Embedding a family of disjoint 3D meshes into a crossed cube

Abstract

Crossed cubes are an important class of hypercube variants. This paper addresses how to embed a family of disjoint 3D meshes into a crossed cube. Two major contributions of this paper are: (1) for n ⩾ 4 , a family of two disjoint 3D meshes of size 2 × 2 × 2 n - 3 can be embedded in an n-D crossed cube with unit dilation and unit expansion, and (2) for n ⩾ 6 , a family of four disjoint 3D meshes of size 4 × 2 × 2 n - 5 can be embedded in an n-D crossed cube with unit dilation and unit expansion. These results mean that a family of two or four 3D-mesh-structured parallel algorithms can be executed on a same crossed cube efficiently and in parallel. Our work extends the results recently obtained by Fan and Jia [J. Fan, X. Jia, Embedding meshes into crossed cubes, Information Sciences 177(15) (2007) 3151–3160].