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

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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=2n is the number of vertices in M n and n≥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−1,n−2,…,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.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (No. 61170021), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20103201110018), Application Foundation Research of Suzhou of China (SYG201240), and the 2011 Program for Postgraduates Research Innovation in University of Jiangsu Province (No. CXZZ11_0100) and sponsored by the Qing Lan Project.

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Authors and Affiliations

  1. School of Computer Science and Technology, Soochow University, Suzhou, 215006, China

    Baolei Cheng, Jianxi Fan & Juncheng Jia

  2. Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou, 215006, China

    Baolei Cheng

  3. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Xiaohua Jia

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  1. Baolei Cheng
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  2. Jianxi Fan
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  3. Xiaohua Jia
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  4. Juncheng Jia
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Correspondence to Jianxi Fan.

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Cheng, B., Fan, J., Jia, X. et al. Parallel construction of independent spanning trees and an application in diagnosis on Möbius cubes. J Supercomput 65, 1279–1301 (2013). https://doi.org/10.1007/s11227-013-0883-1

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