lect16a - Lecture 16 Network Flow 2 Flow Decomposition and...

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Lecture 16 Network Flow
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Flow Decomposition and Transformations
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The Flow Decomposition Algorithm
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begin Initialize while y do begin Select(s, y) Search(s, y) if a cycle C is found then do begin let = Capacity(C, y) Add Flow( , C) to cycle flows Subtract Flow( , C) from y. end if a path P is found then do begin let = Capacity(P, y) Add Flow( , P) to path flows Subtract Flow( , P) from y. end end
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The initial flow 1 2 4 5 3 6 2 3 4 7 3 4 4 8 5 9 2 -2 0 0 0 0 A supply node A demand node A balanced node The flow x
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Find a Path or Cycle 2 4 5 3 6 3 7 3 4 4 8 5 9 2 -2 0 0 Select a supply node 1 Carry out a depth first search until a cycle C or a path P is found Determine the capacity The capacity is 2.
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Update the decomposition 2 4 5 3 6 3 7 3 4 4 8 5 9 2 -2 0 0 Add the cycle flow to the decomposition 1 update the current flow cycle flows path flows 2 units around 1-2-4-5-3-1 2 5 6 7
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Find the next path or cycle 2 4 5 3 6 3 3 4 4 5 2 -2 0 0
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lect16a - Lecture 16 Network Flow 2 Flow Decomposition and...

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