Eliminating cyclic flows from a graph

Posted by Jon Harrop on Stack Overflow See other posts from Stack Overflow or by Jon Harrop
Published on 2011-03-20T17:13:56Z Indexed on 2011/03/20 19:19 UTC
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algorithm

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graph

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cycle

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flow

I have a directed graph with flow volumes along edges and I would like to simplify it by removing all cyclic flows. This can be done by finding the minimum of the flow volumes along each edge in any given cycle and reducing the flows of every edge in the cycle by that minimum volume, deleting edges with zero flow. When all cyclic flows have been removed the graph will be acyclic.

For example, if I have a graph with vertices A, B and C with flows of 1 from A?B, 2 from B?C and 3 from C?A then I can rewrite this with no flow from A?B, 1 from B?C and 2 from C?A. The number of edges in the graph has reduced from 3 to 2 and the resulting graph is acyclic.

Which algorithm(s), if any, solve this problem?

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