Improved Compressions of Cube-Connected Cycles Networks

Abstract

We present a new technique for the embedding of large cube-connected cycles networks (CCC) into 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 xed size. Using the new embedding strategy, we show that the CCC of dimension l can be embedded into the CCC of dimension k with dilation 1 and optimum load for any k; l 2 IN, k 8, such that 5 3 + c k < l k 2, c k = 4k + 3 3 2 2=3k , thus improving known results. Our embedding technique also leads to improved dilation 1 embeddings in the case 3 2 < l k 5 3 + c k .