Mapping Problem and Embedding of Various Networks into Hypercubes

The purpose of embedding (or mapping) is to minimize the communication overhead of parallel algorithms. It appears unlikely that an efficient exact technique of embedding a general guest graph in a general host graph with a minimum-dilation will ever be found. The Research in this area is concentrating on discovering efficient heuristic that find solution in most cases. This article is a survey of techniques for embedding common guest graphs such as linear arrays, trees, meshes, etc. into hypercube. The reason of hypercube as a host graph is that hypercube topology have been considered as parallel architecture due to its powerful interconnection network. We examine the hypercube and embedding problem from the graph theory point of view. Among other things we propose a mathematical framework of the hypercube as an interconnection network and look into a theoretical characterization of embedding various topology into a hypercube.