Efficient Implementation

The GENERIC-MST algorithm and the theorem give some guidance for how to find MSTs simply, but they don't immediately suggest efficient algorithms. How do we quickly find cuts and the smallest edges they have?

We'll look at two classic approaches:

• Prim: Related to shortest path (in a few lectures).

  Pick a point and grow MST from it. Cut is T vs. V-E.

• Kruskal: Related to union-find (next time).

  Continually add the smallest edge that doesn't create a cycle. Cut is defined implicitly by the smallest edge and the disconnected pieces of T.