calculating excess flow and overflowing in max flow algorithm -

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i reading push flow algorithms @ following link.

http://community.topcoder.com/tc?module=static&d1=tutorials&d2=maxflowpushrelabel

it mentioned excess flow - define excess flow e e(u) = f(v,u), net flow u. vertex u ∊ v-{s,t} overflowing / active if e(u) > 0.

i looking example simple flow network how calculate e(u) ?

thanks time , help.

in diagram below there source node (s), sink node (t), , internal node (a).

the numbers give flow (say in litres per second). there 3 litres per second entering a, 1 litre per second leaving a, excess flow 2.

note

  1. in push-relabel algorithm, excess flow internal nodes cannot negative. in other words, not allowed have more flow leaving enters.

  2. the source node is allowed generate flow (it not count internal node note 1 not apply)

  3. during algorithm, excess flow reduced until @ end vertices have 0 excess flow

  4. you compute excess flow adding incoming flow, , subtracting outgoing flow.

  5. however, in practice, algorithm maintains array of excess flows , updates value algorithm progresses.

simple flow


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