Embedding a family of disjoint multi-dimensional meshes into a crossed cube

Crossed cubes are an important class of hypercube variants. This paper addresses how to embed a family of disjoint multi-dimensional meshes into a crossed cube. We prove that for n⩾4 and 1⩽m⩽⌊n/2⌋−1, a family of m2 disjoint k-dimensional meshes of size t12×t22×⋯×tk2 each can be embedded in an n-dimensional crossed cube with unit dilation, where and max1⩽i⩽k{ti}⩾n−2m−1. This result means that a family of mesh-structured parallel algorithms can be executed on a same crossed cube efficiently and in parallel. Our work extends some recently obtained results.