On the bisection width and expansion of butterfly networks

The paper proves tight bounds on the bisection width and expansion of butterfly networks with and without wraparound. Previously it was known that the bisection width of an n-input butterfly with wraparound is n. We show that without wraparound, the bisection width is 2(√2-1)n+o(n)≈.82 n. This result is surprising because it contradicts the prior “folklore” belief that the bisection width is n in both cases. We also show that for every set A of k nodes in a butterfly with wraparound there are at least (4+o(1))k/log k edges from A to A¯, provided that k=o(n)