# Directed graph problem

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Hi, I am looking to find the size of the largest set of non-intersecting paths between given points A and B in a directed graph. As an example, you're a state coordinator and you have towns, and roads between towns. Several groups want to have a parade that day from town A to town B. Each group's parade would take up the whole parade route at once, because of the decorations involved, so they can't share any roads that day. How many parades between towns A and B, given a set of towns and roads, can be accommodated simultaneously? All of the roads are one-way (directed) although it's possible (in my application) for two towns to have two or more roads running directly between them, possibly in differing directions. Finding the actual routes needed to solve this is not relevant to me, only finding the number. That's the sort of algorithm I'm looking for. Does anyone have any ideas that might help?

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You could model this as a flow problem, where A is the source, B is the sink and all edges have capacity 1.
See Wikipedia: Maximum flow problem

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Thanks, I'll try that

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