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International Conference on Algorithmic Applications in Management

AAIM 2020: Algorithmic Aspects in Information and Management pp 448–455Cite as

A Parallel Algorithm for Constructing Two Edge-Disjoint Hamiltonian Cycles in Crossed Cubes

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12290)

Abstract

The n-dimensional crossed cube CQn, a variation of the hypercube Qn, has the same number of vertices and the same number of edges as Qn, but it has only about half of the diameter of Qn. In the interconnection network, some efficient communication algorithms can be designed based on edge-disjoint Hamiltonian cycles. In addition, two edge-disjoint Hamiltonian cycles also provide the edge-fault tolerant Hamiltonicity for the interconnection network. Hung [Discrete Applied Mathematics 181, 109–122, 2015] designed a recursive algorithm to construct two edge-disjoint Hamiltonian cycles on CQn in O(n2n) time. In this paper, we provide an O(n) time algorithm for each vertex in CQn to determine which two edges were used in Hamiltonian cycles 1 and 2, respectively. With the information of each vertex, we can construct two edge-disjoint Hamiltonian cycles in CQn with n ≥ 4.

Keywords

  • Edge-disjoint Hamiltonian cycles
  • Crossed cubes
  • Interconnection networks

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Acknowledgments

This research was partially supported by MOST grants 107-2221-E-131-011 from the Ministry of Science and Technology, Taiwan.

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Authors and Affiliations

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

    Kung-jui Pai

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  1. Kung-jui Pai
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Correspondence to Kung-jui Pai .

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Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, China

    Prof. Zhao Zhang

  2. Texas Southern University, Houston, TX, USA

    Wei Li

  3. University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

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Pai, Kj. (2020). A Parallel Algorithm for Constructing Two Edge-Disjoint Hamiltonian Cycles in Crossed Cubes. In: Zhang, Z., Li, W., Du, DZ. (eds) Algorithmic Aspects in Information and Management. AAIM 2020. Lecture Notes in Computer Science(), vol 12290. Springer, Cham. https://doi.org/10.1007/978-3-030-57602-8_40

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  • DOI: https://doi.org/10.1007/978-3-030-57602-8_40

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