Lecture 17 — Minimum Spanning Tree Parallel and Sequential Data

You have seen Minimum Weight Spanning Trees in 15-122 and possibly in 15-251. These classes went over Kruskal’s and Prim’s algorithms. At a glance, Kruskal’s and Prim’s seem to be two drastically different approaches to solving MST: whereas Kruskal’s sorts edges by weight and considers the edges in order, using a union-find data structure to detect when two vertices are in the same component and join them if not, Prim’s maintains a tree grown so far and a priority queue of edges incident on the current tree, pulling the minimum edge from it to add to the tree. The two algorithms, in fact, rely on the same underlying principle about “cuts” in a graph, which we’ll discuss next.