Web Reference: Feb 24, 2024 · Since the above-described minimum-cost flow algorithm generates a back edge for each directed edge, so it splits the undirected edge into 4 directed edges, and we actually get a multigraph. How do we deal with multiple edges? First the flow for each of the multiple edges must be kept separately. In this final chapter on flows, we consider a significant generalization of the maximum- flow problem that (as far as we know) cannot be solved by modifying the graph and applying a standard flow algorithm. The input to our problem consists of a flow network without special source and target vertices, where each edge e has a cost $(e , in ... The minimum cost flow problem is one of the most fundamental among all flow and circulation problems because most other such problems can be cast as a minimum cost flow problem and also that it can be solved efficiently using the network simplex algorithm.
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