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Jul 11, 2020 at 6:30 comment added Aaron Rotenberg @Eulers I think you might want to remove your follow-up from this question and ask it as a separate question. It sounds like you have a bit of an XY problem because I'm not convinced that the best way to sum a function over all network flows acually involves computing any network flows at all.
Jul 10, 2020 at 3:50 comment added Eulers added in a large amount of clarification/follow-up that I would appreciate your thoughts on. Think the problem is slightly different than I had originally specified.
Jul 9, 2020 at 21:43 comment added Aaron Rotenberg @Eulers Does my edit clear this up?
Jul 9, 2020 at 21:43 history edited Aaron Rotenberg CC BY-SA 4.0
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Jul 9, 2020 at 20:26 comment added Eulers Hi @Aaron Rotenberg just unsure what you mean about splitting the vertex in two with the capacity limited edge to change the constraints from being on nodes rather than on the edges
Jul 8, 2020 at 0:47 comment added Aaron Rotenberg @Eulers Correct. A mincost flow algorithm computes a flow with the minimum cost, whatever that is. Scaling all the costs uniformly doesn't change the set of possible solutions.
Jul 8, 2020 at 0:40 comment added Eulers One last question (f you know). Let's say I put in the diagonal cost to be some non-zero number (and all diagonal edges are penalised the same). So long as the cost is 0 for the non-diagonal edges, it shouldn't matter what the cost is here (can be anything >0)?
Jul 8, 2020 at 0:30 comment added Aaron Rotenberg @Eulers See my edit.
Jul 8, 2020 at 0:30 history edited Aaron Rotenberg CC BY-SA 4.0
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Jul 8, 2020 at 0:12 comment added Eulers Thanks for the description Aaron! Just reading up on this all now, but would this just give me a list of the edges between the nodes or could I also extract from it the actual paths themselves? I guess the latter would just be another step on top once the edges have been constructed correct?
Jul 8, 2020 at 0:10 history edited Aaron Rotenberg CC BY-SA 4.0
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Jul 8, 2020 at 0:05 history answered Aaron Rotenberg CC BY-SA 4.0