Consider a graph on a point process on $R^d$ and a routing algorithm which constructs, for each pair of points, a path of the graph that connects them. We discuss routes defined by a local/greedy algorithm using the notion of point-shift.

A point-shift $f$ maps each point of a stationary point process $Phi$ to some point of $Phi$. The existence of stationary regimes of the routing algorithm is equivalent to that of a probability on counting measures being invariant by $f$.

The point-shift probabilities of $Phi$ are defined from the action of the semigroup of $f$-translations on Palm probabilities. If they are uniquely defined, this provides such a stationary regime under certain continuity conditions. Point-shift probabilities are a strict generalization of Palm probabilities.