Targeting influence in a harmonic opinion model

TL;DR

This paper introduces a mathematically principled adversarial influence model in social networks based on harmonic functions and linear diffusion, providing theoretical analysis and approximation algorithms.

Contribution

It develops a new adversarial influence model using harmonic functions, proves NP-hardness, and offers approximation and relaxation methods for solution.

Findings

The influence maximization problem is NP-hard.

The objective function is monotone and submodular.

Approximate solutions can be obtained via greedy algorithms and convex relaxation.

Abstract

Influence propagation in social networks is a central problem in modern social network analysis, with important societal applications in politics and advertising. A large body of work has focused on cascading models, viral marketing, and finite-horizon diffusion. There is, however, a need for more developed, mathematically principled \emph{adversarial models}, in which multiple, opposed actors strategically select nodes whose influence will maximally sway the crowd to their point of view. In the present work, we develop and analyze such a model based on harmonic functions and linear diffusion. We prove that our general problem is NP-hard and that the objective function is monotone and submodular; consequently, we can greedily approximate the solution within a constant factor. Introducing and analyzing a convex relaxation, we show that the problem can be approximately solved using smooth optimization methods. We illustrate the effectiveness of our approach on a variety of example networks.