The formation of opinions is fundamentally a network-based process, where the opinions of individuals in a social network exchange, evolve, and eventually converge towards a specific distribution. However, this dynamic process may be susceptible to manipulation by adversarial entities, who aim to maliciously influence the opinion formulation. The adversary may engage in extensive influence campaigns, disseminating misinformation among populations, thereby potentially destabilizing societies. It is thus of significance to develop strategies to defend against such attacks, which are essential for fostering a healthy environment for information sharing, social deliberation, and opinion formation. In this paper, we investigate a scenario wherein an external adversary aims to maliciously alter the opinions of a general social graph. This is achieved by targeting several selected nodes, referred to as followers. Concurrently, we explore a counter-strategy, aiming to negate the influence of the adversary with malicious intents. This involves identifying a subset of nodes to act as followers of a defending leader, thereby minimizing the adversary’s impact. Since this problem can be framed as a non-increasing supermodular minimization problem, we develop a $(1-1/e)$ approximation greedy algorithm consequently. Moreover, to overcome the computation challenge for large-scale networks, we establish an efficient approximation to the key quantity of the greedy algorithm. This refinement significantly enhances computational efficiency and scalability, making the algorithm applicable to networks with millions of nodes. Extensive simulation results on various real-world networks demonstrate the superior performance of our improved algorithm over existing algorithms and other baseline schemes based on centrality measures. In particular, our improved algorithm scales to networks of considerable size, with negligible sacrifice on the quality of solutions.

中文翻译：

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防御在线领导者-追随者社交网络中的恶意影响控制

意见的形成从根本上来说是一个基于网络的过程，在这个过程中，社交网络中个体的意见交换、演变，并最终趋向于特定的分布。然而，这个动态过程可能容易受到敌对实体的操纵，这些实体的目的是恶意影响意见的形成。对手可能会进行广泛的影响力活动，在民众中传播错误信息，从而可能破坏社会稳定。因此，制定防御此类攻击的策略具有重要意义，这对于营造信息共享、社会审议和舆论形成的健康环境至关重要。在本文中，我们研究了一种场景，其中外部对手旨在恶意改变一般社交图谱的观点。这是通过瞄准几个选定的节点（称为关注者）来实现的。同时，我们探索反策略，旨在消除恶意对手的影响。这涉及到确定一个节点子集作为防御领导者的追随者，从而最大限度地减少对手的影响。由于这个问题可以被视为一个非增超模最小化问题，我们开发了一个 $(1-1/e)$因此近似贪心算法。此外，为了克服大规模网络的计算挑战，我们建立了贪婪算法关键量的有效近似。这种改进显着提高了计算效率和可扩展性，使该算法适用于具有数百万节点的网络。对各种现实世界网络的广泛模拟结果表明，我们改进的算法相对于现有算法和其他基于中心性度量的基线方案具有优越的性能。特别是，我们改进的算法可以扩展到相当大的网络规模，而对解决方案质量的影响可以忽略不计。