Abstract
Due to the important role that social networks play in advertisements and propaganda, influence maximization (IM) problem which aims at finding some influential users as seeds to trigger large online cascading influence spread has been a hot research topic in the past two decades. As an extension of classical IM problem, profit maximization (PM) problem is inspired by product promotion and focuses on the profit generated by consumer. Given that competitive social advertising is more common in real-world, a series of studies propose some versions of PM problem. However, the competition happening in the information dissemination of imperfect substitutes and the influence of potential consumers’ preference have been mostly ignored. Besides, to the best of our knowledge, no research pays attention on the fact that some companies may snatch seeds to limit the profits of their opponents. Therefore, we propose a novel competition-based diversified-profit maximization (CDM) problem and its adaptive version, i.e., adaptive competition-based diversified-profit maximization (ACDM) problem. Different from prior works, these problems take seed’s preference into consideration and use social welfare to reflect it. These two problems aim at selecting seeds and allocating them to marketers such that the sum of profit generated by consumers for a special entity after information dissemination and social welfare with respect to seed allocation reaches maximum. To address these two problems, we design an algorithm which combines the method of online allocation and the concept of Shapley value. Experimental results on three real-world data sets demonstrate the effectiveness of our proposed algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
As introduced in Section 5.1, three data sets used in this paper can be obtained from Kunegis 2013 and SNAP website.
References
Ali K, Wang CY, Chen YS (2018) Boosting reinforcement learning in competitive influence maximization with transfer learning. In: 2018 IEEE/WIC/ACM international conference on web intelligence (WI), pp 395–400. https://doi.org/10.1109/WI.2018.00-62
Ansari A, Dadgar M, Hamzeh A, Schlötterer J, Granitzer M (2019) Competitive influence maximization: integrating budget allocation and seed selection. arXiv:1912.12283
Bharathi S, Kempe D, Salek H (2007) Competitive influence maximization in social networks. pp 306–311. https://doi.org/10.1007/978-3-540-77105-0_31
Bozorgi A, Samet S, Kwisthout J, Wareham T (2017) Community-based influence maximization in social networks under a competitive linear threshold model. Knowl Based Syst 134:149–158. https://doi.org/10.1016/j.knosys.2017.07.029
Carnes T, Nagarajan C, Wild SM, van Zuylen A (2007) Maximizing influence in a competitive social network: a follower’s perspective. In: Proceedings of the ninth international conference on electronic commerce, ICEC’07. Association for Computing Machinery, New York, pp 351–360. https://doi.org/10.1145/1282100.1282167
Chen W, Wang Y, Yang S (2009) Efficient influence maximization in social networks. In: Proceedings of the 15th ACM SIGKDD international conference on knowledge discovery and data mining, KDD’09. Association for Computing Machinery, New York, pp 199–208. https://doi.org/10.1145/1557019.1557047
Chen W, Wang C, Wang Y (2010) Scalable influence maximization for prevalent viral marketing in large-scale social networks. pp 1029–1038. https://doi.org/10.1145/1835804.1835934
Chen W, Lin T, Tan Z, Zhao M, Zhou X (2016) Robust influence maximization. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. ACM, San Francisco California USA, pp 795–804. https://doi.org/10.1145/2939672.2939745
Du L, Chen S, Gao S, Yang W (2020) Nonsubmodular constrained profit maximization from increment perspective. J Comb Optim. https://doi.org/10.1007/s10878-021-00774-6
Du L, Yang W, Gao S (2021) Generalized self-profit maximization in attribute networks. In: Du DZ, Du D, Wu C, Xu D (eds) Combinatorial optimization and applications. Springer, Cham, pp 333–347. https://doi.org/10.1007/978-3-030-92681-6_27
Goyal A, Lu W, Lakshmanan LV (2011) Celf++: optimizing the greedy algorithm for influence maximization in social networks. In: Proceedings of the 20th international conference companion on world wide web, WWW’11. Association for Computing Machinery, New York, pp 47–48. https://doi.org/10.1145/1963192.1963217
He X, Kempe D (2014) Stability of influence maximization. In: Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining—KDD’14. ACM Press, New York, pp 1256–1265. https://doi.org/10.1145/2623330.2623746
Huang H, Shen H, Meng Z (2020) Community-based influence maximization in attributed networks. Appl Intell 50(2):354–364. https://doi.org/10.1007/s10489-019-01529-x
Huzhang G, Huang X, Zhang S, Bei X (2017) Online roommate allocation problem. In: Proceedings of the twenty-sixth international joint conference on artificial intelligence, IJCAI-17, pp 235–241. https://doi.org/10.24963/ijcai.2017/34
Kempe D, Kleinberg J, Tardos E (2003) Maximizing the spread of influence through a social network. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining, pp 37–146. https://doi.org/10.1145/956750.956769
Kunegis J (2013) KONECT—the Koblenz network collection. In: Proc. Int. Conf. on world wide web companion, pp 1343–1350. https://doi.org/10.1145/2487788.2488173
