论文标题
社交网络中的多数意见扩散:一种对抗性方法
Majority Opinion Diffusion in Social Networks: An Adversarial Approach
论文作者
论文摘要
我们介绍并研究了一种新型的基于多数的意见扩散模型。考虑一个代表社交网络的图形$ g $。假设最初是一个称为种子节点或早期采用者的节点的子集是黑色或白色的,这对应于消费品或技术创新的正面或负面意见。然后,在每个回合中,一个未颜色的节点与至少一个彩色节点相邻,选择了邻居中最常见的颜色。 考虑一项宣传质量较差及其最终目标的营销活动是,超过一半的人群相信在意见扩散过程结束时产品的质量。我们专注于三种类型的攻击者,可以以确定性或随机的方式选择种子节点,并操纵其中几乎一半,以对产品采取积极的看法(即选择黑色)。我们说,如果大多数节点在过程结束时都是黑色的,则攻击者会成功。我们的主要目的是表征攻击者无法成功的图形类别。特别是,我们证明,如果基础图的最大程度不大或具有强大的膨胀属性,则它对此类攻击相当有抵抗力。 此外,我们在确定性和随机选择种子节点的两种设置中都证明了过程的稳定时间(即所需结束的圆数)的紧密界限。我们还为有关稳定时间和种子节点选择的一些优化问题提供了几个硬度结果。
We introduce and study a novel majority-based opinion diffusion model. Consider a graph $G$, which represents a social network. Assume that initially a subset of nodes, called seed nodes or early adopters, are colored either black or white, which correspond to positive or negative opinion regarding a consumer product or a technological innovation. Then, in each round an uncolored node, which is adjacent to at least one colored node, chooses the most frequent color among its neighbors. Consider a marketing campaign which advertises a product of poor quality and its ultimate goal is that more than half of the population believe in the quality of the product at the end of the opinion diffusion process. We focus on three types of attackers which can select the seed nodes in a deterministic or random fashion and manipulate almost half of them to adopt a positive opinion toward the product (that is, to choose black color). We say that an attacker succeeds if a majority of nodes are black at the end of the process. Our main purpose is to characterize classes of graphs where an attacker cannot succeed. In particular, we prove that if the maximum degree of the underlying graph is not too large or if it has strong expansion properties, then it is fairly resilient to such attacks. Furthermore, we prove tight bounds on the stabilization time of the process (that is, the number of rounds it needs to end) in both settings of choosing the seed nodes deterministically and randomly. We also provide several hardness results for some optimization problems regarding stabilization time and choice of seed nodes.