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Integer Linear Programming for Influence Maximization

  • Farzaneh Ghayour Baghbani
  • Masoud AsadpourEmail author
  • Heshaam Faili
Research Paper
  • 5 Downloads

Abstract

Influence Maximization is one of the important research topics in social networks which has many applications, e.g., in marketing, politics and social science. The goal of Influence Maximization is to select a limited number of vertices (called seed set) in a social graph, so that upon their direct activation, the maximum number of vertices is activated through social interaction of the seed set with the other vertices. Social interaction is modeled by diffusion models among which Linear Threshold Model is one of the most popular ones. In Linear Threshold Model, influence of nodes on each other is quantized by edge weights and nodes have a threshold for activation. If sum of the influence of activated neighbors of a node reaches a certain threshold, the node is activated. When thresholds are fixed, Influence Maximization reduces to Target Set Selection Problem. Ackerman et al. solved Target Set Selection Problem by Integer Linear Programming. In this paper, we analyze their work and show that their method cannot properly solve the problem in specific situations, e.g., when graph has cycle. We fix this problem and propose a new method based on Integer Linear Programming and show in the results that our method can handle graphs with cycles as well.

Keywords

Influence Maximization Linear Threshold Model Target Set Selection Problem Integer Linear Programming 

Supplementary material

40998_2019_178_MOESM1_ESM.doc (134 kb)
Supplementary material 1 (DOC 133 kb)

References

  1. Ackerman E, Ben-Zwi O, Wolfovitz G (2010) Combinatorial model and bounds for TSSP. Theor Comput Sci 411(44–46):4017–4022. http://linkinghub.elsevier.com/retrieve/pii/S0304397510004561. Accessed 4 Jan 2014
  2. Chen N (2009) On the approximability of influence in social networks. SIAM J Discrete Math 23(3):1400–1415. http://epubs.siam.org/doi/abs/10.1137/08073617X. Accessed 4 Jan 2014MathSciNetCrossRefzbMATHGoogle Scholar
  3. Chen W, Wang C, Wang Y (2010a) Scalable IM for prevalent viral marketing in large-scale social networks. In: ACM SIGKDD conference on knowledge discovery and data mining. ACM Press, New York, p 1029. http://dl.acm.org/citation.cfm?doid=1835804.1835934. Accessed 23 Nov 2013Google Scholar
  4. Chen W, Yuan Y, Zhang L (2010b) Scalable IM in social networks under the linear threshold model. In: IEEE international conference on data mining, pp 88–97. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5693962. Accessed 18 Nov 2013
  5. Chen W, Lakshmanan LVS, Castillo C (2013) Information and influence propagation in social networks. Synth Lect Data Manag 5(4):1–177. http://www.morganclaypool.com/doi/abs/10.2200/S00527ED1V01Y201308DTM037. Accessed 6 Feb 2014
  6. Fazli M, Ghodsi M, Habibi J (2010) On the spread of influence through cubic, pp 1–14. Technical Report. https://www.researchgate.net/publication/268047866_On_the_Spread_of_Influence_through_Cubic_Networks. Accessed 3 Jan 2014
  7. GLPK (2017) GLPK (GNU Linear Programming Kit). https://www.gnu.org/software/glpk/. Retrieved 21 Nov 2017
  8. Goyal A, Lu W, Lakshmanan LVS (2011) SIMPATH: an efficient algorithm for IM under the linear threshold model. In: 2011 IEEE 11th international conference on data mining. IEEE, pp 211–220. http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6137225. Accessed 16 Dec 2014
  9. Kempe D, Kleinberg J, Tardos É (2003) Maximizing the spread of influence through a social network. In: ACM SIGKDD conference on knowledge discovery and data mining. http://dl.acm.org/citation.cfm?id=956769. Accessed 18 Nov 2013
  10. Kempe D, Kleinberg J, Tardos É (2005) Influential nodes in a diffusion model for social networks. Autom Lang Program. http://link.springer.com/chapter/10.1007/11523468_91. Accessed 18 Nov 2013
  11. Randomized Rounding, Wikipedia. http://en.wikipedia.org/wiki/Randomized_rounding. Retrieved 13 July 2017
  12. Stochastic Programming, Wikipedia. http://en.wikipedia.org/wiki/Stochastic_programming. Retrieved 13 July 2017
  13. Tang Y (2015) IM in near-linear time: a Martingale approach. In: SIGMOD International Conference on Management of Data, pp 1539–1554. https://dl.acm.org/citation.cfm?id=2723734. Accessed 3 Jan 2016

Copyright information

© Shiraz University 2019

Authors and Affiliations

  • Farzaneh Ghayour Baghbani
    • 1
  • Masoud Asadpour
    • 1
    Email author
  • Heshaam Faili
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of TehranTehranIran

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