Abstract
The influence maximization problem that has caused great attention in social network analysis aims at selecting a small set of influential spreaders so that the information cascade triggered by the seed set is maximized. The majority of the existing works mainly focus on developing single-stage seeding strategies that would ignite all the seeds before the influence spread. However, it cannot depict the scenarios of the practical, where ones would like to make further decisions based on observed activation. In this paper, we investigate the policies for the intractable sequential influence maximization problem. A Q-learning-driven discrete differential evolution algorithm based on the reinforcement Q-learning model, which is treated as a parameter controller to adaptively adjust the parameters during the evolution of the algorithm, is proposed. The policy distributes the seeding actions over the spreading process by estimating the latest node status of the network dynamically. Extensive simulations are conducted on six social networks of the practical, and the findings demonstrate the superiority and effectiveness of the hybrid meta-heuristic algorithm compared with the state-of-the-art methods.








Similar content being viewed by others
Availability of data and materials
The authors declare that the data supporting the findings of this study are available within the paper.
References
Azaouzi M, Mnasri W, Romdhane LB (2021) New trends in influence maximization models. Comput Sci Rev 40(100):393. https://doi.org/10.1016/j.cosrev.2021.100393
Kempe D, Kleinberg J, Tardos É (2003) Maximizing the spread of influence through a social network. Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, 137–146
Lin Y, Lui JC (2015) Analyzing competitive influence maximization problems with partial information: an approximation algorithmic framework. Perform Eval 91:187–204. https://doi.org/10.1016/j.peva.2015.06.012
Lu W, Chen W, Lakshmanan LV (2015) From competition to complementarity: comparative influence diffusion and maximization. arXiv preprint arXiv:1507.00317https://doi.org/10.48550/arXiv.1507.00317
Guo J, Zhang Y, Wu W (2021) An overall evaluation on benefits of competitive influence diffusion. IEEE Trans Big Data. https://doi.org/10.1109/TBDATA.2021.3084468
Tong A, Du DZ, Wu W (2018) On misinformation containment in online social networks. Adv Neural Inform Process Syst, 341–351
Zhang Y, Yang W, Du DZ (2021) Rumor correction maximization problem in social networks. Theoret Comput Sci 861(1):102–116. https://doi.org/10.1016/j.tcs.2021.02.014
Zhou Z, Lu H, Deng C et al (2016) User preference learning for online social recommendation. IEEE Trans Knowl Data Eng 28(9):2522–2534. https://doi.org/10.1109/TKDE.2016.2569096
Jankowski J, Szymanski BK, Kazienko P et al (2018) Probing limits of information spread with sequential seeding. Sci Rep 8(1):1–9. https://doi.org/10.1038/s41598-018-32081-2
Jankowski J, Bródka P, Kazienko P et al (2017) Balancing speed and coverage by sequential seeding in complex networks. Sci Rep 7(1):1–11. https://doi.org/10.1038/s41598-017-00937-8
Ni Y (2017) Seeding strategies for viral marketing: an empirical comparison. Appl Soft Comput 56:730–737. https://doi.org/10.1016/j.asoc.2016.04.025
Zhao J, Yang TH, Huang Y et al (2011) Ranking candidate disease genes from gene expression and protein interaction: a katz-centrality based approach. PLoS ONE 6(9):e24,306. https://doi.org/10.1371/journal.pone.0024306
Hu Q, Gao Y, Ma P, et al (2013) A new approach to identify influential spreaders in complex networks. International Conference on Web-Age Information Management, 99–104
Page L, Brin S, Motwani R et al (1999) The pagerank citation ranking: bringing order to the web. Tech. rep, Stanford InfoLab
Brandes U, Borgatti SP, Freeman LC (2016) Maintaining the duality of closeness and betweenness centrality. Soc Netw 44:153–159. https://doi.org/10.1016/j.socnet.2015.08.003
Tang J, Zhang R, Yao Y et al (2018) Maximizing the spread of influence via the collective intelligence of discrete bat algorithm. Knowl-Based Syst 160:88–103. https://doi.org/10.1016/j.knosys.2018.06.013
Leskovec J, Krause A, Guestrin C, et al (2007) Cost-effective outbreak detection in networks. Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, 420–429
Borgs C, Brautbar M, Chayes J, et al (2014) Maximizing social influence in nearly optimal time. Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms, 946–957
Tang Y, Shi Y, Xiao X (2015) Influence maximization in near-linear time: A martingale approach. Proceedings of the 2015 ACM SIGMOD international conference on management of data, 1539–1554
Ko YY, Cho KJ, Kim SW (2018) Efficient and effective influence maximization in social networks: a hybrid-approach. Inf Sci 465:44–161. https://doi.org/10.1016/j.ins.2018.07.003
Li W, Fan Y, Mo J et al (2020) Three-hop velocity attenuation propagation model for influence maximization in social networks. World Wide Web 23:1261–1273. https://doi.org/10.1007/s11280-019-00750-5
Cui L, Hu H, Yu S et al (2018) Ddse: a novel evolutionary algorithm based on degree-descending search strategy for influence maximization in social networks. J Netw Comput Appl 103(FEB):119–130. https://doi.org/10.1016/j.jnca.2017.12.003
