  If the nodes of a graph are considered to be identical barrels - featuring
different water levels - and the edges to be (locked) water-filled pipes in
between the barrels, one might consider the optimization problem of how much
the water level in a fixed barrel can be raised with no pumps available, i.e.
by opening and closing the locks in an elaborate succession. This problem
originated from the analysis of an opinion formation process and proved to be
not only sufficiently intricate in order to be of independent interest, but
also algorithmically complex. We deal with both finite and infinite graphs as
well as deterministic and random initial water levels and find that the
infinite line graph, due to its leanness, behaves much more like a finite graph
in this respect.

Probability