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# hbs8 - CS 473 Algorithms Fall 2010 HBS 8 Problem 1[Go With...

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CS 473: Algorithms, Fall 2010 HBS 8 Problem 1 . [Go With the Flow] The figure below shows a flow network along with a flow. In the figure, the notation a/b for an edge means that the flow on the edge is a and the capacity of the edge is b . s t a b d e c 6/10 2/2 3/4 2/4 4/4 9/13 2/2 0/3 5/7 7/7 5/5 5/8 (a) What is the value of the given flow? Is it maximal? Show the residual graph for the above graph and flow in the figure below. s t a b d e c (b) Show an s - t path in the residual graph and state its bottleneck capacity. You only need to draw the path from the graph you showed in (a). s t a b d e c 1

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(c) Show the new flow on the original graph after augmenting on the path you found in (b). Use the notation a/b to indicate the flow on an edge and its capacity. s t a b d e c 6/10 2/2 3/4 2/4 4/4 9/13 2/2 0/3 5/7 7/7 5/5 5/8 s t a b d e c (d) What is the capacity of a minimum-cut in the given graph? Find a cut with that capacity. Problem 2 . [Residual Graph Properties] Prove the following property about residual graphs:
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