A feedback edge set of an undirected graph G is a subset F of the edges such that every cycle in G contains at least one edge in F. In other words, removing every edge in F makes the graph G acyclic. Describe and analyze a fast algorithm to compute the minimum weight feedback edge set of a given edge-weighted graph.

The running time for both parts should be in terms of V and E, the number of vertices and edges in the input graph.