Leskovec J, Krause A, Guestrin C, Faloutsos C, VanBriesen J, Glance N (2007) Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD international conference on knowledge discovery and data mining, KDD’07. Association for Computing Machinery, New York, pp 420-429. https://doi.org/10.1145/1281192.1281239
Li H, Bhowmick SS, Cui J, Gao Y, Ma J (2015) Getreal: towards realistic selection of influence maximization strategies in competitive networks. In: Proceedings of the 2015 ACM SIGMOD international conference on management of data, SIGMOD’15. Association for Computing Machinery, New York, pp 1525–1537. https://doi.org/10.1145/2723372.2723710
Li H, Pan L, Wu P (2017) Dominated competitive influence maximization with time-critical and time-delayed diffusion in social networks. J Comput Sci. https://doi.org/10.1016/j.jocs.2017.10.015
Lin SC, Lin SD, Chen MS (2015) A learning-based framework to handle multi-round multi-party influence maximization on social networks. pp 695–704. https://doi.org/10.1145/2783258.2783392
Lu W, Chen W, Lakshmanan LVS (2015) From competition to complementarity: comparative influence diffusion and maximization. Proc VLDB Endow 9(2):60–71. https://doi.org/10.14778/2850578.2850581
Masucci A, Silva A (2014) Strategic resource allocation for competitive influence in social networks
Masucci AM, Silva A (2017) Advertising competitions in social networks. https://doi.org/10.23919/ACC.2017.7963668
Narayanam R, Narahari Y (2011) A shapley value-based approach to discover influential nodes in social networks. IEEE Trans Automat Sci Eng 8(1):130–147. https://doi.org/10.1109/TASE.2010.2052042
Shang J, Zhou S, Li X, Liu L, Wu H (2017) CoFIM: a community-based framework for influence maximization on large-scale networks. Knowl Based Syst 117:88–100. https://doi.org/10.1016/j.knosys.2016.09.029
Shi Q, Wang C, Ye D, Chen J, Feng Y, Chen C (2019) Adaptive influence blocking: minimizing the negative spread by observation-based policies. In: 2019 IEEE 35th international conference on data engineering (ICDE), pp 1502–1513. https://doi.org/10.1109/ICDE.2019.00135
Shi Q, Wang C, Ye D, Chen J, Zhou S, Feng Y, Chen C, Huang Y (2021) Profit maximization for competitive social advertising. Theor Comput Sci 868:12–29. https://doi.org/10.1016/j.tcs.2021.03.036
Song J, Liu Y, Guo L, Xuan P (2019) Research on social network propagation model and influence maximization algorithm based on emotion. J Comb Optim 055(013):85–92
Sun L, Huang W, Yu PS, Chen W (2018) Multi-round influence maximization (extended version)
Tang S, Yuan J (2020) Influence maximization with partial feedback. Oper Res Lett 48(1):24–28. https://doi.org/10.1016/j.orl.2019.10.013
Tang Y, Shi Y, Xiao X (2015) Influence maximization in near-linear time: a martingale approach. In: Proceedings of the 2015 ACM SIGMOD international conference on management of data, SIGMOD’15. Association for Computing Machinery, New York, pp 1539–1554. https://doi.org/10.1145/2723372.2723734
Tang J, Tang X, Yuan J (2017) Towards profit maximization for online social network providers. arXiv:1712.08963
Tang J, Tang X, Yuan J (2018) Profit maximization for viral marketing in online social networks: algorithms and analysis. IEEE Trans Knowl Data Eng 30(6):1095–1108. https://doi.org/10.1109/TKDE.2017.2787757
Varma VS, Morărescu IC, Lasaulce S, Martin S (2018) Marketing resource allocation in duopolies over social networks. IEEE Control Syst Lett 2(4):593–598. https://doi.org/10.1109/LCSYS.2018.2846185
Varma VS, Lasaulce S, Mounthanyvong J, Morărescu IC (2019) Allocating marketing resources over social networks: a long-term analysis. IEEE Control Syst Lett 3(4):1002–1007. https://doi.org/10.1109/LCSYS.2019.2919959
Wang X, Xu J, Sun Y, Zhu Z, You Z, Tu C (2017) Near infrared passively Q-switched solid state laser based on Sb2Te3 topological insulator saturable absorber. J Lumin 192:1–5. https://doi.org/10.1016/j.jlumin.2017.06.027
Yan R, Zhu Y, Li D, Zilong Y (2019) Minimum cost seed set for threshold influence problem under competitive models. World Wide Web. https://doi.org/10.1007/s11280-018-0607-9
Yu H, Kim SK, Kim J (2013) Scalable and parallelizable processing of influence maximization for large-scale social networks? In: Proceedings of the 2013 IEEE international conference on data engineering (ICDE 2013), ICDE’13. IEEE Computer Society, USA, pp 266–277. https://doi.org/10.1109/ICDE.2013.6544831
Yuan J, Tang SJ (2017) Adaptive discount allocation in social networks. In: Proceedings of the 18th ACM international symposium on mobile ad hoc networking and computing, Mobihoc’17. Association for Computing Machinery, New York. https://doi.org/10.1145/3084041.3084043
Funding
This paper is supported by the National Natural Science Foundation of China under Grant Nos. 12071459 and 11991022 and the Fundamental Research Funds for the Central Universities under Grant No. E1E40107X2.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there are no conflict of interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supported by the National Natural Science Foundation of China under Grant Nos. 12071459 and 11991022 and the Fundamental Research Funds for the Central Universities under Grant No. E1E40107X2. This is an extended version of a paper appeared in the 16th International Conference on Algorithmic Aspects in Information and Management (AAIM 2022).
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Du, L., Gao, S. & Yang, W. Diversified-profit maximization in competitive social advertising. J Comb Optim 45, 36 (2023). https://doi.org/10.1007/s10878-022-00967-7
Accepted:
Published:
DOI: https://doi.org/10.1007/s10878-022-00967-7