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The maximal flow solution algorithm allows the user to choose a path through the network from the origin to the destination by any criteria.

Question

The maximal flow solution algorithm allows the user to choose a path through the network from the origin to the destination by any criteria.

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Solution

Yes, the maximal flow solution algorithm, also known as the Ford-Fulkerson method, allows the user to choose any path from the source (origin) to the sink (destination) in a network. The algorithm works by repeatedly augmenting the flow along these paths. Here are the steps:

  1. Start with an initial flow, which could be zero flow for all edges in the network.

  2. Find an augmenting path from the source to the sink in the residual graph. The residual graph is a graph which indicates additional possible flow. If no such path exists, go to step 4.

  3. Augment the flow along this path. This means to increase the flow on that path by the amount of the smallest capacity on the path. Update the residual graph to reflect this change.

  4. If no augmenting paths are left, the current flow is maximal. The algorithm terminates.

The choice of the augmenting path can be done by any criteria, as long as it is a valid path from the source to the sink in the residual graph. The algorithm does not specify a particular method for choosing the path.

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