Integer Linear Programming for Influence Maximization

Abstract

Influence Maximization is one of the important research topics in social networks which has many applications, e.g., in marketing, politics and social science. The goal of Influence Maximization is to select a limited number of vertices (called seed set) in a social graph, so that upon their direct activation, the maximum number of vertices is activated through social interaction of the seed set with the other vertices. Social interaction is modeled by diffusion models among which Linear Threshold Model is one of the most popular ones. In Linear Threshold Model, influence of nodes on each other is quantized by edge weights and nodes have a threshold for activation. If sum of the influence of activated neighbors of a node reaches a certain threshold, the node is activated. When thresholds are fixed, Influence Maximization reduces to Target Set Selection Problem. Ackerman et al. solved Target Set Selection Problem by Integer Linear Programming. In this paper, we analyze their work and show that their method cannot properly solve the problem in specific situations, e.g., when graph has cycle. We fix this problem and propose a new method based on Integer Linear Programming and show in the results that our method can handle graphs with cycles as well.