Parallel construction of independent spanning trees and an application in diagnosis on Möbius cubes

  • Authors:

  • Baolei Cheng;Jianxi Fan;Xiaohua Jia;Juncheng Jia

  • Affiliations:

  • School of Computer Science and Technology, Soochow University, Suzhou, China 215006 and Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou, China ...;School of Computer Science and Technology, Soochow University, Suzhou, China 215006;Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong;School of Computer Science and Technology, Soochow University, Suzhou, China 215006

  • Venue:
  • The Journal of Supercomputing
  • Year:
  • 2013

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Abstract

Independent spanning trees (ISTs) on networks have applications to increase fault-tolerance, bandwidth, and security. Möbius cubes are a class of the important variants of hypercubes. A recursive algorithm to construct n ISTs on n-dimensional Möbius cube M n was proposed in the literature. However, there exists dependency relationship during the construction of ISTs and the time complexity of the algorithm is as high as O(NlogN), where N=2 n is the number of vertices in M n and n驴2. In this paper, we study the parallel construction and a diagnostic application of ISTs on Möbius cubes. First, based on a circular permutation n驴1,n驴2,驴,0 and the definitions of dimension-backbone walk and dimension-backbone tree, we propose an O(N) parallel algorithm, called PMCIST, to construct n ISTs rooted at an arbitrary vertex on M n . Based on algorithm PMCIST, we further present an O(n) parallel algorithm. Then we provide a parallel diagnostic algorithm with high efficiency to diagnose all the vertices in M n by at most n+1 steps, provided the number of faulty vertices does not exceed n. Finally, we present simulation experiments of ISTs and an application of ISTs in diagnosis on 0-M 4.