cyclecancelingalgorithm

cyclecancelingalgorithm - 15.082 and 6.855J Cycle Canceling...

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15.082 and 6.855J Cycle Canceling Algorithm
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2 A minimum cost flow problem 1 2 4 3 5 10, $4 20, $1 20, $2 25, $2 25, $5 20, $6 30, $7 25 0 0 0 -
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3 The Original Capacities and Feasible Flow 1 2 4 3 5 10, 10 20, 20 20, 10 25, 5 25, 15 20, 0 30, 25 25 0 0 0 The feasible flow can be found by solving a max flow. -
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4 Capacities on the Residual Network 1 2 4 3 5 10 20 20 5 25 10 10 15 5 20 10
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5 Costs on the Residual Network 1 2 4 3 5 2 2 6 7 -7 -5 -2 -2 -1 -4 5 Find a negative cost cycle, if there is one.
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6 Send flow around the cycle Send flow around the negative cost cycle 1 2 4 3 5 20 25 15 The capacity of this cycle is 15. Form the next residual network.
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7 Capacities on the residual network 1 2 4 3 5 10 20 5 20 10 10 25 5 20 10 15
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8 Costs on the residual network 1 2 4 3 5 2 2 6 7 -7 -2 -2 -1 -4 -6 Find a negative cost cycle, if there is one. 5
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Send flow around the cycle 1 2 4 3 5 Send flow around the negative cost cycle The capacity of this cycle is 10. Form the next residual network.
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cyclecancelingalgorithm - 15.082 and 6.855J Cycle Canceling...

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