Influence Blocking Maximization: ILP Formulation and Hardness Results

The rapid spread of misinformation on social networks has intensified the need for effective Influence Blocking Maximization (IBM) strategies. While this problem has been widely studied, current literature focuses predominantly on methods which often lack optimality guarantees. This paper fills this gap by introducing a novel Integer Linear Programming (ILP) formulation for the IBM problem under the Simplified Competitive Linear Threshold (SCLT) model. We address a critical limitation in the field: despite existing efforts to use ILP, current formulations suffer from structural inconsistencies that fail to accurately capture the diffusion process. Our approach rectifies these inaccuracies, ensuring a precise representation of activation dynamics. Additionally, we provide the first formal proof of NP-hardness for the IBM problem in this specific setting. Computational experiments evaluate the model’s performance, demonstrating its efficiency in providing exact solutions. The results indicate a tight formulation, establishing its potential as a rigorous benchmark for approximate methodologies.