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Three edge-disjoint Hamiltonian cycles in crossed cubes with applications to fault-tolerant data broadcasting

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Abstract

Multiple edge-disjoint Hamiltonian cycles (EDHCs) provide the advantages of data broadcast in parallel and edge fault-tolerance in network communications. This paper investigates how to construct more EDHCs in a hypercube-variant network called crossed cube, denoted as \(CQ_n\). The topology of \(CQ_n\) has more wealth than normal hypercubes in network properties, e.g., it has about half of the diameter of a hypercube with the same dimension. Then, we obtain the following results in this paper: (1) We first provide the construction of three EDHCs in \(CQ_6\). (2) According to the recursive structure of \(CQ_n\), we prove by induction that there exist also three EDHCs in \(CQ_n\) for \(n\geqslant 7\). (3) Finally, we evaluate the performance of data broadcasting by simulation through three EDHCs and compare it against the best previous result in [18] using two EDHCs. In particular, our findings significantly improved the average success rate in edge fault-tolerant data broadcasting and two specific metrics concerning the broadcasting delivery time (latency).

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Acknowledgements

This research was partially supported by MOST grants 111-2221-E-131-012 (K.-J. Pai), 111-2221-E-262-004 (R.-Y. Wu), 111-2221-E-141-007 (S.-L. Peng), and 111-2221-E-141-006 (J.-M. Chang) 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, 243303, Taiwan

    Kung-Jui Pai

  2. Department of Industrial Management, Lunghwa University of Science and Technology, Taoyüan, 333326, Taiwan

    Ro-Yu Wu

  3. Department of Product Innovation and Entrepreneurship, National Taipei University of Business, Taoyüan, 324022, Taiwan

    Sheng-Lung Peng

  4. Institute of Information and Decision Sciences, National Taipei University of Business, Taipei, 10051, Taiwan

    Jou-Ming Chang

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  1. Kung-Jui Pai
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Correspondence to Jou-Ming Chang.

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A preliminary version of this paper was presented at 23rd International Conference on High Performance Computing and Communications (HPCC 2021), Dec. 20-22, Haikou, Hainan, China.

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Pai, KJ., Wu, RY., Peng, SL. et al. Three edge-disjoint Hamiltonian cycles in crossed cubes with applications to fault-tolerant data broadcasting. J Supercomput 79, 4126–4145 (2023). https://doi.org/10.1007/s11227-022-04825-5

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