  Let $G$ be a graph, which represents a social network, and suppose each node
$v$ has a threshold value $\tau(v)$. Consider an initial configuration, where
each node is either positive or negative. In each discrete time step, a node
$v$ becomes/remains positive if at least $\tau(v)$ of its neighbors are
positive and negative otherwise. A node set $\mathcal{S}$ is a Target Set (TS)
whenever the following holds: if $\mathcal{S}$ is fully positive initially, all
nodes in the graph become positive eventually. We focus on a generalization of
TS, called Timed TS (TTS), where it is permitted to assign a positive state to
a node at any step of the process, rather than just at the beginning.
  We provide graph structures for which the minimum TTS is significantly
smaller than the minimum TS, indicating that timing is an essential aspect of
successful target selection strategies. Furthermore, we prove tight bounds on
the minimum size of a TTS in terms of the number of nodes and maximum degree
when the thresholds are assigned based on the majority rule.
  We show that the problem of determining the minimum size of a TTS is NP-hard
and provide an Integer Linear Programming formulation and a greedy algorithm.
We evaluate the performance of our algorithm by conducting experiments on
various synthetic and real-world networks. We also present a linear-time exact
algorithm for trees.
