  We incorporate self activation into influence propagation and propose the
self-activation independent cascade (SAIC) model: nodes may be self activated
besides being selected as seeds, and influence propagates from both selected
seeds and self activated nodes. Self activation reflects the real-world
scenarios such as people naturally share product recommendations with their
friends even without marketing intervention. It also leads to two new forms of
optimization problems: (a) {\em preemptive influence maximization (PIM)}, which
aims to find $k$ nodes that, if self-activated, can reach the most number of
nodes before other self-activated nodes; and (b) {\em boosted preemptive
influence maximization (BPIM)}, which aims to select $k$ seeds that are
guaranteed to be activated and can reach the most number of nodes before other
self-activated nodes. We propose scalable algorithms for PIM and BPIM and prove
that they achieve $1-\varepsilon$ approximation for PIM and $1-1/e-\varepsilon$
approximation for BPIM, for any $\varepsilon > 0$. Through extensive tests on
real-world graphs, we demonstrate that our algorithms outperform the baseline
algorithms significantly for the PIM problem in solution quality, and also
outperform the baselines for BPIM when self-activation behaviors are
non-uniform across nodes.
