  The task of the broadcast problem is, given a graph G and a source vertex s,
to compute the minimum number of rounds required to disseminate a piece of
information from s to all vertices in the graph. It is assumed that, at each
round, an informed vertex can transmit the information to at most one of its
neighbors. The broadcast problem is known to NP-hard. We show that the problem
is FPT when parametrized by the size k of a feedback edge-set, or by the size k
of a vertex-cover, or by k=n-t where t is the input deadline for the broadcast
protocol to complete.
