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Hw4s - ENGRI 1101 Engineering Applications of OR Fall 2008...

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ENGRI 1101 Engineering Applications of OR Fall 2008 Homework 4 Homework 4 Solutions 1. (a) First of all one must realize which node is the source and which is the sink. A source is a node which has net outward flow and a sink is a node which has net inward flow (or equivalently, negative net outward flow). Summing the flows out of each node in the graph yields 11 for node 1, 0 for nodes 2 through 5, and -11 for node 6. Therefore node 1 must be the souce and node 6 must be the sink. In order to finish the execution of the algorithm we must construct the residual graph of the figure above, which is shown in the following figure: There are several several paths from source to sink. We arbitrarily choose path { (1,2),(2,3),(3,6) } by as much as possible: δ = 1 (arc (3,6) is the bottleneck). The graph after we have done the first iteration is shown below: 1
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We then construct the next residual graph: Again there are several different paths to choose. We choose the path { (1,2),(2,3),(3,4),(4,5),(5,6) } , which has δ = 1.
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