Skip to main content
SpringerLink
Log in

Efficient approximation algorithms for adaptive influence maximization

  • Regular Paper
  • Published:
The VLDB Journal Aims and scope Submit manuscript

Abstract

Given a social network G and an integer k, the influence maximization (IM) problem asks for a seed set S of k nodes from G to maximize the expected number of nodes influenced via a propagation model. The majority of the existing algorithms for the IM problem are developed only under the non-adaptive setting, i.e., where all k seed nodes are selected in one batch without observing how they influence other users in real world. In this paper, we study the adaptive IM problem where the k seed nodes are selected in batches of equal size b, such that the i-th batch is identified after the actual influence results of the former \(i-1\) batches are observed. In this paper, we propose the first practical algorithm for the adaptive IM problem that could provide the worst-case approximation guarantee of \(1-{\mathrm {e}}^{\rho _b(\varepsilon -1)}\), where \(\rho _b=1-(1-1/b)^b\) and \(\varepsilon \in (0, 1)\) is a user-specified parameter. In particular, we propose a general framework AdaptGreedy that could be instantiated by any existing non-adaptive IM algorithms with expected approximation guarantee. Our approach is based on a novel randomized policy that is applicable to the general adaptive stochastic maximization problem, which may be of independent interest. In addition, we propose a novel non-adaptive IM algorithm called EPIC which not only provides strong expected approximation guarantee, but also presents superior performance compared with the existing IM algorithms. Meanwhile, we clarify some existing misunderstandings in recent work and shed light on further study of the adaptive IM problem. We conduct experiments on real social networks to evaluate our proposed algorithms comprehensively, and the experimental results strongly corroborate the superiorities and effectiveness of our approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Notes

  1. Note that \(c_1=0\) and \(c_2=1\) can always satisfy the requirement. Thus, we can always find some \(c_1\) and \(c_2\) such that \(0\le c_1\le c_2\le 1\).

  2. Usually, the random source \(\omega \) indicates sampling for IM, e.g., reverse influence sampling [3].

  3. Expected approximation for influence maximization.

References

  1. Arora, A., Galhotra, S., Ranu, S.: Debunking the myths of influence maximization: an in-depth benchmarking study. In: Proceedings of ACM SIGMOD, pp. 651–666 (2017)

  2. Badanidiyuru A, Papadimitriou, C., Rubinstein, A., Seeman, L., Singer, Y.: Locally adaptive optimization: adaptive seeding for monotone submodular functions. In: Proceedings of SODA, pp. 414–429 (2016)

  3. Borgs, C., Brautbar, M., Chayes, J., Lucier, B.: Maximizing social influence in nearly optimal time. In: Proceedings of SODA, pp. 946–957 (2014)

  4. Chen, W., Peng, B.: On adaptivity gaps of influence maximization under the independent cascade model with full adoption feedback. In: Proceedings of ISAAC, pp. 24:1–24:19 (2019)

  5. Chen, W., Wang, Y., Yang, S.: Efficient influence maximization in social networks. In: Proceedings of ACM KDD, pp. 199–208 (2009)

  6. Chen, W., Wang, C., Wang, Y.: Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: Proceedings of ACM KDD, pp. 1029–1038 (2010a)

  7. Chen, W., Yuan, Y., Zhang, L.: Scalable influence maximization in social networks under the linear threshold model. In: Proceedings of IEEE ICDM, pp. 88–97 (2010b)

  8. Chen, W., Peng, B., Schoenebeck, G., Tao, B.: Adaptive greedy versus non-adaptive greedy for influence maximization. In: Proceedings of AAAI (2020)

  9. Chen, Y., Krause, A.: Near-optimal batch mode active learning and adaptive submodular optimization. In: Proceedings of ICML, pp. 160–168 (2013)

  10. Chen, Y., Hassani, S.H., Karbasi, A., Krause, A.: Sequential information maximization: when is greedy near-optimal? In: Proceedings of COLT, pp. 338–363 (2015)

  11. Cuong, N.V., Lee, W.S., Ye, N., Chai, K.M.A., Chieu, H.L.: Active learning for probabilistic hypotheses using the maximum gibbs error criterion. In: Proceedings of NeurIPS, pp. 1457–1465 (2013)

  12. Feige, U.: A threshold of \(\ln n\) for approximating set cover. J. ACM 45(4), 634–652 (1998)

    Article  MathSciNet  Google Scholar 

  13. Galhotra, S., Arora, A., Roy, S.: Holistic influence maximization: Combining scalability and efficiency with opinion-aware models. In: Proceedings of ACM SIGMOD, pp. 743–758 (2016)

  14. Golovin, D., Krause, A.: Adaptive submodularity: theory and applications in active learning and stochastic optimization. J. Artif. Intell. Res. 42(1), 427–486 (2011)

    MathSciNet  MATH  Google Scholar 

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

  16. Han, K., Huang, K., Xiao, X., Tang, J., Sun, A., Tang, X.: Efficient algorithms for adaptive influence maximization. Proc. VLDB Endowment 11(9), 1029–1040 (2018)

    Article  Google Scholar 

  17. Hollinger, G.A., Englot, B., Hover, F.S., Mitra, U., Sukhatme, G.S.: Active planning for underwater inspection and the benefit of adaptivity. Int. J. Robot. Res. 32(1), 3–18 (2013)

