A Polyhedral Approach to Least Cost Influence Maximization in Social Networks

TL;DR

This paper introduces a polyhedral approach to solve the least cost influence maximization problem in social networks, providing new inequalities and algorithms for efficient optimization on various graph structures.

Contribution

It develops novel polyhedral inequalities and separation algorithms for influence maximization, advancing optimization techniques for complex social network models.

Findings

Polyhedral inequalities improve solution bounds.

Efficient separation algorithms enable faster optimization.

Effective in computational experiments on different graph types.

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.