We study the information spreading yielded by the (Parsimonious) 1-Flooding
Protocol} in geometric Mobile Ad-Hoc Networks. We consider n agents on a convex
plane region of diameter D performing independent random walks with move radius
\rho. At any time step, every active agent $v$ informs every non-informed agent
which is within distance R from v (R>0 is the transmission radius). An agent
is only active at the time step immediately after the one in which has been
informed and, after that, she is removed. At the initial time step, a source
agent is informed and we look at the \emph{completion time} of the protocol,
i.e., the first time step (if any) in which all agents are informed. This random
process is equivalent to the well-known Susceptible-Infective-Removed (SIR)
infection process in Mathematical Epidemiology. No analytical results are
available for this random process over any explicit mobility model. The presence
of removed agents makes this process much more complex than the (standard)
flooding. We prove optimal bounds on the completion time depending on the
parameters n, D, R, and rho. The obtained bounds hold with high probability. We
remark that our method of analysis provides a clear picture of the dynamic shape
of the information spreading (or infection wave) over the time.

end of abstract.

Guest: Andrea Clementi