We consider Mobile Ad-hoc NETworks (MANETs) formed by n nodes that move independently at random over a finite square region of the plane. Nodes exchange data if they are at distance at most r within each other, where r > 0 is the node transmission radius. The flooding time is the number of time steps required to broadcast a message from a source node to every node of the network. Flooding time is an important measure of the speed of information spreading in dynamic networks. We derive a nearly-tight upper bound on the flooding time which is a decreasing function of the maximal velocity of the nodes. It turns out that, when the node velocity is "sufficiently" high, even if the node transmission radius r is far below the connectivity threshold, the flooding time does not asymptotically depend on r. So, flooding can be very fast even though every snapshot (i.e. the static random geometric graph at any fixed time) of the MANET is fully disconnected. Our result is the first analytical evidence of the fact that high, random node mobility strongly speed-up information spreading and, at the same time, let nodes save energy.
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