To explain the running of FORD-FULKERSON algorithm on the flow network in figure 26.8( c ).

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Chapter 26.3, Problem 1E

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To explain the running of FORD-FULKERSON algorithm on the flow network in figure 26.8( c ).

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Show the network with the flow that results from augmenting the flow based on the path (?, ?2, ?3, ?1, ?4, ?) of the residual graph you have given in answer to part. Show the residual graph for the network flow given in answer to part. Show the final flow that the Ford-Fulkerson Algorithm finds for this network, given that it proceeds to completion from the flow rates you have given in your answer to part (i), and augments flow along the edges (?,?1,?3,?) and (?,?2,?5,?).

True or false. If true, give a brief explanation justifying the statement. If false, provide a counterexample. - If you are given a flow network (labeled F), let (L,R) be a minimum capacity cut in the flow graph. If the capacity of all of the graph edges is increased by 1, then (L,R) is still a minimum capacity cut in our new modified graph.

Question 1Draw the residual network obtained from this flow. Question2Perform two steps of the Ford Fulkerson algorithm on this network, each using the residual graph of the cumulative flow, and the augmenting paths and flow amounts specified below. After each augment, draw two graphs, preferably side by side; these are graphs of: a) The flow values on the edges b) Residual network The augmenting paths and flow amounts are: i) s→b→d→c→t with flow amount 7 Units ii) s→b→c→t with 4 units. Note for continuity your second graph should be coming from the one in (i) NOT from the initial graph. Question 3Exhibit a maximum flow with flow values on the edges, state its value, and exhibit a cut (specified as a set of vertices) with the same value.