I'm studying a routing problem on a cyclic butterfly network. The paper I am reading states that two properties of the cyclic butterfly network make it efficient for the routing algorithm it describes. I'm new to this subject, and I'm struggling to understand the first property, which is:
"(1) It embeds a Benes network - meaning that if we traverse the columns and back any permutation of the row labels can take place without collisions"
It adds that this is trivially true for a square grid. In this context do collisions mean collision of packets of information? Why is this trivially true for a square grid, but not the cyclic butterfly network?