# What is this variation of the traveling salesman problem called?

I've encountered a description of a well-known, hard to compute problem. Let us consider $n$ sites that need to be connected in the shortest possible way. If I am only allowed to connect the sites I have a traveling salesman problem. Now, I am allowed to add nodes to the map and connect the sites to those nodes (or even connect two nodes). What it the name of this problem?

-
It's hard to understand what you're asking here. You said $n$ sites and that they have to be connected in the "shortest" way; are you given pairwise distances for all sites? When you add a new site, what are the distances from it to all other sites? –  Fixee Sep 20 '11 at 6:48