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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

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Part of the book series: Lecture Notes in Computer Science ((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.

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References

  1. Bae, M.M., Bose, B.: Edge disjoint Hamiltonian cycles in k-ary n-cubes and hypercubes. IEEE Trans. Comput. 52, 1271–1284 (2003)

    Article  Google Scholar 

  2. Barden, B., Libeskind-Hadas, R., Davis, J., Williams, W.: On edge-disjoint spanning trees in hypercubes. Inf. Process. Lett. 70, 13–16 (1999)

    Article  MathSciNet  Google Scholar 

  3. Barth, D., Raspaud, A.: Two edge-disjoint Hamiltonian cycles in the butterfly graph. Inf. Process. Lett. 51, 175–179 (1994)

    Article  MathSciNet  Google Scholar 

  4. Efe, K.: A variation on the hypercube with lower diameter. IEEE Trans. Comput. 40, 1312–1316 (1991)

    Article  Google Scholar 

  5. Efe, K.: The crossed cube architecture for parallel computing. IEEE Trans. Parallel Distrib. Syst. 3, 513–524 (1992)

    Article  Google Scholar 

  6. Efe, K., Blackwell, P.K., Slough, W., Shiau, T.: Topological properties of the crossed cube architecture. Parallel Comput. 20, 1763–1775 (1994)

    Article  MathSciNet  Google Scholar 

  7. Hung, R.W.: Embedding two edge-disjoint Hamiltonian cycles into locally twisted cubes. Theor. Comput. Sci. 412, 4747–4753 (2011)

    Article  MathSciNet  Google Scholar 

  8. Hung, R.W.: Constructing two edge-disjoint Hamiltonian cycles and two-equal path cover in augmented cubes. J. Comput. Sci. 39, 42–49 (2012)

    Google Scholar 

  9. Hung, R.W.: The property of edge-disjoint Hamiltonian cycles in transposition networks and hypercube-like networks. Discrete Appl. Math. 181, 109–122 (2015)

    Article  MathSciNet  Google Scholar 

  10. Hung, R.W., Chan, S.J., Liao, C.C.: Embedding two edge-disjoint Hamiltonian cycles and two equal node-disjoint cycles into twisted cubes. Lect. Notes Eng. Comput. Sci. 2195, 362–367 (2012)

    Google Scholar 

  11. Hung, H.S., Fu, J.S., Chen, G.H.: Fault-free Hamiltonian cycles in crossed cubes with conditional link faults. Inf. Sci. 177, 5664–5674 (2007)

    Article  MathSciNet  Google Scholar 

  12. Kulasinghe, P.D., Bettayeb, S.: Multiplytwisted hypercube with 5 or more dimensions is not vertex transitive. Inf. Process. Lett. 53, 33–36 (1995)

    Article  Google Scholar 

  13. Lin, T.J., Hsieh, S.Y., Juan, J.S.-T.: Embedding cycles and paths in product networks and their applications to multiprocessor systems. IEEE Trans. Parallel Distrib. Syst. 23, 1081–1089 (2012)

    Article  Google Scholar 

  14. Pai, K.J.: An interactive verification of constructing two edge-disjoint Hamiltonian cycles in crossed cubes (2020). http://poterp.iem.mcut.edu.tw/2HC_in_CQn/

  15. Petrovic, V., Thomassen, C.: Edge-disjoint Hamiltonian cycles in hypertournaments. J. Graph Theory 51, 49–52 (2006)

    Article  MathSciNet  Google Scholar 

  16. Rowley, R., Bose, B.: Edge-disjoint Hamiltonian cycles in de Bruijn networks. In: Proceedings of the 6th Distributed Memory Computing Conference, pp. 707–709 (1991)

    Google Scholar 

  17. Saad, Y., Schultz, M.H.: Topological properties of hypercubes. IEEE Trans. Comput. 37, 867–872 (1988)

    Article  Google Scholar 

  18. Wang, D.: A low-cost fault-tolerant structure for the hypercube. J. Supercomput. 20, 203–216 (2001)

    Article  Google Scholar 

  19. Wang, D.: On embedding Hamiltonian cycles in crossed cubes. IEEE Trans. Parallel Distrib. Syst. 19, 334–346 (2008)

    Article  Google Scholar 

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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

    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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57601-1

  • Online ISBN: 978-3-030-57602-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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