8

I need to find the easiest cost path between two vertices of a graph. Easiest here means the path with the smallest maximum-weigth edge.

enter image description here

In the above graph, the easiest path from 1 to 2 is: 

1 > 3 > 4 > 2

Because the maximum edge weight is only 2. On the other hand, the shortest path 1 -> 2 has maximum weight 4.

So it's an MST problem. I am thinking I will use Kruskal's algorithm to build the tree, but I'm not sure how exactly. I will know the edges but how do I "reconstruct" the path? For example, given vertices 3 and 2, how do I know to go left (top) of right in the tree? Or do I try both ways?

Raphael
  • 73,212
  • 30
  • 182
  • 400
Jiew Meng
  • 231
  • 2
  • 3
  • 6

1 Answers1

5

You're right; it's essentially a MST problem. First build the minimum spanning tree, then use breadth-first or depth-first search to find the unique path in the tree between the two vertices.

Joe
  • 4,105
  • 1
  • 21
  • 38