Compressing cube-connected cycles and butterfly networks

Abstract

We consider the simulation of large cube-connected cycles (CCC) and large butterfly networks (BFN) on smaller ones, a problem that arises when algorithms designed for an architecture of an ideal size are to be executed on an existing architecture of a fixed size. We show that large CCCs and BFNs can be embedded into smaller networks of the same type with (a) dilation 2 and optimum load, (b) dilation 1 and optimum load in most cases, and (c) dilation 1 and nearly optimum load in all cases. Our results show that large CCCs and BFNs can be simulated very efficiently on smaller ones. Additionally, we implemented our algorithm for compressing CCCs and ran several experiments on a Transputer network, which showed that our technique also behaves very well from a practical point of view.