Arbitrary Size Benes Networks

Abstract

The Benes network is a rearrangeable nonblocking network which can realize any arbitrary permutation. Overlall, the r-dimensional Benes network connects 2r inputs to 2r outputs through 2r - 1 levels of 2 × 2 switches. Each level of switches consists of 2r - 1 switches, and hence the size of the network has to be a power of two. In this paper, we extend Benes networks to arbitrary sizes. We also show that the looping routing algorithm used in Benes networks can be slightly modified and applied to arbitrary size Benes networks.