The single shot query for the shortest path between two points in a plane environment with polygonal obstacles of complexity $O(n)$ can be solved in time $O(n \log n)$ using the continuous Dijkstra method.
What happens if I am given a set $P$ of $k$ points in the plane, and I want to preprocess them, s.t. the shortest path between any two points in $P$ can be computed efficiently. Are there any algorithms known for this problem?
Thank you
Stefan