  Influence maximization (IM), which selects a set of $k$ users (called seeds)
to maximize the influence spread over a social network, is a fundamental
problem in a wide range of applications such as viral marketing and network
monitoring. Existing IM solutions fail to consider the highly dynamic nature of
social influence, which results in either poor seed qualities or long
processing time when the network evolves. To address this problem, we define a
novel IM query named Stream Influence Maximization (SIM) on social streams.
Technically, SIM adopts the sliding window model and maintains a set of $k$
seeds with the largest influence value over the most recent social actions.
Next, we propose the Influential Checkpoints (IC) framework to facilitate
continuous SIM query processing. The IC framework creates a checkpoint for each
window slide and ensures an $\varepsilon$-approximate solution. To improve its
efficiency, we further devise a Sparse Influential Checkpoints (SIC) framework
which selectively keeps $O(\frac{\log{N}}{\beta})$ checkpoints for a sliding
window of size $N$ and maintains an
$\frac{\varepsilon(1-\beta)}{2}$-approximate solution. Experimental results on
both real-world and synthetic datasets confirm the effectiveness and efficiency
of our proposed frameworks against the state-of-the-art IM approaches.
