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ORIE PS _4

ORIE PS _4 - 1 A Given graph Note for the residual graphs...

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1. A. Given graph: Note: for the residual graphs the backward arcs are blue and the forward arcs are red. Residual graph from given graph: a path form residual graph above: increase each arcs flow by 1. The resulting graph:

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The residual graph for the above graph is: Path from the residual: The arc form node 4 to node 5 is blue therefore is a backwards arc. This means you will decrease by one on this arc, and increase one on the other arcs. The new graph is:
The residual associated with the above graph is: There is not another feasible path that goes from the source to the sink. Therefore the algorithm is over. The final graph is:

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B. To determine the cut: In the residual graph, the nodes you can reach from a path starting at the source are on the source side of the cut and the nodes that are not reached from the a path starting at the source are on the sink side. Starting at 1: Reach 2 by (1,2) Reach 3 by (1,2) then (2,3) Reach 4 by (1,4) Can’t reach 5 in the residual graph Can’t reach 6 in the residual graph Therefore, the nodes on the source side (S) are {1,2,3,4} and the nodes on the sink side (T) are {5,6}.
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