Embedding shuffle networks in hypercubes

Abstract

We consider the problem of embedding perfect shuffle and shuffle exchange networks in hypercubes. We prove that perfect embedding is possible for perfect shuffle with 2 k nodes only when k is a power of 2, and we give an efficient algorithm for embedding perfect shuffle networks with 2 k nodes when k is a power of 2. We also discuss a scheme for embedding shuffle exchange networks with 2 k nodes, k being a power of 2, and give its extensions to the general case.