Talk:Multi-commodity flow problem

Applications
There is a need to add some real applications of multi-commodity flow problem of both the types (fractional flows allowed and not allowed). Amit 06:52, 20 June 2022 (UTC) — Preceding unsigned comment added by Qx2020 (talk • contribs)

The description of the flow splitting is unclear and uses very similar (although with {0,1} and [0,1] differences in the brackets used) example for fractional (multipath) and whole (singlepath) flows. What is the significance of the different brackets? --DuncanECameron (talk) 08:55, 21 August 2019 (UTC)

I'm pretty sure the constraint $$f_i(u,v) = -f_i(v,u)$$ needs to be specified explicitly. Otherwise one can easily find a solution satisfying the three constraints, unless of course the first (capacity constraint) and third (demand constraint) conflict, in which case there is clearly no solution. At a casual glance it seems that the second constraint takes care of this, but it doesn't. 220.227.184.145 08:18, 18 July 2007 (UTC)Parakram

In the section "Software solving the problem: http://www.zib.de/Optimization/Software/Mcf/" seems to be wrong. I've read the documentation and it only states that it's an implementation of the network simplex and. MCF does not stand for "multi commodity flow" but for "minimal cost flow" in that case. On the other hand, http://www-eio.upc.es/~jcastro/pprn.html states to solve multi commodity flows. --Xor2k (talk) 15:45, 14 June 2010 (UTC)

"Papers by Clifford Stein about this problem: http://www.cs.dartmouth.edu/~cliff/papers/#mcf" is broken, 404. --Xor2k (talk) 15:45, 14 June 2010 (UTC)

The "maximum multi-commodity flow problem" is explained as maximizing this sum:


 * $$\sum_{i=1}^{k} \sum_{w \in V} f_i(s_i,w)$$

But constraint 3 shows that:


 * $$ \sum_{w \in V} f_i(s_i,w) = di$$

So there is no point on maximizing it. There must be something wrong, im not an expert though. --vingarcia (talk) 21:41, 03 May 2015 (UTC)

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