  Influence maximization which asks for $k$-size seed set from a social network
such that maximizing the influence over all other users (called influence
spread) has widely attracted attention due to its significant applications in
viral marketing and rumor control. In real world scenarios, people are
interested in the most influential users in particular topics, and want to
subscribe the topics-of-interests over social networks. In this paper, we
formulate the problem of influential users subscription on time-decaying social
stream, which asks for maintaining the $k$-size influential users sets for each
topic-aware subscription queries. We first analyze the widely adopted sliding
window model and propose a newly time-decaying influence model to overcome the
shortages when calculating the influence over social stream. Developed from
sieve based streaming algorithm, we propose an efficient algorithm to support
the calculation of time-decaying influence over dynamically updating social
networks. Using information among subscriptions, we then construct the Prefix
Tree Structure to allow us minimizing the times of calculating influence of
each update and easily maintained. Pruning techniques are also applied to the
Prefix Tree to optimize the performance of social stream update. Our approach
ensures a $\frac{1}{2}-\epsilon$ approximation ratio. Experimental results show
that our approach significantly outperforms the baseline approaches in
efficiency and result quality.
