Once the working nodes have been identified, new paths from the inputs
to the outputs of the multi-Benes network can be established using
an algorithm that is essentially the same as the circuit-switching
algorithm for multibutterflies described in Section 4.3.
There are two main differences. First, in the multi-Benes
network, only working nodes are used. However, by
Lemmas 4.9 and 4.10
the working switches have an 
unshared neighbors
property. Hence, we can run the algorithm of Section 4.3
with 
. Second, routing in the first half of the
multi-Benes network is actually easier than in the second half,
which is a multibutterfly, since there is no notion of up or down
edges. The goal is simply to get each new path from an input on level
to any working node on level 0. The algorithm uses
placeholders and cancellation signals in the first half in the same
way that they are used in the second half.