If you are asked to design an algorithm, please provide: (a) the pseudocode or a precise English description of the algorithm, (b) an explanation of the intuition for the algorithm, (c) a proof of correctness, (d) the running time of your algorithm and (e) justi cation for your running time analysis.

(10 points) Connectivity in Weighted Graphs. Let G (V, E, W) be a connected weighted graph where each edge e has an associated non-negative weight w(e). We call a subset of edges FCE unseparating if the graph G' (V, F) is connected. This means that if you remove all of the edges F from the original edge set, this new graph is still connected. For a set of edges E c E the weight of the set is just the sum of the weights of the individual edges that is w(E eEE (e) Give a polynomial time algorithm to find the unseparating set with maximum weight (10 points) Connectivity in Weighted Graphs. Let G (V, E, W) be a connected weighted graph where each edge e has an associated non-negative weight w(e). We call a subset of edges FCE unseparating if the graph G' (V, F) is connected. This means that if you remove all of the edges F from the original edge set, this new graph is still connected. For a set of edges E c E the weight of the set is just the sum of the weights of the individual edges that is w(E eEE (e) Give a polynomial time algorithm to find the unseparating set with maximum weight