Understanding the Ford-Fulkerson method


The Ford-Fulkerson method uses the max-flow min-cut theorem to solve the maximum flow problem for flow networks. It is called a method because some parts of its protocol do not specify implementation. A method is a more general algorithm where individual steps can be implemented differently. For the Ford-Fulkerson method to work, a graph should have at least one source and sink node, where the maximum flow must be calculated from the source to the sink. Consider the flow network below, where values in edges denote their maximum capacity.

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A flow network with source and sink where edge weight denotes the capacity of an edge.

Algorithm

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