Optimal Selection of Intervention Timing in Opinion Dynamics

Differing from existing research on intervention strategies such as leader selection and edge addition, we investigate the impact of intervention timing in opinion dynamics. We employ the leader-based DeGroot model to formulate the evolution of opinions in social networks, wherein leaders represent organizations or parties that influence public opinion. We propose an optimal timing selection problem, in which a leader maximizes public opinion at a specific time by strategically selecting intervention times given a limited number of interventions. Our theoretical analysis shows that more interventions do not necessarily lead to better results, but additional interventions based on the existing intervention certainly do not worsen outcomes. Furthermore, we rigorously prove that intervention timing does not affect effectiveness if and only if all agents have the same weighted degree. Using the monotonicity and submodularity of the objective function, we develop a greedy algorithm and a time-importance-based heuristic algorithm to solve the problem. Our numerical simulations confirm the efficacy of these algorithms across both real-world social networks and synthetic random networks.