Travelling salesman problem vs. Minimum cost spanning tree vs. Shortest path

Question

i want to understand these better....
please explain someone.
Travelling salesman problem vs. Minimum cost spanning tree vs. Shortest path

Also I was just wondering if there was any relation of TSP to GOOGLE's maps finding shortest distance?
because travelling salesman problem in O(n!) and there is no better solution other than dynamic programming. So do they use dynamic programming only?

Answer 1

not important for gate! :P