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flowdecomposition

# flowdecomposition - 15.082 and 6.855J Flow Decomposition...

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15.082 and 6.855J Flow Decomposition

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2 begin Initialize while y ≠ ∅ do begin Select(s, y) Search(s, y) if a cycle C is found begin let = Capacity(C, y) Add Flow( , C) to cycle flows Subtract Flow( , C) from y. end if a path P is found begin let = Capacity(P, y) Add Flow( , P) to path flows Subtract Flow( , P) from y. end end then do then do
3 The initial flow 1 2 4 5 3 6 2 3 4 7 3 4 4 8 5 9 2 0 0 0 0 A supply node A demand node A balanced node The flow x -2

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4 Find a Path or Cycle 1 2 4 5 3 6 2 3 4 7 3 4 4 8 5 9 2 -2 0 0 1 Carry out a depth first search until a cycle C or a path P is found Determine the capacity The capacity is 2.
5 Update the decomposition 1 2 4 5 3 6 3 3 4 4 5 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 0

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6 Find the next path or cycle 1 2 4 5 3 6 3 3 4 4 5 2 -2 0 0 Start at a supply node and find the next cycle or path 1 cycle flows path flows 2 units around 1-2-4-5-3-1 2 5 6 7
7

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