Optimal fault-tolerant embedding of paths in twisted cubes

  • Authors:

  • Jianxi Fan;Xiaola Lin;Yi Pan;Xiaohua Jia

  • Affiliations:

  • Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong;College of Information Science and Technology, Sun Yat-sen University, Guangzhou, China;Department of Computer Science, Georgia State University, Atlanta, GA 30303-3083, USA;Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong

  • Venue:
  • Journal of Parallel and Distributed Computing
  • Year:
  • 2007

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Abstract

The twisted cube is an important variation of the hypercube. It possesses many desirable properties for interconnection networks. In this paper, we study fault-tolerant embedding of paths in twisted cubes. Let TQ"n(V,E) denote the n-dimensional twisted cube. We prove that a path of length l can be embedded between any two distinct nodes with dilation 1 for any faulty set F@?V(TQ"n)@?E(TQ"n) with |F|==3). This result is optimal in the sense that the embedding has the smallest dilation 1. The result is also complete in the sense that the two bounds on path length l and faulty set size |F| for a successful embedding are tight. That is, the result does not hold if l==n-2. We also extend the result on (n-3)-Hamiltonian connectivity of TQ"n in the literature.