Abstract
People with the same interests, hobbies or political orientation always form a group to share all kinds of topics in Online Social Networks (OSN). Product producers often hire the OSN provider to propagate their advertisements in order to influence all possible potential groups. In this paper, a group is assumed to be activated if \(\beta \) percent of members are activated. Product producers will gain revenue from all activated groups through group-buying behavior. Meanwhile, to propagate influence, producers need pay diffusion cost to the OSN provider, while the cost is usually relevant to total hits on the advertisements. We aim to select k seed users to maximize the expected profit that combines the benefit of activated groups with the diffusion cost of influence propagation, which is called Group Profit Maximization (GPM) problem. The information diffusion model is based on Independent Cascade (IC), and we prove GPM is NP-hard and the objective function is neither submodular nor supermodular. We develop an upper bound and a lower bound that both are difference of two submodular functions. Then we design an Submodular-Modular Algorithm (SMA) for solving difference of submodular functions and SMA is proved to converge to local optimal. Further, we present an randomized algorithm based on weighted group coverage maximization for GPM and apply Sandwich framework to get theoretical results. Our experiments verify the effectiveness of our method, as well as the advantage of our method against the other heuristic methods.
The work is supported by the US National Science Foundation under Grant No. 1747818, National Natural Science Foundation of China under Grant No. 91324012 and Project of Promoting Scientific Research Ability of Excellent Young Teachers in University of Chinese Academy of Sciences.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bach, F., et al.: Learning with submodular functions: a convex optimization perspective. Found. Trends® Mach. Learn. 6(23), 145–373 (2013)
Borgs, C., Brautbar, M., Chayes, J., Lucier, B.: Maximizing social influence in nearly optimal time. In: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 946–957. SIAM (2014)
Dagum, P., Karp, R., Luby, M., Ross, S.: An optimal algorithm for Monte Carlo estimation. SIAM J. Comput. 29(5), 1484–1496 (2000)
Forsyth, D.R.: Group Dynamics. Cengage Learning, Belmont (2018)
Fujishige, S.: Submodular Functions and Optimization, vol. 58. Elsevier, Amsterdam (2005)
Hung, H.J., et al.: When social influence meets item inference. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 915–924. ACM (2016)
Iyer, R., Bilmes, J.: Algorithms for approximate minimization of the difference between submodular functions, with applications. arXiv preprint arXiv:1207.0560 (2012)
Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 137–146. ACM (2003)
Lu, W., Chen, W., Lakshmanan, L.V.: From competition to complementarity: comparative influence diffusion and maximization. Proc. VLDB Endowment 9(2), 60–71 (2015)
Lu, W., Lakshmanan, L.V.: Profit maximization over social networks. In: 2012 IEEE 12th International Conference on Data Mining (ICDM), pp. 479–488. IEEE (2012)
Meeker, M., Wu, L.: Internet Trends Report 2018, vol. 5, p. 30. Kleiner Perkins (2018)
Narasimhan, M., Bilmes, J.A.: A submodular-supermodular procedure with applications to discriminative structure learning. arXiv preprint arXiv:1207.1404 (2012)
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 the 2016 International Conference on Management of Data. pp. 695–710. ACM (2016)
Opsahl, T.: Triadic closure in two-mode networks: redefining the global and local clustering coefficients. Soc. Netw. 35(2), 159–167 (2013)
Schoenebeck, G., Tao, B.: Beyond worst-case (in)approximability of nonsubmodular influence maximization. In: International Conference on Web and Internet Economics (2017)
Tang, J., Tang, X., Yuan, J.: Towards profit maximization for online social network providers. arXiv preprint arXiv:1712.08963 (2017)
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)
Tang, Y., Shi, Y., Xiao, X.: Influence maximization in near-linear time: a martingale approach. In: Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, pp. 1539–1554. ACM (2015)
Tang, Y., Xiao, X., Shi, Y.: Influence maximization: near-optimal time complexity meets practical efficiency. In: Proceedings of the 2014 ACM SIGMOD International Conference on Management of data, pp. 75–86. ACM (2014)
Wu, W.L., Zhang, Z., Du, D.Z.: Set function optimization. J. Oper. Res. Soc. China 3, 1–11 (2018)
Zhu, J., Zhu, J., Ghosh, S., Wu, W., Yuan, J.: Social influence maximization in hypergraph in social networks. IEEE Transactions on Network Science and Engineering, p. 1 (2018). https://doi.org/10.1109/TNSE.2018.2873759
Zhu, Y., Lu, Z., Bi, Y., Wu, W., Jiang, Y., Li, D.: Influence and profit: two sides of the coin. In: 2013 IEEE 13th International Conference on Data Mining (ICDM), pp. 1301–1306. IEEE (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Zhu, J., Ghosh, S., Wu, W., Gao, C. (2019). Profit Maximization Under Group Influence Model in Social Networks. In: Tagarelli, A., Tong, H. (eds) Computational Data and Social Networks. CSoNet 2019. Lecture Notes in Computer Science(), vol 11917. Springer, Cham. https://doi.org/10.1007/978-3-030-34980-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-34980-6_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-34979-0
Online ISBN: 978-3-030-34980-6
eBook Packages: Computer ScienceComputer Science (R0)