A polyhedral approach to least cost influence maximization in social networks

Cheng-Lung Chen (), Eduardo L. Pasiliao () and Vladimir Boginski ()
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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

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 43, 31 pages

Abstract: 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.

Keywords: Influence maximization; Social networks; Valid inequalities; Delayed cut generation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-022-00971-x

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