In this paper, we tackle a challenging problem inherent in a series of applications: tracking the influential nodes in dynamic networks. Specifically, we model a dynamic network as a stream of edge weight updates. This general model embraces many practical scenarios as special cases, such as edge and node insertions, deletions as well as evolving weighted graphs. Under the popularly adopted linear threshold model and independent cascade model, we consider two essential versions of the problem: finding the nodes whose influences passing a user specified threshold and finding the top- @math most influential nodes. Our key idea is to use the polling-based methods and maintain a sample of random RR sets so that we can approximate the influence of nodes with provable quality guarantees. We develop an efficient algorithm that incrementally updates the sample random RR sets against network changes. We also design methods to determine the proper sample sizes for the two versions of the problem so that we can provide strong quality guarantees and, at the same time, be efficient in both space and time. In addition to the thorough theoretical results, our experimental results on five real network data sets clearly demonstrate the effectiveness and efficiency of our algorithms.
@cite_15: The problem of maximizing influence spread has been widely studied in social networks, because of its tremendous number of applications in determining critical points in a social network for information dissemination. All the techniques proposed in the literature are inherently static in nature, which are designed for social networks with a fixed set of links. However, many forms of social interactions are transient in nature, with relatively short periods of interaction. Any influence spread may happen only during the period of interaction, and the probability of spread is a function of the corresponding interaction time. Furthermore, such interactions are quite fluid and evolving, as a result of which the topology of the underlying network may change rapidly, as new interactions form and others terminate. In such cases, it may be desirable to determine the influential nodes based on the dynamic interaction patterns. Alternatively, one may wish to discover the most likely starting points for a given infection pattern. We will propose methods which can be used both for optimization of information spread, as well as the backward tracing of the source of influence spread. We will present experimental results illustrating the effectiveness of our approach on a number of real data sets.
Aggarwal @cite_15 explored how to find a set of nodes that has the highest influence within a time window @math . They modeled influence propagation as a non-linear system which is very different from triggering models like the Linear Threshold model or the Independent Cascade model. The algorithm in @cite_15 is heuristic and the results produced do not come with any provable quality guarantee.