Low expansion packings and embeddings of hypercubes into star graphs

Let G(κ) and H(n) be respectively a κ-dimensional and an n-dimensional graph. Packing is a technique by which p/sub κ/ many copies of each G(κ), κ/sub min/⩽κ⩽κ/sub max/, are embedded into H(n). Packings can use H(n) efficiently by assigning independent tasks to the embedded copies of G(κ), and are a useful foundation, from which node allocation and task migration strategies can be built. Copies of G(κ), packed into H(n) with dilation d/sub base/, can be combined to produce a variable-dilation embedding of G(κ+l) into H(n). Such an embedding has dilation d/sub i/ along dimension i of G(κ+l), where d/sub i/=d/sub base/ for i⩽κ, and d/sub i/>d/sub base/ for κ