1. Warm Up – Friday

2. We are going to build a network to bring telephone, cable, and internet to the people in the Amazon.
Naturally we want to do this in the cheapest way possible.

5. The use of a Tree
This is why we use trees! If towns X and Y are already connected, why bother wasting more money and building more lines to connect them?

6. Minimum Spanning Trees

7. Finding the Optimal Spanning Tree
This network has A LOT of spanning trees.
Give me some ideas as to how we could possibly find the minimum spanning tree on this graph without Brute Forcing it?

12. 7 vertices… 6 steps
We are done after the sixth edge. Always one less than the number of vertices!

13. Kruskal’s Algorithm vs. Nearest Neighbor
Nearest Neighbor we are following a path.
Kruskal’s algorithm we are picking our cheapest options and then making sure we do not end up with a cycle. Once all of our vertices are connected and we have a network we are finished!