Embedding a family of meshes into twisted cubes

  • Authors:

  • Chia-Jui Lai;Chang-Hsiung Tsai

  • Affiliations:

  • Department of Finance and Banking, Dahan Institute of Technology, Hualien, Taiwan 970, R.O.C.;Department of Computer and Information Science, National Hualien University of Education, Hualien, Taiwan 970, R.O.C.

  • Venue:
  • Information Processing Letters
  • Year:
  • 2008

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Abstract

The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. The twisted cube is an important variation of the hypercube. Let TQ"n denote the n-dimensional twisted cube. In this paper, we consider embedding a family of 2-dimensional meshes into a twisted cube. The main results obtained in this paper are: (1) For any odd integer n=1, there exists a mesh of size 2x2^n^-^1 that can be embedded in the TQ"n with unit dilation and unit expansion. (2) For any odd integer n=5, there exists a mesh of size 4x2^n^-^2 that can be embedded in the TQ"n with dilation 2 and unit expansion. (3) For any odd integer n=5, a family of two disjoint meshes of size 4x2^n^-^3 can be embedded into the TQ"n with unit dilation and unit expansion. Results (1) and (3) are optimal in the sense that the dilations and expansions of the embeddings are unit values.