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NETWORK FLOWS

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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NETWORK FLOWS

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  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 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

  3. The final flow along each arc should then be represented on a fresh diagram: The Maximum Flow is 10

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