Here is how I would tackle this problem.

For simplicity, let's just assume that G is connected (The algorithm to be described below can be easily extended for the case when G is not connected).

First, for any feedback-edge set F, it must be true that the graph G' = (V, E-F) doesn't have any cycle. This follows directly from the definition of feedback-edge sets.

Since we are looking for the set F that has minimum total weight, G' should be a tree and the edges in G' must have the maximum total weight possible (why ?)
→ G' must be a maximum spanning tree.

So now the original problem is reduced to finding a maximum spanning tree. You may already know that the Kruskal's algorithm can be used for finding a minimum spanning tree. With a little modification, you can use Kruskal's algorithm to find a maximum spanning tree. http://stackoverflow.com/questions/4992664/how-to-find-maximum-spanning-tree

So in conclusion, the algorithm I just described has running time of O(E log V) time (which is just the running time of Kruskal's algorithm)

Here is how I would tackle this problem.

For simplicity, let's just assume that G is connected (The algorithm to be described below can be easily extended for the case when G is not connected).

First, for any feedback-edge set F, it must be true that the graph G' = (V, E-F) doesn't have any cycle. This follows directly from the definition of feedback-edge sets.

Since we are looking for the set F that has minimum total weight, G' should be a tree and the edges in G' must have the maximum total weight possible (why ?)
→ G' must be a maximum spanning tree.

So now the original problem is reduced to finding a maximum spanning tree. You may already know that the Kruskal's algorithm can be used for finding a minimum spanning tree. With a little modification, you can use Kruskal's algorithm to find a maximum spanning tree. https://stackoverflow.com/questions/4992664/how-to-find-maximum-spanning-tree

So in conclusion, the algorithm I just described has running time of O(E log V) time (which is just the running time of Kruskal's algorithm)

Here is how I would tackle this problem.

For simplicity, let's just assume that G is connected (The algorithm to be described below can be easily extended for the case when G is not connected).

First, for any feedback-edge set F, it must be true that the graph G' = (V, E-F) doesn't have any cycle. This follows directly from the definition of feedback-edge sets.

Since we are looking for the set F that has minimum total weight, G' should be a tree and the edges in G' must have the maximum total weight possible (why ?)
→ G' must be a maximum spanning tree.

So now the original problem is reduced to finding a maximum spanning tree. You may already know that the Kruskal's algorithm can be used for finding a minimum spanning tree. With a little modification, you can use Kruskal's algorithm to find a maximum spanning tree. http://stackoverflow.com/questions/4992664/how-to-find-maximum-spanning-tree

So in conclusion, the algorithm I just described has running time of O(E log V) time (which is just the running time of Kruskal's algorithm)

Here is how I would tackle this problem.

For simplicity, let's just assume that G is connected (The algorithm to be described below can be easily extended for the case when G is not connected).

First, for any feedback-edge set F, it must be true that the graph G' = (V, E-F) doesn't have any cycle. This follows directly from the definition of feedback-edge sets.

Since we are looking for the set F that has minimum total weight, G' should be a tree and the edges in G' must have the maximum total weight possible (why ?)
→ G' must be a maximum spanning tree.

So now the original problem is reduced to finding a maximum spanning tree. You may already know that the Kruskal's algorithm can be used for finding a minimum spanning tree. With a little modification, you can use Kruskal's algorithm to find a maximum spanning tree. http://stackoverflow.com/questions/4992664/how-to-find-maximum-spanning-tree

So in conclusion, the algorithm I just described has running time of O(E log V) time (which is just the running time of Kruskal's algorithm)