BACK FLOWS IN NETWORKS

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
The stage below was reached when trying to obtain
the maximal flow by using flow-augmenting paths
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.
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