  In this paper, we study the adaptivity gap of the influence maximization
problem under independent cascade model when full-adoption feedback is
available. Our main results are to derive upper bounds on several families of
well-studied influence graphs, including in-arborescences, out-arborescences
and bipartite graphs. Especially, we prove that the adaptivity gap for the
in-arborescence is between $[\frac{e}{e-1}, \frac{2e}{e - 1}]$ and for the
out-arborescence, the gap is between $[\frac{e}{e-1}, 2]$. These are the first
constant upper bounds in the full-adoption feedback model. We provide several
novel ideas to tackle with correlated feedback appearing in the adaptive
stochastic optimization, which we believe to be of independent interests.