    Article  Google Scholar 

  18. Horel, T., Singer, Y.: Scalable methods for adaptively seeding a social network. In: Proceedings of WWW, pp. 441–451 (2015)

  19. Huang, K., Wang, S., Bevilacqua, G., Xiao, X., Lakshmanan, L.V.S.: Revisiting the stop-and-stare algorithms for influence maximization. Proc. VLDB Endowment 10(9), 913–924 (2017)

    Article  Google Scholar 

  20. Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: Proceedings of ACM KDD, pp. 137–146 (2003)

  21. Leskovec, J., Krevl, A.: SNAP datasets: stanford large network dataset collection (2014) http://snap.stanford.edu/data

  22. Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J.M., Glance, N.S.: Cost-effective outbreak detection in networks. In: Proceedings of ACM KDD, pp. 420–429 (2007)

  23. Li, R., Qin, L., Yu, J.X., Mao, R.: Finding influential communities in massive networks. VLDB J. 26(6), 751–776 (2017)

    Article  Google Scholar 

  24. Lin, C., Lu, J., Wei, Z., Wang, J., Xiao, X.: Optimal algorithms for selecting top-k combinations of attributes: theory and applications. VLDB J. 27(1), 27–52 (2018)

    Article  Google Scholar 

  25. Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, Cambridge (2005)

    Book  Google Scholar 

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

  27. Ohsaka, N., Akiba, T., Yoshida, Y., Kawarabayashi, K.: Fast and accurate influence maximization on large networks with pruned monte-carlo simulations. In: Proceedings of AAAI, pp. 138–144 (2014)

  28. Ohsaka, N., Sonobe, T., Fujita, S., Kawarabayashi, K.: Coarsening massive influence networks for scalable diffusion analysis. In: Proceedings of ACM SIGMOD, pp. 635–650 (2017)

  29. Peng, B., Chen, W.: Adaptive influence maximization with myopic feedback. In: Proceedings of NeurIPS, pp. 5575–5584 (2019)

  30. Seeman, L., Singer, Y.: Adaptive seeding in social networks. In: Proceedings of IEEE FOCS, pp. 459–468 (2013)

  31. Sun, L., Huang, W., Yu, P.S., Chen, W.: Multi-round influence maximization. In: Proceedings of ACM KDD, pp. 2249–2258 (2018)

  32. Tang, J., Tang, X., Yuan, J.: Influence maximization meets efficiency and effectiveness: a hop-based approach. In: Proceedings of IEEE/ACM ASONAM, pp. 64–71 (2017)

  33. Tang, J., Tang, X., Xiao, X., Yuan, J.: Online processing algorithms for influence maximization. In: Proceedings of ACM SIGMOD, pp. 991–1005 (2018a)

  34. Tang, J., Tang, X., Yuan, J.: An efficient and effective hop-based approach for inluence maximization in social networks. Soc. Netw. Anal. Min. 8, 10 (2018b)

    Article  Google Scholar 

  35. Tang, J., Huang, K., Xiao, X., Lakshmanan, L.V., Tang, X., Sun, A., Lim, A.: Efficient approximation algorithms for adaptive seed minimization. In: Proceedings of ACM SIGMOD, pp. 1096–1113 (2019)

  36. Tang, Y., Xiao, X., Shi, Y.: Influence maximization: Near-optimal time complexity meets practical efficiency. In: Proceedings of ACM SIGMOD, pp. 75–86 (2014)

  37. Tang, Y., Shi, Y., Xiao, X.: Influence maximization in near-linear time: A martingale approach. In: Proceedings of ACM SIGMOD, pp. 1539–1554 (2015)

  38. Vaswani, S., Lakshmanan, L.V.S.: Adaptive influence maximization in social networks: why commit when you can adapt? arXiv preprint, arXiv:1604.08171 (2016)

  39. Yadav, A., Chan, H., Xin Jiang, A., Xu, H., Rice, E., Tambe, M.: Using social networks to aid homeless shelters: dynamic influence maximization under uncertainty. In: Proceedings of AAMAS, pp. 740–748 (2016)

  40. Yuan, J., Tang, S.: No time to observe: adaptive influence maximization with partial feedback. In: Proceedings of IJCAI, pp. 3908–3914 (2017)

Download references

Author information

Author notes

  1. Keke Huang and Jing Tang have contributed equally

Authors and Affiliations

  1. School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore

    Keke Huang, Aixin Sun & Xueyan Tang

  2. Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore, Singapore

    Jing Tang & Andrew Lim

  3. School of Computer Science and Technology, University of Science and Technology of China, Hefei, China

    Kai Han

  4. School of Computing, National University of Singapore, Singapore, Singapore

    Xiaokui Xiao

  5. Microsoft Research, Beijing, China

    Wei Chen

Authors
  1. Keke Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kai Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaokui Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wei Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Aixin Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Xueyan Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Andrew Lim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jing Tang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, K., Tang, J., Han, K. et al. Efficient approximation algorithms for adaptive influence maximization. The VLDB Journal 29, 1385–1406 (2020). https://doi.org/10.1007/s00778-020-00615-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00778-020-00615-8

Keywords

Search

Navigation