25.4 Chapter Summary
In this chapter, we learned about Minimum Spanning Trees and the Cut Property:
MST: the lightest set of edges in a graph possible such that all the vertices are connected and acyclic.
The Cut Property: given any cut, the minimum weight crossing edge is in the MST.
Cut: an assignment of a graph’s nodes to two non-empty sets
Crossing Edge: an edge which connects a node from one set to a node from the other set.
We also learned about how to find MSTs of a graph with two algorithms:
Prim's Algorithm: Construct MST through a mechanism similar to Dijkstra's Algorithm, with the only difference of inserting vertices into the fringe not based on distance to goal vertex but distance to the MST under construction.
Kruskal's Algorithm: Construct MST by first sorting edges from lightest to heaviest, then add edges sequentially if no cycles are formed until there are V - 1 edges.
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