I'm wondering: given a fixed graph G, if we're to calculate the max flow between the vertices s and t, how different is the problem to calculate the max flow between the vertices s' and t, or similarly, s and t' (on the same graph)?
I've just started reading a paper by Altner and Ergun -- Rapidly Solving an Online Sequence of Maximum Flow Problems -- where they discuss a method to efficiently recalculate the max flow of a graph given small pertubations in the topology of that graph (for example, deleting or adding an edge). They do this by using the results from the previous max flow as a 'warm start' to calculating the new max flow.
I'm wondering if there is a similar story for recalculating the max flow given a change in source or sink? That is, is it possible to 'warm start' a max flow problem when a different source or sink is chosen?
Any pointers at all would be most welcome :)