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The complexity of influence maximization problem in the deterministic linear threshold model

Author

Listed:
  • Zaixin Lu

    (University of Texas at Dallas)

  • Wei Zhang

    (Xi’an JiaoTong University)

  • Weili Wu

    (University of Texas at Dallas)

  • Joonmo Kim

    (Dankook University)

  • Bin Fu

    (University of Texas–Pan American)

Abstract

The influence maximization is an important problem in the field of social network. Informally it is to select few people to be activated in a social network such that their aggregated influence can make as many as possible people active. Kempe et al. gave a $(1-{1 \over e})$ -approximation algorithm for this problem in the linear threshold model and the independent cascade model. In addition, Chen et al. proved that the exact computation of the influence given a seed set is #P-hard in the linear threshold model. Both of the two models are based on randomized propagation, however such information might be obtained by surveys and data mining techniques. This will make great difference on the complexity of the problem. In this note, we study the complexity of the influence maximization problem in deterministic linear threshold model. We show that in the deterministic linear threshold model, there is no n 1−ε -factor polynomial time approximation for the problem unless P=NP. We also show that the exact computation of the influence given a seed set can be solved in polynomial time.

Suggested Citation

  • Zaixin Lu & Wei Zhang & Weili Wu & Joonmo Kim & Bin Fu, 2012. "The complexity of influence maximization problem in the deterministic linear threshold model," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 374-378, October.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9393-3
    DOI: 10.1007/s10878-011-9393-3
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    Citations

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    Cited by:

    1. Xiaodong Liu & Xiangke Liao & Shanshan Li & Si Zheng & Bin Lin & Jingying Zhang & Lisong Shao & Chenlin Huang & Liquan Xiao, 2017. "On the Shoulders of Giants: Incremental Influence Maximization in Evolving Social Networks," Complexity, Hindawi, vol. 2017, pages 1-14, September.
    2. Hemant Gehlot & Shreyas Sundaram & Satish V. Ukkusuri, 2023. "Algorithms for influence maximization in socio-physical networks," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-28, January.
    3. Xiao, Yunpeng & Wang, Zheng & Li, Qian & Li, Tun, 2019. "Dynamic model of information diffusion based on multidimensional complex network space and social game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 578-590.
    4. Eszter Julianna Csókás & Tamás Vinkó, 2023. "An exact method for influence maximization based on deterministic linear threshold model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(1), pages 269-286, March.

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