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The two algorithms you mentioned are working ONLY when you have a ready directed network (i.e., all edges have given directions). In here the only given is the capacity of each edge, but no direction. So, I asked if there is an algorithm that can assign directions that give max-flow to undirected network.
I don't think the solution will be unique in most useful instances, otherwise I would suggest using a branch-and-bound algorithm. You might just solve the max flow problem with edges in both directions except where that doesn't make sense (e.g. at the source and the sink) with a constraint that one of the edges in each pair must have 0 flow. (edit: Unless your problem includes assigning the source and sink.)
And exactly what stops you from defining each undirected edge twice, once in each direction, with the same maximum flow?
Oops, ta0kira posted before I wrote my reply. My thoughts exactly. You probably have to apply the constraint by canceling opposing flows on the same edge, but I cannot see any reason why it should not work reliably.
Last edited by Nominal Animal; 04-26-2012 at 11:40 PM.
First of all, I would like to ask you about your question. Orientation is a property of the graph which arises from the system which is intended to be modeled. That is why I am asking... are you sure that the problem you are modeling is not already giving you a direction?
Both of the preceding replies are quite valid BUT again ali2011, isn't a directionality pattern being already provided from your problem?