  A widely studied model of influence diffusion in social networks represents
the network as a graph $G=(V,E)$ with an influence threshold $t(v)$ for each
node. Initially the members of an initial set $S\subseteq V$ are influenced.
During each subsequent round, the set of influenced nodes is augmented by
including every node $v$ that has at least $t(v)$ previously influenced
neighbours. The general problem is to find a small initial set that influences
the whole network. In this paper we extend this model by using
\emph{incentives} to reduce the thresholds of some nodes. The goal is to
minimize the total of the incentives required to ensure that the process
completes within a given number of rounds. The problem is hard to approximate
in general networks. We present polynomial-time algorithms for paths, trees,
and complete networks.
