A Tight Layout of the Butterfly Network

Abstract.

We establish upper and lower bounds on the layout area of the butterfly network (without wraparound), which differ only in low-order terms. Specifically, the N -input, N -output butterfly network can be laid out in area (1 + o(1)) N ² , while no layout of the network can have area smaller than (1 - o(1)) N ² . These results improve both the known upper bound and the known lower bound on the area of butterfly network layouts.