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<p class="owaPara">Dear all,</p>
<p class="owaPara"> </p>
<p class="owaPara">May I refer to the query below:</p>
<p class="owaPara"><a href="http://lemon.cs.elte.hu/pipermail/lemon-user/2010-October/000287.html">http://lemon.cs.elte.hu/pipermail/lemon-user/2010-October/000287.html</a></p>
<p class="owaPara">...and ask you what if we had a flow that starts from s, and before reaching t, has split and follows two parallel paths for a while and then meets at t.
</p>
<p class="owaPara"> </p>
<p class="owaPara">For example, lets say we have a flow of 10 units from node 1 to node 7. Here are some possible flows:</p>
<p class="owaPara"> </p>
<p class="owaPara">Node 1 -Node 2: 10 units flow. then:<br>
Node 2-Node 3: 5 units<br>
Node 3-node 4:5 units<br>
Node 4-Node 7:5 units and...</p>
<p class="owaPara"><br>
Node 2-Node 6:5 units<br>
Node 6-Node 7:5 units</p>
<p class="owaPara"> </p>
<p class="owaPara">With 2-3-4-7 and 2-6-7 two parallel paths that start from Node 2 and end at node 7.
</p>
<p class="owaPara"> </p>
<p class="owaPara">Will the following procedure (posted by Alpár) identify the parallel flows of this commodity?
</p>
<p class="owaPara"> </p>
<p class="owaPara">* Repeat the following for each destination t.<br>
* Find a maximum s-t flow x_t with y[e] as the capacity of<br>
e for each arc e.<br>
* Decrease y by x_t. (i.e. y[e]:=y[e]-x_t[e] for each arc e)</p>
<p class="owaPara"> </p>
<p class="owaPara">As with the case of Aran (link given above), I have different commodity flows with s-t and k, and I would like to know which arcs were used by each commodity, when solving the MCF.
</p>
<p class="owaPara"> </p>
<p class="owaPara">Any solution that would solve my problem, is greatly appreciated.
</p>
<p class="owaPara"> </p>
<p class="owaPara">Many thanks!</p>
<p class="owaPara"> </p>
<p class="owaPara">Dimitris </p>
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