Question: 2. The following network N has source x and sink y with arc capacities as shown, and an initial flow in parentheses. (a) Verify that

2. The following network N has source x and sink y

2. The following network N has source x and sink y with arc capacities as shown, and an initial flow in parentheses. (a) Verify that the initial flow is a flow (b) State the value of the initial flow (c) Use the labelling algorithm presented in lectures to find a maximum flow in N 5 marks [5 marks] Show every stage of the algorithm. [10 marks] (d) State the value of a maximum flow 5 marks (e) Show a maximum flow and a minimum cut. Are the arcs in the minimum cut saturated? [5 marks] 9(0) 2(2) 4(0) 5(3) 5(0) 10(3) 2. The following network N has source x and sink y with arc capacities as shown, and an initial flow in parentheses. (a) Verify that the initial flow is a flow (b) State the value of the initial flow (c) Use the labelling algorithm presented in lectures to find a maximum flow in N 5 marks [5 marks] Show every stage of the algorithm. [10 marks] (d) State the value of a maximum flow 5 marks (e) Show a maximum flow and a minimum cut. Are the arcs in the minimum cut saturated? [5 marks] 9(0) 2(2) 4(0) 5(3) 5(0) 10(3)

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