Embedding meshes into twisted-cubes

  • Authors:

  • Xi Wang;Jianxi Fan;Xiaohua Jia;Shukui Zhang;Jia Yu

  • Affiliations:

  • School of Computer Science and Technology, Soochow University, Suzhou 215006, China;School of Computer Science and Technology, Soochow University, Suzhou 215006, China;Department of Computer Science, City University of Hong Kong, Hong Kong;School of Computer Science and Technology, Soochow University, Suzhou 215006, China;College of Information Engineering, Qingdao University, Qingdao 266071, China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

The n-dimensional twisted-cube, TN"n, is a variation of the hypercube. In this paper, we study embedding of meshes into TN"n. We prove three major results in this paper: (1) For any integer n=1, a 2x2^n^-^1 mesh can be embedded into TN"n with dilation 1 and expansion 1. (2) For any integer n=4, an mxk(m=3,k=3) mesh cannot be embedded into TN"n with dilation 1. (3) For any integer n=4, two node-disjoint 4x2^n^-^3 meshes can be embedded into TN"n with dilation 2 and expansion 1.