(Solved): Consider the following network (the numbers are edge capacities). S (a) Find the maximum flow f and ...

Consider the following network (the numbers are edge capacities). S (a) Find the maximum flow f and a minimum cut. (b) Draw the residual graph G (along with its edge capacities). In this residual network, mark the vertices reachable from S and the vertices from which T is reachable. (C) An edge of a network is called a bottleneck edge if increasing its capacity results in an increase in the maximum flow. List all bottleneck edges in the above network. (d) Give a very simple example (containing at most four nodes) of a networ which has no bottleneck edges. (e) Give an efficient algorithm to identify all bottleneck edges in a network. (Hint: Start by running the usual network flow algorithm, and then examine the residual graph.) Show transcribed image text Consider the following network (the numbers are edge capacities). S (a) Find the maximum flow f and a minimum cut. (b) Draw the residual graph G (along with its edge capacities). In this residual network, mark the vertices reachable from S and the vertices from which T is reachable. (C) An edge of a network is called a bottleneck edge if increasing its capacity results in an increase in the maximum flow. List all bottleneck edges in the above network. (d) Give a very simple example (containing at most four nodes) of a networ which has no bottleneck edges. (e) Give an efficient algorithm to identify all bottleneck edges in a network. (Hint: Start by running the usual network flow algorithm, and then examine the residual graph.)