Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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
up vote 4 down vote accepted

Assuming the sites are given as points in the plane, this is the Steiner tree problem.

By the way, if you are trying to do the same thing without introducing additional nodes, as in the initial part of your question, then this is the problem of computing a minimum spanning tree, not the travelling salesman problem, and can be solved in polynomial time.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.