Successive_Shortest_Path - 15.082J and 6.855J Successive...

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1 15.082J and 6.855J Successive Shortest Path Algorithm
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2 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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3 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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4 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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5 Update the Node Potentials and the Reduced Costs 1 2 3 5 4 4 1 2 2 5 6 7 0 -7 -8 -8 -6 0 0 0 0 6 3
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6 Send Flow From a Supply Node to a Demand Node Along Shortest Paths (along arcs with reduced costs of 0) 1 2 3 5 4 10 20 20 25 25 20 30 23 5 -2 -7 -19 send 7 units from node 1 to node 3 Arc numbers are residual capacities. Red arcs have a reduced cost of 0
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7 Update the Residual Network 1 2 3 5 4 10 20 20 25 25 13 30 23 5 -2 -7 -19 Arc (3,1) has a reduced cost of 0 7 16 0 If an arc is added to G(x), then it has a reduced cost of 0, and it is red. Arcs in the residual network will always have a non-negative reduced cost
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8 A comment At this point, one would choose a source node, and
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