Warm Up – 4.4 - Friday.

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Presentation transcript:

Warm Up – 4.4 - Friday

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.

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?

Minimum Spanning Trees

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?

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

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!