While social networks are widely used as a media for information diffusion, attackers can also strategically employ analytical tools, such as influence maximization, to maximize the spread of adversarial content through the networks. We investigate the problem of limiting the diffusion of negative information by blocking nodes and edges in the network. We formulate the interaction between the defender and the attacker as a Stackelberg game where the defender first chooses a set of nodes to block and then the attacker selects a set of seeds to spread negative information from. This yields an extremely complex bi-level optimization problem, particularly since even the standard influence measures are difficult to compute. Our approach is to approximate the attackers problem as the maximum node domination problem. To solve this problem, we first develop a method based on integer programming combined with constraint generation. Next, to improve scalability, we develop an approximate solution method that represents the attackers problem as an integer program, and then combines relaxation with duality to yield an upper bound on the defenders objective that can be computed using mixed integer linear programming. Finally, we propose an even more scalable heuristic method that prunes nodes from the consideration set based on their degree. Extensive experiments demonstrate the efficacy of our approaches.
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