On The Max-Min Influence Spread Problem: A Multi-Objective Optimization Approach

A central problem in network dynamics is understanding how influence spreads through a social network. This problem can be studied from an optimization approach. The aim is to find an initial seed of actors, with certain size restrictions, capable of maximizing or minimizing the activation of other actors in the network through a given influence spread model. The maximization and minimization versions of this problem have been extensively studied. In recent years, the min–max multi-objective version was defined, which involves finding the smallest seed capable of maximizing the influence spread in the network. Searching for exact solutions in these optimization problems is not feasible, even for relatively small networks. Hence, various approximation techniques have been proposed in recent years, with bio-inspired algorithms based on metaheuristics standing out among them. However, the max–min multi-objective version of the problem remains open. This article formally defines the max–min influence spread problem, aiming to find the maximum seed with the minimum spread capacity. We propose a strategy that uses solutions from the min–max version of the problem to reduce the search space, allowing us to avoid trivial solutions. The potential applications of this max–min version are diverse, e.g., finding clusters less susceptible to diseases in a contagion network or the most inefficient coalitions in a voting system. Using swarm intelligence metaheuristics methods as in the min–max version, the results obtained on real social networks show that this approach exhibits rapid convergence, reaching a seed encompassing 51.3% of the actors who could not influence others within the network. Similarly, for a more complex network, the approach is able to generate a seed where 71.8% of the actors showed no influence over others.