Use Dijkstra's to find a Minimum Spanning Tree?

Question

Dijkstra's is typically used to find the shortest distance between two nodes in a graph. Can it be used to find a minimum spanning tree? If so, how?

Edit: This isn't homework, but I am trying to understand a question on an old practice exam.

Answer 1

I'd keep to a greedy algorithm such as Prim's or Kruskal's. I fear Djikstra's won't do, simply because it minimizes the cost between pairs of nodes, not for the whole tree.

Answer 2

Strictly, the answer is no. Dijkstra's algorithm finds the shortest path between 2 vertices on a graph. However, a very small change to the algorithm produces another algorithm which does efficiently produce an MST.

The Algorithm Design Manual is the best book I've found to answer questions like this one.

Answer 3

Prim's algorithm uses the same underlying principle as Dijkstra's algorithm.