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Optimal price profile for influential nodes in online social networks

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Abstract

Influential nodes with rich connections in online social networks (OSNs) are of great values to initiate marketing campaigns. However, the potential influence spread that can be generated by these influential nodes is hidden behind the structures of OSNs, which are often held by OSN providers and unavailable to advertisers for privacy concerns. A social advertising model known as influencer marketing is to have OSN providers offer and price candidate nodes for advertisers to purchase for seeding marketing campaigns. In this setting, a reasonable price profile for the candidate nodes should effectively reflect the expected influence gain they can bring in a marketing campaign. In this paper, we study the problem of pricing the influential nodes based on their expected influence spread to help advertisers select the initiators of marketing campaigns without the knowledge of OSN structures. We design a function characterizing the divergence between the price and the expected influence of the initiator sets. We formulate the problem to minimize the divergence and derive an optimal price profile. An advanced algorithm is developed to estimate the price profile with accuracy guarantees. Experiments with real OSN datasets show that our pricing algorithm can significantly outperform other baselines.

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Notes

  1. https://newsroom.fb.com/company-info/

  2. https://famebit.com/

  3. Tang et al. [38] directly gave the lower tail result without providing the detailed proof. Our analysis is based on Lemma 3 requiring \( Y_1\le a \) and \( Y_k-Y_{k-1}\le a \), whereas Tang et al. [38] utilized a similar lemma requiring \( |Y_1|\le a \) and \( |Y_k-Y_{k-1}|\le a \), which might be insufficient for deriving the lower tail result.

References

  1. Aslay, C., Lu, W., Bonchi, F., Goyal, A., Lakshmanan, L.V.: Viral marketing meets social advertising: ad allocation with minimum regret. Proc. VLDB Endow. 8(7), 814–825 (2015)

    Article  Google Scholar 

  2. Aslay, C., Bonchi, F., Lakshmanan, L.V., Lu, W.: Revenue maximization in incentivized social advertising. Proc. VLDB Endow. 10(11), 1238–1249 (2017)

    Article  Google Scholar 

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

  4. Chalermsook, P., Das Sarma, A., Lall, A., Nanongkai, D.: Social network monetization via sponsored viral marketing. ACM SIGMETRICS Perform. Eval. Rev. 43(1), 259–270 (2015)

    Article  Google Scholar 

  5. Chen, W., Wang, Y., Yang, S.: Efficient influence maximization in social networks. In: Proc. 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: Proc. ACM KDD, pp. 1029–1038 (2010)

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

  8. Cheng, S., Shen, H., Huang, J., Chen, W., Cheng, X.: Imrank: influence maximization via finding self-consistent ranking. In: Proc. ACM SIGIR, pp. 475–484 (2014)

  9. Chung, F., Lu, L.: Concentration inequalities and martingale inequalities: a survey. Internet Math. 3(1), 79–127 (2006)

    Article  MathSciNet  Google Scholar 

  10. Cohen, E., Delling, D., Pajor, T., Werneck, R.F.: Sketch-based influence maximization and computation: scaling up with guarantees. In: Proc. ACM CIKM, pp. 629–638 (2014)

  11. Dagum, P., Karp, R., Luby, M., Ross, S.: An optimal algorithm for Monte Carlo estimation. SIAM J. Comput. 29(5), 1484–1496 (2000)

    Article  MathSciNet  Google Scholar 

  12. Domingos, P., Richardson, M.: Mining the network value of customers. In: Proc. ACM KDD, pp. 57–66 (2001)

  13. eMarketer: Social network ad spending worldwide, by region, 2013–2017. https://www.emarketer.com/Chart/Social-Network-Ad-Spending-Worldwide-by-Region-2013-2017/168356 (2015)

  14. eMarketer: Influencer marketing is about data, not celebrity deals. https://www.emarketer.com/Article/Influencer-Marketing-About-Data-Not-Celebrity-Deals/1016683 (2017)

  15. eMarketer: How much are brands paying influencers?. https://www.emarketer.com/content/how-much-are-brands-paying-influencers (2019)

