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.
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The datasets analyzed during the current study are available from the corresponding author on reasonable request.
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We are grateful to the two anonymous reviewers who provided constructive feedback that helped us improve the contents of this paper. We also thank Demetrios Papazaharias in the early discussion of the separation problem for the minimum influencing subset inequalities. This material is based upon work supported by the Air Force Research Laboratory (AFRL) Mathematical Modeling and Optimization Institute and AFRL award FA8651-16-2-0009. Preliminary results of this study were presented at the 9th International Conference on Computational Data and Social Networks (CSoNet 2020, December 11–13, 2020, Dallas, TX) and published in the respective conference proceedings volume (Chen et al. 2020).
This research was supported in part by AFRL award FA8651-16-2-0009.
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Chen, CL., Pasiliao, E.L. & Boginski, V. A polyhedral approach to least cost influence maximization in social networks. J Comb Optim 45, 44 (2023). https://doi.org/10.1007/s10878-022-00971-x
- Influence maximization
- Social networks
- Valid inequalities
- Delayed cut generation