# lect14 - Lecture 14 Max Flows 3 Preflow-Push Algorithms...

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Lecture 14 Max Flows 3 Preflow-Push Algorithms

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Review

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The Ford Fulkerson Maximum Flow Algorithm Begin x := 0; create the residual network G(x); while there is some directed path from s to t in G(x) do begin let P be a path from s to t in G(x); := δ (P); send units of flow along P; update the r's; End end {the flow x is now maximum}.

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e(3)=1

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Exact distance: d(i) equals the length of the shortest path from node i to node t in G(x)
The Goldberg-Tarjan Preflow Push Algorithm for the Maximum Flow Problem

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Preflow Push 4 1 4 1 2 3 1 s 2 5 3 t This is the original network, plus reversals of the arcs.
Preflow Push 4 1 1 4 1 2 3 1 s 2 5 3 t This is the original network, and the original residual network.

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Initialize Distances 4 1 1 4 1 2 3 1 The node label henceforth will be the distance label. 0 5 4 3 2 1 t 4 5 3 s 2 d(j) is at most the distance of j to t in G(x) 0 2 2 1 1 1
Saturate Arcs out of node s 4 1 1 4 1 2 3 1 Saturate arcs out of node s. 0

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lect14 - Lecture 14 Max Flows 3 Preflow-Push Algorithms...

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