I was wondering if this is a solution to the TSP problem. For a set of $n$ points on the plane, the number of 'roads' in the plane such that there is a road between every point is $n\Bbb C 2$ = $n^2-n \over 2$
The total number of possible paths which connect all the points together is $n!$.
The Algorithm is as such:
*Assign weights(the length of the roads) to each road.
*Calculate the minimum spanning Tree for the graph (Algorithms exist to calculate in linear time.)
*Between the two end(free) vertices of the MST take the road.
*The cycle formed thus is the solution.