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BACK FLOWS IN NETWORKS

BACK FLOWS IN NETWORKS. Sometimes there appears to be no more Flow Augmenting Paths in a network flow diagram due to flows along certain paths being in the wrong direction.

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BACK FLOWS IN NETWORKS

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  1. BACK FLOWS IN NETWORKS Sometimes there appears to be no more Flow Augmenting Paths in a network flow diagram due to flows along certain paths being in the wrong direction However, we can decrease the capacity along an arc by an amount of units up to the number as indicated by the back capacity

  2. We can decrease the flow on CB by up to 2 units as indicated by the back capacity. This is known as a back flow. The stage below was reached when trying to obtain the maximal flow by using flow-augmenting paths: DECREASE by 1 along BC 0 3 2 4 Increase by 1 along SB Increase by 1 along CT 1 3 At first sight there appears to be no more flow-augmenting paths as you would have to go along SB and then the flow along BC is in the wrong direction. However, as the excess capacity along SB is only 1, we use the path SBCT flow 1 SB is now saturated and there can be no more Flow Augmenting Paths

  3. The final pattern, which is maximal, is: Total Flow = 13

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