Given a set of nodes $N$ on an undirected, weighted graph $G$ and a query node $n$, what is the fastest algorithm for finding the node in $N$ that is closest to $n$?
Furthermore, say we are doing many of these queries, so have many $n$'s, is there some data structure that could speed up this computation?
Thank you for any feedback or guidance.
Addendum: One other detail I did not mention, every time a query is made, $n$ is added to $N$, so for the next query, $N$ is larger by one node. Is there some version of Dijkstra's or bellman ford that can handle this dynamic situation?