On optimal embeddings into incomplete hypercubes

The authors show the embeddings of various types of n-node incomplete binary trees into n-node or (n +1)-node composite hypercubes with dilation of at most 2. They also present lower bound proofs showing optimality of the dilation. They characterize the class of incomplete binary trees which are subgraphs of composite hypercubes. They present dilation 1 embedding of a two-dimensional n-node mesh, where one dimension is a power of two, into its optimal n-node composite hypercube. When neither dimension is a power of two, it is shown that a dilation 1 embedding is not possible; thereby characterizing the class of two-dimensional meshes that can be embedded into composite hypercubes with dilation 1. All two-dimensional meshes are shown to be embeddable with dilation 1 if expansion greater than 1 but less than 2 is allowed. The authors also consider two types of incomplete meshes and their embeddings into their optimal composite hypercubes