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Question 3 Consider the directed network (D, c) given by the following drawing, where each arc e = A(D) is labelled by its capacity c(e) and two vertices s and t have been identified. 3 7 3 4 5 t 3 3 8 2 (a) Give an s-t-flow of (D, c) that is not a maximum s-t-flow. Justify your answer. (b) Give an s-t-cut of (D, c) that is not a minimum s-t-cut. Justify your answer. (c) Use the Ford-Fulkerson algorithm to find a maximum s-t-flow of (D,c). Draw the residual network after each iteration of the algorithm and give the size of the maximum flow. (d) Show that the flow you have found is indeed a maximum s-t-flow.

Question 3 Consider the directed network (D, c) given by the following drawing, where each arc e = A(D) is labelled by its capacity c(e) and two vertices s and t have been identified. 3 7 3 4 5 t 3 3 8 2 (a) Give an s-t-flow of (D, c) that is not a maximum s-t-flow. Justify your answer. (b) Give an s-t-cut of (D, c) that is not a minimum s-t-cut. Justify your answer. (c) Use the Ford-Fulkerson algorithm to find a maximum s-t-flow of (D,c). Draw the residual network after each iteration of the algorithm and give the size of the maximum flow. (d) Show that the flow you have found is indeed a maximum s-t-flow.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 7RE
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Question 3 Consider the directed network (D, c) given by the following drawing, where each arc e = A(D) is labelled by its capacity c(e) and two vertices s and t have been identified. 3 7 3 4 5 t 3 3 8 2 (a) Give an s-t-flow of (D, c) that is not a maximum s-t-flow. Justify your answer. (b) Give an s-t-cut of (D, c) that is not a minimum s-t-cut. Justify your answer. (c) Use the Ford-Fulkerson algorithm to find a maximum s-t-flow of (D,c). Draw the residual network after each iteration of the algorithm and give the size of the maximum flow. (d) Show that the flow you have found is indeed a maximum s-t-flow.
Transcribed Image Text:Question 3 Consider the directed network (D, c) given by the following drawing, where each arc e = A(D) is labelled by its capacity c(e) and two vertices s and t have been identified. 3 7 3 4 5 t 3 3 8 2 (a) Give an s-t-flow of (D, c) that is not a maximum s-t-flow. Justify your answer. (b) Give an s-t-cut of (D, c) that is not a minimum s-t-cut. Justify your answer. (c) Use the Ford-Fulkerson algorithm to find a maximum s-t-flow of (D,c). Draw the residual network after each iteration of the algorithm and give the size of the maximum flow. (d) Show that the flow you have found is indeed a maximum s-t-flow.
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