Network Flows Max Flow Min Cut Theorem Ford Fulkerson Algorithm

Network Flow problems deal with the optimal way to send flow through a network from a source to a sink while respecting capacity constraints on edges. A central result in this area is the Max-Flow Min-Cut Theorem, which states that the maximum amount of flow that can be sent from the source to the sink in a flow network is equal to the minimum capacity of a cut that separates the source and sink. The Ford-Fulkerson Algorithm is a classic method to compute the maximum flow in such networks. It works by repeatedly finding augmenting paths from source to sink with available capacity and increasing the flow along those paths until no more augmenting paths exist. The final flow obtained corresponds to the maximum flow, and the corresponding cut identifies the minimum cut, thereby proving the theorem in practice.

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