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 attacker's 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 attacker's problem as an integer program, and then combines relaxation with duality to yield an upper bound on the defender's 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.

中文翻译：

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阻止社交网络中的对抗性影响

虽然社交网络被广泛用作信息传播的媒体，但攻击者还可以战略性地使用分析工具，例如影响最大化，以最大限度地通过网络传播对抗性内容。我们研究了通过阻塞网络中的节点和边来限制负面信息扩散的问题。我们将防御者和攻击者之间的交互表述为 Stackelberg 博弈，其中防御者首先选择一组要阻止的节点，然后攻击者选择一组种子来传播负面信息。这产生了一个极其复杂的双层优化问题，特别是因为即使是标准的影响度量也难以计算。我们的方法是将攻击者的问题近似为最大节点控制问题。为了解决这个问题，我们首先开发了一种基于整数规划结合约束生成的方法。接下来，为了提高可扩展性，我们开发了一种近似解决方法，将攻击者的问题表示为整数程序，然后将松弛与对偶性相结合，以产生可以使用混合整数线性规划计算的防御者目标的上限。最后，我们提出了一种更具可扩展性的启发式方法，该方法根据节点的程度从考虑集中修剪节点。大量实验证明了我们方法的有效性。然后将松弛与对偶相结合，以产生防御者目标的上限，该上限可以使用混合整数线性规划计算。最后，我们提出了一种更具可扩展性的启发式方法，该方法根据节点的程度从考虑集中修剪节点。大量实验证明了我们方法的有效性。然后将松弛与对偶相结合，以产生防御者目标的上限，该上限可以使用混合整数线性规划计算。最后，我们提出了一种更具可扩展性的启发式方法，该方法根据节点的程度从考虑集中修剪节点。大量实验证明了我们方法的有效性。