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

  • Authors:

  • Qiang Dong;Xiaofan Yang;Juan Zhao;Yuan Yan Tang

  • Affiliations:

  • College of Computer Science, Chongqing University, Chongqing 400044, China;College of Computer Science, Chongqing University, Chongqing 400044, China;Department of Foreign Language, Aba Teachers College, Aba 623000, Sichuan, China;College of Computer Science, Chongqing University, Chongqing 400044, China and Department of Computer Science, Hong Kong Baptist University, Kowloon, Hong Kong

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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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 2x2x2^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 4x2x2^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].