  16. eMarketer: Is everyone on instagram an influencer?. https://www.emarketer.com/content/is-everyone-on-instagram-an-influencer (2019)

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

    Article  Google Scholar 

  18. Huang, K., Tang, J., Han, K., Xiao, X., Chen, W., Sun, A., Tang, X., Lim, A.: Efficient approximation algorithms for adaptive influence maximization. VLDB J. 29(6), 1385–1406 (2020)

    Article  Google Scholar 

  19. Huang, K., Tang, J., Xiao, X., Sun, A., Lim, A.: Efficient approximation algorithms for adaptive target profit maximization. In: Proc. IEEE ICDE, pp. 649–660 (2020)

  20. Hub, I.M.: The remarkable rise of influencer marketing. https://influencermarketinghub.com/the-rise-of-influencer-marketing/ (2020)

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

  22. Khan, A., Zehnder, B., Kossmann, D.: Revenue maximization by viral marketing: a social network host’s perspective. In: Proc. IEEE ICDE, pp. 37–48 (2016)

  23. Kwak, H., Lee, C., Park, H., Moon, S.: What is Twitter, a social network or a news media? In: Proc. WWW, pp. 591–600 (2010)

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

  25. Lu, W., Lakshmanan, L.V.: Profit maximization over social networks. In: Proc. IEEE ICDM, pp. 479–488 (2012)

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

  27. Nguyen, H.T., Nguyen, T.P., Vu, T.N., Dinh, T.N.: Outward influence and cascade size estimation in billion-scale networks. In: Proc. ACM SIGMETRICS, p. 63 (2017)

  28. Reuters: Social media ad spending is expected to pass newspapers by 2020. http://fortune.com/2016/12/05/social-media-ad-spending-newspapers-zenith-2020/ (2016)

  29. Richardson, M., Domingos, P.: Mining knowledge-sharing sites for viral marketing. In: Proc. ACM KDD, pp. 61–70 (2002)

  30. Tang, J., Tang, X., Yuan, J.: Profit maximization for viral marketing in online social networks. In: Proc. IEEE ICNP, pp. 1–10 (2016)

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

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

  33. Tang, J., Tang, X., Yuan, J.: An efficient and effective hop-based approach for influence maximization in social networks. Soc. Netw. Anal. Min. 8(1), 10 (2018)

    Article  Google Scholar 

  34. Tang, J., Tang, X., Yuan, J.: Profit maximization for viral marketing in online social networks: algorithms and analysis. IEEE Trans. Knowl. Data Eng. 30(6), 1095–1108 (2018)

    Article  Google Scholar 

  35. Tang, J., Tang, X., Yuan, J.: Towards profit maximization for online social network providers. In: Proc. IEEE INFOCOM, pp. 1178–1186 (2018)

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

  37. Tang, Y., Xiao, X., Shi, Y.: Influence maximization: near-optimal time complexity meets practical efficiency. In: Proc. ACM SIGMOD, pp. 75–86 (2014)

  38. Tang, Y., Shi, Y., Xiao, X.: Influence maximization in near-linear time: a martingale approach. In: Proc. ACM SIGMOD, pp. 1539–1554 (2015)

  39. Zhu, Y., Tang, J., Tang, X.: Pricing influential nodes in online social networks. Proc. VLDB Endow. 13(10), 1614–1627 (2020)

    Article  Google Scholar 

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Acknowledgements

This work is partially supported by HKUST(GZ) under a Startup Grant, and by Singapore Ministry of Education Academic Research Fund Tier 1 under Grants 2018-T1-002-063 and 2019-T1-002-042.

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Authors and Affiliations

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

    Yuqing Zhu & Xueyan Tang

  2. Data Science and Analytics Thrust, The Hong Kong University of Science and Technology, Guangzhou, China

    Jing Tang

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  1. Yuqing Zhu
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  2. Jing Tang
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Correspondence to Jing Tang.

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Zhu, Y., Tang, J. & Tang, X. Optimal price profile for influential nodes in online social networks. The VLDB Journal 31, 779–795 (2022). https://doi.org/10.1007/s00778-021-00727-9

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