If this question belongs to another stackexchange site, please, redirect me.
I would like to know if the problem I describe here has known solution approaches.
Let $G$ be a connected unweighted graph with a diameter $d$. We can add 1 or 2 new nodes to the graph and then connect them with some (read on) vertices. Our goal is to make graph diameter as shorter as possible. The task is trivial if we there are no limitations on which nodes are available for connection - we could just add edges from new nodes to each inital node and diameter becomes 2 (or remains 1 if $G$ is fully connected).
The catch is that each graph node is placed at a euclidean plane (or 3D euclidean space - in a more complex version of the problem) and new nodes can only connect to those vertices, whose positions are not further from its own position than $r$. We need to find optimal coordinates for new nodes.
Are there known approaches for this problem or there aren't?