Shortest_Augmenting_Path - The Shortest Augmenting Path...

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The Shortest Augmenting Path Algorithm for the Maximum Flow Problem
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2 Shortest Augmenting Path 4 1 4 1 2 3 1 s 2 5 3 t This is the original network, plus reversals of the arcs.
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3 Shortest Augmenting Path 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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4 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
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5 Representation of admissible arcs 4 1 1 4 1 2 3 1 An arc (i,j) is admissible if d(i) = d(j) + 1. 0 5 4 3 2 1 t 4 5 3 s 2 An s-t path of admissible arcs is a shortest path 0 2 2 1 1 Admissible arcs will be represented with thick lines
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6 4 2 Look for a shortest s-t path 4 1 1 1 3 1 Start with s and do a depth first search using admissible arcs. 0 5 4 3 2 1 t 4 5 3 s 2 2 1 1 Next. Send flow, and update the residual capacities. 2 1 0
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7 4 2 2 Update residual capacities 4 1 1 1 3 3 1 Here are the updated residual capacities. 0
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This note was uploaded on 04/15/2010 for the course INDUSTRIAL ie513 taught by Professor Zeynephuygur during the Spring '10 term at Bilkent University.

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Shortest_Augmenting_Path - The Shortest Augmenting Path...

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