Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: Proceeding of KDD. New York: ACM, 2010. 1029–1038

  11. 11

    Chen W, Wang Y, Yang S. Efficient influence maximization in social networks. In: Proceeding of KDD. New York: ACM, 2009. 199–208

  12. 12

    Leskovec J, Krause A, Guestrin C, et al. Cost-effective outbreak detection in networks. In: Proceeding of KDD. New York: ACM, 2007. 420–429

  13. 13

    Kempe D, Kleinberg J, TardosÉ. Influential nodes in a diffusion model for social networks. In: Proceeding of ICALP, 2005. 1127–1138

  14. 14

    Chen N. On the approximability of influence in social networks. SIAM J Discrete Math, 2009, 23: 1400–1415

  15. 15

    Long C, Wong R-W. Minimizing seed set for viral marketing. In: Proceedings of IEEE 11th International Conference on Data Mining (ICDM), 2011. 427–436

  16. 16

    Goyal A, Bonchi F, Lakshmanan L V, et al. On minimizing budget and time in influence propagation over social networks. Social Netw Anal Min, 2013, 3: 179–192

  17. 17

    Zhang P, Chen W, Sun X, et al. Minimizing seed set selection with probabilistic coverage guarantee in a social network. In: Proceeding of KDD. New York: ACM, 2014. 1306–1315

  18. 18

    He J, Ji S, Beyah R, et al. Minimum-sized influential node set selection for social networks under the independent cascade model. In: Proceeding of MobiHoc. New York: ACM, 2014. 93–102

  19. 19

    Gruhl D, Guha R, Liben-Nowell D, et al. Information diffusion through blogspace. In: Proceeding of WWW. New York: ACM, 2004. 491–501

  20. 20

    Tang J, Sun J, Wang C, et al. Social influence analysis in large-scale networks. In: Proceeding of KDD. New York: ACM, 2009. 807–816

  21. 21

    Nemhauser G L, Wolsey L A, Fisher M L. An analysis of approximations for maximizing submodular set functions-I. Math Programming, 1978, 14: 265–294

  22. 22

    Chen W, Li F, Lin T, et al. Combining traditional marketing and viral marketing with amphibious influence maximization. In: Proceeding of EC. New York: ACM, 2015. 779–796

  23. 23

    Feige U. A threshold of ln n for approximating set cover. J ACM, 1998, 45: 634–652

  24. 24

    Farajtabar M, Du N, Gomez-Rodriguez M, et al. Shaping social activity by incentivizing users. In: Proceeding of NIPS, 2014. 2474–2482

  25. 25

    Feige U, Peleg D, Kortsarz G. The dense k-subgraph problem. Algorithmica, 2001, 29: 410–421

  26. 26

    Bhaskara A, Moses C, Chlamtáč E, et al. Detecting high log-densities: an o(n1/4) approximation for densest ksubgraph. In: Proceeding of STOC. New York: ACM, 2010. 201–210

  27. 27

    Khot S. Ruling out PTAS for graph min-bisection, dense k-subgraph, and bipartite clique. SIAM J Comput, 2006, 36: 1025–1071

  28. 28

    Manurangsi P. Almost-polynomial ratio eth-hardness of approximating densest k-subgraph. In: Proceeding of STOC. New York: ACM, 2017. 954–961

  29. 29

    Hajiaghayi M T, Jain K, Konwar K, et al. The minimum k-colored subgraph problem in haplotyping and DNA primer selection. In: Proceeding of IWBRA, 2006

  30. 30

    Barbieri N, Bonchi F, Manco G. Topic-aware social influence propagation models. In: Proceedings of IEEE 12th International Conference on Data Mining (ICDM), 2012. 81–90

  31. 31

    Goyal A, Lu W, Lakshmanan S V L. SIMPATH: an efficient algorithm for influence maximization under the linear threshold model. In: Proceeding of ICDM, 2011. 211–220

  32. 32

    Wang C, Chen W, Wang Y. Scalable influence maximization for independent cascade model in large-scale social networks. Data Min Knowl Disc, 2012, 25: 545–576

  33. 33

    Brin S, Page L. The anatomy of a large-scale hypertextual web search engine. Comput Netw ISDN Syst, 1998, 30: 107–117

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61433014, 61502449, 61602440), National Basic Research Program of China (973) (Grant No. 2016YFB1000201).

Author information

Correspondence to Xiaohan Shan or Wei Chen or Qiang Li or Xiaoming Sun or Jialin Zhang.

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Cite this article

Shan, X., Chen, W., Li, Q. et al. Cumulative activation in social networks. Sci. China Inf. Sci. 62, 52103 (2019). https://doi.org/10.1007/s11432-018-9609-7

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Keywords

  • social networks
  • cumulative activation
  • influence maximization
  • seed minimization