AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
PDF (1.8 MB)
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Open Access

Approximating Special Social Influence Maximization Problems

Department of Computer and Information Sciences, Temple University, Philadelphia, PA 19122, USA.
Department of Computer Science, Rowan University, Glassboro, NJ 08028, USA.
Show Author Information

Abstract

Social Influence Maximization Problems (SIMPs) deal with selecting k seeds in a given Online Social Network (OSN) to maximize the number of eventually-influenced users. This is done by using these seeds based on a given set of influence probabilities among neighbors in the OSN. Although the SIMP has been proved to be NP-hard, it has both submodular (with a natural diminishing-return) and monotone (with an increasing influenced users through propagation) that make the problem suitable for approximation solutions. However, several special SIMPs cannot be modeled as submodular or monotone functions. In this paper, we look at several conditions under which non-submodular or non-monotone functions can be handled or approximated. One is a profit-maximization SIMP where seed selection cost is included in the overall utility function, breaking the monotone property. The other is a crowd-influence SIMP where crowd influence exists in addition to individual influence, breaking the submodular property. We then review several new techniques and notions, including double-greedy algorithms and the supermodular degree, that can be used to address special SIMPs. Our main results show that for a specific SIMP model, special network structures of OSNs can help reduce its time complexity of the SIMP.

References

[1]
H. Nguyen and R. Zheng, On budgeted influence maximization in social networks, IEEE Journal on Selected Areas in Communications, vol. 31, no. 6, pp. 1084-1094, 2013.
[2]
X. Yang, H. Steck, and Y. Liu, Circle-based recommendation in online social networks, in Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’14), Beijing, China, 2014, pp. 1267-1275.
[3]
D. Kempe, J. Kleinberg, and É. Tardos, Maximizing the spread of influence through a social network, in Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’13), Washington, DC, USA, 2003, pp. 137-146.
[4]
J. Tang, X. Tang, and J. Yuan, Profit maximization for viral marketing in online social networks, in Proceedings of the IEEE International Conference on Network Protocols (ICNP’16), Singapore, 2016. pp. 1095-1108.
[5]
N. Buchbinder, M. Feldman, J. Seffi, and R. Schwartz, A tight linear time (1/2)-approximation for unconstrained submodular maximization, SIAM Journal on Computing, vol. 44, no. 5, pp. 1384-1402, 2015.
[6]
M. Feldman and R. Izsak, Constrained monotone function maximization and the supermodular degree, arXiv preprint arXiv: 1407.6328, 2014.
[7]
H. Zheng, N. Wang, and J. Wu, Non-submodularity and approximability: Influence maximization in online social networks, in Proceedings of the IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks (WoWMoM’19), Washington, DC, USA, 2019, pp. 1-10.
[8]
A. Mislove, M. Marcon, K. P. Gummadi, P. Druschel, and B. Bhattacharjee, Measurement and analysis of online social networks, in Proceedings of the ACM SIGCOMM Conference on Internet Measurement (IMC’07), San Diego, CA, USA, 2007, pp. 29-42.
[9]
R. Kumar, J. Novak, and A. Tomkins, Structure and evolution of online social networks, in Link Mining: Models, Algorithms, and Applications. New York, NY, USA: Springer, 2010, pp. 337-357.
[10]
L. Lovász, Submodular functions and convexity, in Mathematical Programming the State of the Art, Heidelberg, German: Springer, 1983, pp. 235-257.
[11]
S. Iwata and K. Nagano, Submodular function minimization under covering constraints, in Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS’09), Atlanta, GA, USA, 2009, pp. 671-680.
[12]
U. Feige, V. S. Mirrokni, and J. Vondrak, Maximizing non-monotone submodular functions, SIAM Journal on Computing, vol. 40, no. 4, pp. 1133-1153, 2011.
[13]
P.-J. Wan, D.-Z. Du, P. Pardalos, and W. Wu, Greedy approximations for minimum submodular cover with submodular cost, in Computational Optimization and Applications, Springer, 2010, pp. 463-474.
[14]
H.-J. Hung, H.-H. Shuai, D.-N. Yang, L.-H. Huang, W.-C. Lee, J. Pei, and M.-S. Chen, When social influence meets item inference, in Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’16), San Francisco, CA, USA, 2016, pp. 915-924.
[15]
S. Fujishige and S. Isotani, A submodular function minimization algorithm based on the minimum-norm base, presented at the Fourth Sino-Japanese Optimization Meeting, Tainan, China, 2008.
[16]
M. Sviridenko, J. Vondrák, and J. Ward, Optimal approximation for submodular and supermodular optimization with bounded curvature, Mathematics of Operations Research, vol. 42, no. 4, pp. 1197-1218, 2017.
[17]
S. Dughmi, Algorithmic information structure design: A survey, ACM SIGecom Exchanges, vol. 15, no. 2, pp. 2-24, 2017.
[18]
T. Gradowski and A. Krawiecki, Majority-vote model on scale-free hypergraphs, Acta Physica Polonica A, vol. 127, no. 3A, pp. 1-4, 2015.
[19]
H. Zheng and J. Wu, NSFA: Nested scale-free architecture for scalable publish/subscribe over p2p networks, in Proceedings of the IEEE International Conference on Network Protocols (ICNP’16), Singapore, 2016, pp. 1-10.
[20]
J. Leskovec, J. Kleinberg, and C. Faloutsos, Graph evolution: Densification and shrinking diameters, ACM Transactions on Knowledge Discovery from Data, vol. 1, no. 1, pp. 1-41, 2007.
[21]
O. Tore, tnet dataset, https://toreopsahl.com/datasets/\#newman2001, 2001.
Tsinghua Science and Technology
Pages 703-711
Cite this article:
Wu J, Wang N. Approximating Special Social Influence Maximization Problems. Tsinghua Science and Technology, 2020, 25(6): 703-711. https://doi.org/10.26599/TST.2019.9010017

651

Views

22

Downloads

6

Crossref

N/A

Web of Science

9

Scopus

6

CSCD

Altmetrics

Received: 19 April 2019
Accepted: 29 April 2019
Published: 07 May 2020
© The author(s) 2020

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).

Return