On the Bisection Width and Expansion of Butter y Networks

This paper proves tight bounds on the bisection width and expansion of butter y networks with and without wraparound. We show that the bisection width of an n-input butter y network is 2(p2 1)n+ o(n) :82n without wraparound, and n with wraparound. The former result is surprising, since it contradicts the prior \folklore" belief that the bisection width was n. We also show that every set of k nodes has at least k=(2 logk) neighbors in a butter y without wraparound, and at least k= logk neighbors in a butter y with wraparound, if k is o(pn) and o(n) respectively.