Water transport on infinite graphs
Journal article, 2019

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, consider the optimization problem of how much the water level in a fixed barrel can be raised with no pumps available, that is, by opening and closing the locks in an elaborate succession. This model is related to an opinion formation process, the so‐called Deffuant model. We consider the initial water profile to be given by i.i.d. unif(0,1) random variables, investigate the supremum of achievable water levels at a given node – or to be more precise, the support of its distribution – and ask in which settings it becomes degenerate, that is, reduces to a single value. This turns out to be the case for all infinite connected quasi‐transitive graphs, with exactly one exception: the two‐sided infinite path.

graph algorithms

Deffuant model

infinite path

Water transport



Timo Hirscher

Goethe University Frankfurt

Olle Häggström

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Random Structures and Algorithms

1042-9832 (ISSN)

Vol. 54 3 515-527


Basic sciences

Subject Categories

Probability Theory and Statistics



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