NETWORK FLOWS

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# NETWORK FLOWS - PowerPoint PPT Presentation

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,

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## PowerPoint Slideshow about 'NETWORK FLOWS' - wells

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Presentation Transcript
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.

0

SB is now saturated

AC is now saturated

BC is now saturated

CT is now saturated

1

3

2

4

3

1

1

3

2

0

4

1

0

1

1

2

2

6

3

3

5

4

2

4

1

2

3

4

5

Flow out of S and into T is now 9

Flow out of S and into T is now 8

The Initial Flow is 7.

7 out of S and 7 into T

2

6

4

Flow out of S and into T is now 10

1

BD is now saturated

0

0

We now look for Flow Augmenting Paths

There are no other flows through the network

as every route is now blocked by a saturated arc.

Initial Flow: SACT Flow 3

SBDT Flow 4

Next path is SBCDT Flow 1

Next path is SABCDT Flow 1

One such path is SBCT Flow 1

The final flow along each arc should then

be represented on a fresh diagram:

The Maximum Flow is 10