lect16c - 15.082 and 6.855J The Capacity Scaling Algorithm...

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15.082 and 6.855J The Capacity Scaling Algorithm
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The Capacity Scaling Algorithm Animation
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9 The Original Costs and Node Potentials 1 2 3 5 4 4 1 2 2 5 6 7 0 0 0 0 0
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12 The Original Capacities and Supplies/Demands 1 2 3 5 4 10 20 20 25 25 20 30 23 5 -2 -7 -19
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13 Set = 16. This begins the -scaling phase. 1 2 3 5 4 10 20 20 25 25 20 30 23 5 -2 -7 -19 We send flow from nodes with excess to nodes with deficit . We ignore arcs with capacity .
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14 Select a supply node and find the shortest paths 1 2 3 5 4 4 1 2 2 5 6 7 7 0 6 8 8 shortest path distance The shortest path tree is marked in bold and blue.
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15 Update the Node Potentials and the Reduced Costs 2 3 5 4 4 1 2 2 5 6 7 0 -7 -8 -8 -6 0 0 0 0 6 3 1 To update a node potential, subtract the shortest path distance.
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16 Send Flow Along a Shortest Path in G(x, 16) 2 3 5 4 1 Send flow from node 1 to node 5. 20 20 25 25 20 30 23 5 -2 -7 -19 How much flow should be sent? 10
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17 Update the Residual Network 2 3 5 4 1 19 units of flow were sent from node 1 to node 5.
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lect16c - 15.082 and 6.855J The Capacity Scaling Algorithm...

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