ECE165_2008FALL_EXAM1__[0]

# ECE165_2008FALL_EXAM1__[0] - Data Structures and Algorithms...

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Unformatted text preview: Data Structures and Algorithms II Fall 2008 Midterm Name: __________________________________________________________________ E-mail: _________________________________________________________________ Write all of your answers directly within this test booklet. Use the backs of pages if necessary. You may use whatever scrap paper you like, but do not hand it in. Please also write your name at the top of each page. (1) Consider the following network flow graph (i.e., flow network): The labels of edges represent their capacities. Start by pumping 4 units along the path s → a → d → t. (a) Draw the residual graph at this stage. (b) At this point, what augmenting path allows the biggest increase in flow, and how much flow can you pump through it? (c) What is that maximum flow that can be pumped through this flow network? (d) Simply prove that you can not do any better than your answer to part (c), using only the original graph . In other words, I do not want you to carry out the entire Ford- Fulkerson method and show that it stops at this point, and I do not want you to apply logic to specific nodes to prove your answer. I want you to point to something in the original graph that shows you can not do any better than your answer to (c). (2)...
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ECE165_2008FALL_EXAM1__[0] - Data Structures and Algorithms...

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