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International Workshop on Frontiers in Algorithmics

FAW 2019: Frontiers in Algorithmics pp 88–99Cite as

Constructing Three Completely Independent Spanning Trees in Locally Twisted Cubes

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11458)

Abstract

For the underlying graph G of a network, k spanning trees of G are called completely independent spanning trees (CISTs for short) if they are mutually inner-node-disjoint. It has been known that determining the existence of k CISTs in a graph is an NP-hard problem, even for \(k=2\). Accordingly, researches focused on the problem of constructing multiple CISTs in some famous networks. Pai and Chang [28] proposed a unified approach to recursively construct two CISTs with diameter \(2n-1\) in several n-dimensional hypercube-variant networks for \(n\geqslant 4\), including locally twisted cubes \(LTQ_n\). Later on, they provided a new construction for \(LTQ_n\) and showed that the diameter of two CISTs can be reduced to \(2n-2\) if \(n=4\) (and thus is optimal) and \(2n-3\) if \(n\geqslant 5\). In this paper, we intend to construct more CISTs of \(LTQ_n\). We develop a novel tree searching algorithm, called two-stages tree-searching algorithm, to construct three CISTs of \(LTQ_6\) and show that the three CISTs of the high-dimensional \(LTQ_n\) for \(n\geqslant 7\) can be constructed by recursion. The diameters of three CISTs for \(LTQ_n\) we constructed are 9, 12 and 14 when \(n=6\), and are \(2n-3\), \(2n-1\) and \(2n+1\) when \(n\geqslant 7\).

Keywords

  • Completely independent spanning trees
  • Interconnection networks
  • Locally twisted cubes
  • Diameter

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Acknowledgments

This research was partially supported by MOST grants 107-2221-E-131-011 (K.-J. Pai), 107-2221-E-141-002 (R.-S. Chang) and 107-2221-E-141-001-MY3 (J.-M. Chang), from the Ministry of Science and Technology, Taiwan.

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Management, Ming Chi University of Technology, New Taipei City, Taiwan

    Kung-Jui Pai

  2. Institute of Information and Decision Sciences, National Taipei University of Business, Taipei, Taiwan

    Ruay-Shiung Chang & Jou-Ming Chang

  3. Department of Industrial Management, Lunghwa University of Science and Technology, Taoyuan, Taiwan

    Ro-Yu Wu

Authors
  1. Kung-Jui Pai
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  2. Ruay-Shiung Chang
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  3. Jou-Ming Chang
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  4. Ro-Yu Wu
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Corresponding author

Correspondence to Kung-Jui Pai .

Editor information

Editors and Affiliations

  1. Fudan University, Shanghai, China

    Yijia Chen

  2. Peking University, Beijing, China

    Xiaotie Deng

  3. Tsinghua University, Beijing, China

    Mei Lu

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Pai, KJ., Chang, RS., Chang, JM., Wu, RY. (2019). Constructing Three Completely Independent Spanning Trees in Locally Twisted Cubes. In: Chen, Y., Deng, X., Lu, M. (eds) Frontiers in Algorithmics. FAW 2019. Lecture Notes in Computer Science(), vol 11458. Springer, Cham. https://doi.org/10.1007/978-3-030-18126-0_8

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  • DOI: https://doi.org/10.1007/978-3-030-18126-0_8

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