Wang L, Ma L, Wang C et al (2021) Identifying influential spreaders in social networks through discrete moth-flame optimization. IEEE Trans Evol Comput 25(6):1091–1102. https://doi.org/10.1109/TEVC.2021.3081478
Qiu L, Tian X, Zhang J et al (2021) Lidde: A differential evolution algorithm based on local-influence-descending search strategy for influence maximization in social networks. J Netw Comput Appl 178(102):973. https://doi.org/10.1016/j.jnca.2020.102973
Chen W, Wang Y, Yang S (2009) Efficient influence maximization in social networks. Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, 199–208
Sela A, Goldenberg D, Ben-Gal I et al (2018) Active viral marketing: Incorporating continuous active seeding efforts into the diffusion model. Expert Syst Appl 107:45–60. https://doi.org/10.1016/j.eswa.2018.04.016
Shakarian P, Eyre S, Paulo D (2013) A scalable heuristic for viral marketing under the tipping model. Soc Netw Anal Min 3(4):1225–1248. https://doi.org/10.1007/s13278-013-0135-7
Banerjee A, Chandrasekhar AG, Duflo E et al (2013) The diffusion of microfinance. Science 341(6144):1236,498. https://doi.org/10.1126/science.1236498
Tong G, Wang R (2020) On adaptive influence maximization under general feedback models. IEEE Trans Emerg Top Comput. https://doi.org/10.1109/TETC.2020.3031057
Michalski R, Jankowski J, Bródka P (2020) Effective influence spreading in temporal networks with sequential seeding. IEEE Access 8:151,208-151,218. https://doi.org/10.1109/ACCESS.2020.3016913
Ni C, Yang J, Kong D (2020) Sequential seeding strategy for social influence diffusion with improved entropy-based centrality. Physica A 545(123):659. https://doi.org/10.1016/j.physa.2019.123659
Bródka P, Jankowski J, Michalski R (2021) Sequential seeding in multilayer networks. Chaos: An Interdisciplin J Nonlinear Sci 31(3):033,130. https://doi.org/10.1063/5.0023427
Seeman L, Singer Y (2013) Adaptive seeding in social networks. 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 459–468
Tong G, Wu W, Tang S et al (2016) Adaptive influence maximization in dynamic social networks. IEEE/ACM Trans Netw 25(1):112–125. https://doi.org/10.1109/TNET.2016.2563397
Goldenberg D, Sela A, Shmueli E (2018) Timing matters: Influence maximization in social networks through scheduled seeding. IEEE Trans Comput Soc Syst 5(3):621–638. https://doi.org/10.1109/TCSS.2018.2852742
Lev T, Ben-Gal I, Shmueli E (2021) Influence maximization through scheduled seeding in a real-world setting. IEEE Trans Comput Soc Syst PP(99):1–14. https://doi.org/10.1109/TCSS.2021.3109043
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
Tong G, Wang R, Dong Z et al (2020) Time-constrained adaptive influence maximization. IEEE Trans Comput Soc Syst 8(1):33–44. https://doi.org/10.1109/TCSS.2020.3032616
Golovin D, Krause A (2011) Adaptive submodularity: theory and applications in active learning and stochastic optimization. J Artificial Intell Res 42:427–486. https://doi.org/10.1613/jair.3278
Zhu T, Wang B, Wu B et al (2014) Maximizing the spread of influence ranking in social networks. Inf Sci 278:535–544. https://doi.org/10.1016/j.ins.2014.03.070
Lü L, Chen D, Ren XL et al (2016) Vital nodes identification in complex networks. Phys Rep 650:1–63. https://doi.org/10.1016/j.physrep.2016.06.007
Pant M, Zaheer H, Garcia-Hernandez L et al (2020) Differential evolution: a review of more than two decades of research. Eng Appl Artif Intell 90(103):479. https://doi.org/10.1016/j.engappai.2020.103479
Leskovec J, Krevl A, Datasets S (2011) Stanford large network dataset collection. http://snap.stanford.edu/data/
Gong M, Yan J, Shen B et al (2016) Influence maximization in social networks based on discrete particle swarm optimization. Inf Sci 367:600–614. https://doi.org/10.1016/j.ins.2016.07.012
Acknowledgements
This work was financially supported by the Gansu Provincial Science Fund for Distinguished Young Scholars [grant number 23JRRA766], the Lanzhou University of Technology Fund for Outstanding Young Scholars, the National Natural Science Foundations of China [grant number 62162040] and the Natural Science Foundation of Zhejiang Province [grant number LQ20F020011].
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethical approval
This article does not contain any studies with animals performed by any of the authors.
Conflict of interest
The authors have no competing interests to declare that are relevant to the content of this paper.
Authors’ contributions
Jianxin Tang was involved in conceptualization, supervision, project administration, funding acquisition, and writing—review and editing. Shihui Song was involved in methodology, software, validation, and writing—original draft. Hongyu Zhu contributed to resources and software. Qian Du was involved in data curation and visualization. Jitao Qu was involved in formal analysis and writing—review and editing. All authors reviewed the manuscript.
Funding
This work was not supported by any organization.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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
Tang, J., Song, S., Zhu, H. et al. Sequential seeding policy on social influence maximization: a Q-learning-driven discrete differential evolution optimization. J Supercomput 80, 3334–3359 (2024). https://doi.org/10.1007/s11227-023-05601-9
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11227-023-05601-9