Algorithms for updating minimal spanning trees canton ohio dating sites
On the other hand, if you draw a path tracing around the minimum spanning tree, you trace each edge twice and visit all points, so the TSP weight is less than twice the MST weight.
Therefore this tour is within a factor of two of optimal.
It's also not really an algorithm, because you'd still need to know how to list all the trees.
A better idea is to find some key property of the MST that lets us be sure that some edge is part of it, and use this property to build up the MST one edge at a time.
It has smaller weight than t since e has smaller weight than f.
I'll go through three simple classical algorithms (spending not so much time on each one).
There is a more complicated way (Christofides' heuristic) of using minimum spanning trees to find a tour within a factor of 1.5 of optimal; I won't describe this here but it might be covered in ICS 163 (graph algorithms) next year.
The stupid method is to list all spanning trees, and find minimum of list. But there are far too many trees for this to be efficient.