NETWORK FLOWS

1
NETWORK FLOWS
THE LABELLING PROCEDURE
Use the forward facing arrow to indicate the
spare capacity in that arc - the amount by which
the flow can be increased - the excess capacity.
Use the backward facing arrow to indicate the
flow along the arc, i.e. the amount by which the
flow could be decreased - the back capacity.
2
0
AC is now saturated
CT is now saturated
SB is now saturated
BC is now saturated
1
3
2
4
3
1
1
3
2
0
4
1
0
1
1
2
2
6
3
3
4
5
2
4
1
2
3
4
5
2
The Initial Flow is 7. 7 out of S and 7 into T
Flow out of S and into T is now 8
Flow out of S and into T is now 9
6
4
1
Flow out of S and into T is now 10
BD is now saturated
0
0
We now look for Flow Augmenting Paths
Initial Flow SACT Flow 3 SBDT Flow 4
There are no other flows through the network as
every route is now blocked by a saturated arc.
Next path is SBCDT Flow 1
Next path is SABCDT Flow 1
One such path is SBCT Flow 1
3
The final flow along each arc should then be
represented on a fresh diagram
The Maximum Flow is 10