  Delay-tolerant networks (DTNs) are characterized by a possible absence of
end-to-end communication routes at any instant. Still, connectivity can
generally be established over time and space. The optimality of a temporal path
(journey) in this context can be defined in several terms, including
topological (e.g. {\em shortest} in hops) and temporal (e.g. {\em fastest,
foremost}). The combinatorial problem of computing shortest, foremost, and
fastest journeys {\em given full knowledge} of the network schedule was
addressed a decade ago (Bui-Xuan {\it et al.}, 2003). A recent line of research
has focused on the distributed version of this problem, where foremost,
shortest or fastest {\em broadcast} are performed without knowing the schedule
beforehand. In this paper we show how to build {\em fastest} broadcast trees
(i.e., trees that minimize the global duration of the broadcast, however late
the departure is) in Time-Varying Graphs where intermittent edges are available
periodically (it is known that the problem is infeasible in the general case
even if various parameters of the graph are know). We address the general case
where contacts between nodes can have arbitrary durations and thus fastest
routes may consist of a mixture of {\em continuous} and {\em discontinuous}
segments (a more complex scenario than when contacts are {\em punctual} and
thus routes are only discontinuous). Using the abstraction of \tclocks to
compute the temporal distances, we solve the fastest broadcast problem by first
learning, at the emitter, what is its time of {\em minimum temporal
eccentricity} (i.e. the fastest time to reach all the other nodes), and second
by building a {\em foremost} broadcast tree relative to this particular
emission date.
