Problem 5 Updating Minimum Spanning Trees (12 points) Problem 6b in Chapter 20 of Jeff's notes: Let G be an edge-weighted, undirected, and connected graph. You are already given the MST, T, of G. Give an algorithm to update the MST when the weight of a single edge e E G is increased, producing a new graph G. Specifically, your are given the edge e and its new weight, and your algorithm should modify T so that it is an MST in G', and do so in O(V El) time Useful Fact from class: The min weight edge across any vertex bi-partition must be in the MST. Moreover, (the removal of) any edge e in the MST defines a vertex bi-partition, call it B(e), and as e is the only edge from the MST which goes across B(e), e must be the minimum weight edge across B(e) in G