Analysis of Solution Quality

This is the interesting part. How does the tour we find relate to the optimal tour?

Recall is the length of the best tour, M is the size of the MST we found, and C is the length of the tour we return. Facts:

• . Tour spans nodes.
• . Touring the tree is 2 M, shortcuts only make it smaller.
• Therefore, ! (Ratio of 2.)

So even though we don't know , we know it can't be too far away!