Influence Maximization From Cascade Information Traces in Complex Networks in the Absence of Network Structure

Abstract

Influence maximization refers to the problem of selecting the most influential source set of a given size in a diffusion network. Most of the existing literature assumes the knowledge of the underlying network and the knowledge of the diffusion model of propagation to solve the influence maximization problem. However, both the real-world information networks and their diffusion models are not easy to determine in practice. In this article, an influence maximization algorithm based on the observed cascades has been proposed. A novel idea that a good subset of nodes for influence maximization should be composed of nodes that are not only active and strong or influential by themselves but also independent of each other has been proposed. Based on this premise, the problem has been cast as a quadratic integer programming problem with constraints. Furthermore, this problem has been shown to be equivalent to a particular class of Max-GP problem, namely, max-not-cut with size ${k}$ (MNC), for which the state-of-the-art semidefinite programming (SDP) solution techniques exist with guaranteed performance ratios, although the original problem is NP-hard. The new SDP-based method presented in this article is tested on a number of synthetic as well as real-world data sets and has been shown to perform better than the state-of-the-art influence maximization algorithms which work with the apriori knowledge of the network and assume a particular diffusion model. The results demonstrate its practical applicability in applications using Twitter, blogosphere, and other social networks which are being increasingly used to target influential customers for viral marketing.