minCostFlowsex

# minCostFlowsex - Engineering Exercises 1 The diagram shown...

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Engineering xercises 2. The figure below represents an instance of the Exercises 1. The diagram shown below represents the residual raph for some flow The numbers next to the edges minimum cost, maximum flow problem. What is the cost of the flow that is shown? 2,0,2 5,3,2 6,0,4 3,0,4 4,0,4 01 ,0,2 2,0,2 f c a graph for some flow. The numbers next to the edges are the edge costs. Is the flow corresponding to this residual graph a min-cost flow? Why or why not? 3,0,2 2,2,1 3,3,1 7,2,4 7,3,4 5,0,2 3,3,3 3,0,1 1,0,2 2,0,1 1,0,3 4,0,3 s t g h b d e 4,2,3 cap, flow, cost c a 3 The cost of the original flow is 46. Show the residual graph corresponding to this flow (including the edge costs) and show the minimum cost augmenting path in the residual graph. 6 b t s 4 4 -3 3 -5 -1 d 3 -4 It is not a min cost flow because the cycle acdba has a cost of -2. Explain how you can reduce the cost by 6 if all edges gg p g p 2,2 2,2 6,4 3,4 4,4 3, 3 3,1 1,2 2,2 4,3 s f c a 2,3 3, 2 in the residual graph have capacity 3? Since the edges in the residual graph all have capacity 3, we can push 3 units of flow around the cycle acdba. This

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minCostFlowsex - Engineering Exercises 1 The diagram shown...

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