Viral Marketing in Social Networks with Competing Products

TL;DR

This paper studies viral marketing strategies in social networks with competing products, providing a computationally efficient approximation algorithm and analyzing the convergence time of the diffusion process.

Contribution

It introduces a polynomial-time approximation algorithm for maximizing red nodes, proves its optimality, and analyzes the convergence time with new bounds and techniques.

Findings

The problem is computationally hard.

The proposed algorithm outperforms others in experiments.

Tight bounds on convergence time are established.

Abstract

Consider a directed network where each node is either red (using the red product), blue (using the blue product), or uncolored (undecided). Then in each round, an uncolored node chooses red (resp. blue) with some probability proportional to the number of its red (resp. blue) out-neighbors. What is the best strategy to maximize the expected final number of red nodes given the budget to select $k$ red seed nodes? After proving that this problem is computationally hard, we provide a polynomial time approximation algorithm with the best possible approximation guarantee, building on the monotonicity and submodularity of the objective function and exploiting the Monte Carlo method. Furthermore, our experiments on various real-world and synthetic networks demonstrate that our proposed algorithm outperforms other algorithms. Additionally, we investigate the convergence time of the aforementioned process both theoretically and experimentally. In particular, we prove several tight bounds on the convergence time in terms of different graph parameters, such as the number of nodes/edges, maximum out-degree and diameter, by developing novel proof techniques.