社交网络中的布道：算法与复杂性
Evangelism in Social Networks: Algorithms and Complexity
摘要：
我们考虑一个相互关联的个体群体，就一条信息而言，在每个时刻都可以细分为三个（依赖于时间的）类别：不可知论者，受影响者和福音传道者。信息扩散的动态过程在种群的个体之间按照以下规则演化。起初，所有的人都是不可知论者。然后，从外面选出一批人，说服他们开始传福音，即，开始传播信息当一个节点v与一个福音传道者的数量大于一个给定的阈值时，这个节点v就会受到影响，而一旦这个节点v被足够多的福音传道者联系上，它本身就会转变为一个福音传道者，从而开始传播信息。问题是：如何选择一个有界的基数初始集合的福音，以最大限度地提高最终的人数影响的个人？我们证明了这个问题很难解决，即使在近似意义上。在积极的一面，我们提出了树和完全图的精确多项式时间算法。对于一般的图，我们推导出精确的参数化算法。我们还调查的问题时，目标是选择一个最小数量的布道者能够影响整个网络。我们研究这些问题的动机来自于病毒式营销和对社交网络中影响力传播的定量模型的分析。
英文摘要：
We consider a population of interconnected individuals that, with respect to a piece of information, at each time instant can be subdivided into three (time-dependent) categories: agnostics, influenced, and evangelists. A dynamical process of information diffusion evolves among the individuals of the population according to the following rules. Initially, all individuals are agnostic. Then, a set of people is chosen from the outside and convinced to start evangelizing, i.e., to start spreading the information. When a number of evangelists, greater than a given threshold, communicate with a node v, the node v becomes influenced, whereas, as soon as the individual v is contacted by a sufficiently much larger number of evangelists, it is itself converted into an evangelist and consequently it starts spreading the information. The question is: How to choose a bounded cardinality initial set of evangelists so as to maximize the final number of influenced individuals? We prove that the problem is hard to solve, even in an approximate sense. On the positive side, we present exact polynomial time algorithms for trees and complete graphs. For general graphs, we derive exact parameterized algorithms. We also investigate the problem when the objective is to select a minimum number of evangelists capable of influencing the whole network. Our motivations to study these problems come from the areas of Viral Marketing and the analysis of quantitative models of spreading of influence in social networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
