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A Parallel Algorithm for Constructing Multiple Independent Spanning Trees in Bubble-Sort Networks

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Algorithmic Aspects in Information and Management (AAIM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13153))

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Abstract

The use of multiple independent spanning trees (ISTs) for data broadcasting in networks provides a number of advantages, including the increase of fault-tolerance and secure message distribution. Thus, the designs of multiple ISTs on several classes of networks have been widely investigated. Kao et al. [Journal of Combinatorial Optimization 38 (2019) 972–986] proposed an algorithm to construct independent spanning trees in bubble-sort networks. The algorithm is executed in a recursive function and thus is hard to parallelize. In this paper, we focus on the problem of constructing ISTs in bubble-sort networks \(B_{n}\) and present a non-recursive algorithm. Our approach can be fully parallelized, i.e., every vertex can determine its parent in each spanning tree in constant time. This solves the open problem from the paper by Kao et al. Furthermore, we show that the total time complexity \(\mathcal {O}(n \cdot n!)\) of our algorithm is asymptotically optimal, where n is the dimension of \(B_{n}\) and n! is the number of vertices of the network.

This research was supported by the LaBRI under the “Projets émergents” program. This study has been carried out in the frame of the “Investments for the future” Programme IdEx Bordeaux - SysNum (ANR-10-IDEX-03-02).

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Author information

Authors and Affiliations

  1. CNRS, LaBRI, Université de Bordeaux, 351 Cours de la Libération, 33405, Talence, France

    Shih-Shun Kao & Ralf Klasing

  2. Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan, Taiwan

    Shih-Shun Kao & Sun-Yuan Hsieh

  3. Department of Creative Technologies and Product Design, National Taipei University of Business, No. 100, Sec. 1, Fulong Road, Taoyuan, Taiwan

    Ling-Ju Hung

  4. Institute of Medical Informatics, National Cheng Kung University, No. 1, University Road, Tainan, Taiwan

    Sun-Yuan Hsieh

Authors
  1. Shih-Shun Kao
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  2. Ralf Klasing
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  3. Ling-Ju Hung
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  4. Sun-Yuan Hsieh
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Corresponding author

Correspondence to Shih-Shun Kao .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

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Kao, SS., Klasing, R., Hung, LJ., Hsieh, SY. (2021). A Parallel Algorithm for Constructing Multiple Independent Spanning Trees in Bubble-Sort Networks. In: Wu, W., Du, H. (eds) Algorithmic Aspects in Information and Management. AAIM 2021. Lecture Notes in Computer Science(), vol 13153. Springer, Cham. https://doi.org/10.1007/978-3-030-93176-6_22

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  • DOI: https://doi.org/10.1007/978-3-030-93176-6_22

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