  The problem of quickest detection of dynamic events in networks is studied.
At some unknown time, an event occurs, and a number of nodes in the network are
affected by the event, in that they undergo a change in the statistics of their
observations. It is assumed that the event is dynamic, in that it can propagate
along the edges in the network, and affect more and more nodes with time. The
event propagation dynamics is assumed to be unknown. The goal is to design a
sequential algorithm that can detect a "significant" event, i.e., when the
event has affected no fewer than $\eta$ nodes, as quickly as possible, while
controlling the false alarm rate. Fully connected networks are studied first,
and the results are then extended to arbitrarily connected networks. The
designed algorithms are shown to be adaptive to the unknown propagation
dynamics, and their first-order asymptotic optimality is demonstrated as the
false alarm rate goes to zero. The algorithms can be implemented with linear
computational complexity in the network size at each time step, which is
critical for online implementation. Numerical simulations are provided to
validate the theoretical results.
