  A rerouting sequence is a sequence of shortest st-paths such that consecutive
paths differ in one vertex. We study the the Shortest Path Rerouting Problem,
which asks, given two shortest st-paths P and Q in a graph G, whether a
rerouting sequence exists from P to Q. This problem is PSPACE-hard in general,
but we show that it can be solved in polynomial time if G is planar. To this
end, we introduce a dynamic programming method for reconfiguration problems.
