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A polyhedral approach to least cost influence maximization in social networks

Author

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  • Cheng-Lung Chen

    (University of Central Florida)

  • Eduardo L. Pasiliao

    (Air Force Research Laboratory, Eglin AFB)

  • Vladimir Boginski

    (University of Central Florida)

Abstract

The least cost influence maximization problem aims to determine minimum cost of partial (e.g., monetary) incentives initially given to the influential spreaders on a social network, so that these early adopters exert influence toward their neighbors and prompt influence propagation to reach a desired penetration rate by the end of cascading processes. We first conduct polyhedral analysis on a substructure that describes influence propagation assuming influence weights are unequal, linear and additively separable. Two classes of facet-defining inequalities based on a mixed 0–1 knapsack set contained in this substructure are proposed. We characterize another exponential class of valid and facet-defining inequalities utilizing the concept of minimum influencing subset. We show that these inequalities can be separated in polynomial time efficiently. Furthermore, a polynomial-time dynamic programming recursion is presented to solve this problem on a simple cycle graph. For arbitrary graphs, we propose a new exponential class of valid inequalities that dominates the cycle elimination constraints and an efficient separation algorithm for them. A compact convex hull description for a special case is presented. We illustrate the effectiveness of these inequalities via a delayed cut generation algorithm in the computational experiments.

Suggested Citation

  • Cheng-Lung Chen & Eduardo L. Pasiliao & Vladimir Boginski, 2023. "A polyhedral approach to least cost influence maximization in social networks," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-31, January.
  • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00971-x
    DOI: 10.1007/s10878-022-00971-x
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    References listed on IDEAS

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    1. Hao-Hsiang Wu & Simge Küçükyavuz, 2018. "A two-stage stochastic programming approach for influence maximization in social networks," Computational Optimization and Applications, Springer, vol. 69(3), pages 563-595, April.
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    3. Hossein Soltani & Babak Moazzez, 2019. "A polyhedral study of dynamic monopolies," Annals of Operations Research, Springer, vol. 279(1), pages 71-87, August.
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    6. Dilek Günneç & S. Raghavan & Rui Zhanga, 2020. "Least-Cost Influence Maximization on Social Networks," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 289-302, April.
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