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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