rec6 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 15.053...

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M ASSACHUSETTS I NSTITUTE OF T ECHNOLOGY 15.053 – Optimization Methods in Management Science (Spring 2007) Recitation 6, April 5 th and April 6 th , 2007 Problem 1 ( Eulerian Graphs ) Which of the graphs below have Eulerian cycles/paths? Problem 2: Ford-Fulkerson Algorithm Consider the following Maximum Flow network.
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s 1 3 4 2 t 7 5 3 4 6 3 2 8 And consider the following residual network resulting from two iterations of the Ford- Fulkerson algorithm. s 1 3 4 2 t 2 3 4 4 1 5 5 2 2 2 8 Part A: Perform the final two iterations of the Ford-Fulkerson algorithm to determine the maximum flow. Part B: Determine the corresponding minimum cut based on the final residual network. Problem 3 ( Max Flow ) For parts A through C, please consider the following Maximum Flow Problem, which represents a matching problem. All arcs have capacity 1.
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s 1 3 4 2 t A C D B 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 To achieve a maximum flow of 3 using the Ford-Fulkerson algorithm, we choose the following three augmenting paths, s 1 A t, s 2 C t, and s 3 B t. Part A Draw the final residual network based on this choice of augmenting paths.
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rec6 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 15.053...

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