Given a weighted directed graph with one source and one sink where all weights are nonnegative integers, the maximum flow problem asks to assign a flow on the edges of the graphs, which is as large as possible, under the constraints of the capacity and the conservation conditions. The algorithm applied for this problem selects in each stage a path from source to sink, augmenting the flow with the value of the bottleneck of the path. The number of iterations is bounded by the sum of all capacities on the edges. As the running time depends on the size of the numbers in the input, the Ford-Fulkerson algorithm does not run in strongly polynomial time.
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an iterative algorithm for maximum flow: the Ford-Fulkerson algorithm
- Рет қаралды 60
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