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Hamiltonian properties of HCN and BCN networks

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Abstract

Data center network plays an important role in improving the performance of cloud computing. Hamiltonian properties and Hamiltonian connectivity have important applications in communication network. The existence of Hamiltonian path can make the network more efficient communication. HCN and BCN networks are two important data center networks with nice routing performance and excellent scalability. In this paper, we study the Hamiltonian properties and disjoint path covers of these two networks. Firstly, we prove that HCN(n, h) is Hamiltonian-connected with \(n\ge 4\) and \(h\ge 0\). Secondly, we prove that BCN\((\alpha ,\beta ,h,\gamma )\) is Hamiltonian-connected with \(h<\gamma\), \(\alpha \ge 4\), \(\beta \ge 1\), \(h\ge 0\), \(\gamma \ge 0\). Finally, we design Hamiltonian path construction algorithms for HCN and BCN networks. Simulation experiments verify the construction process of Hamiltonian path. Moreover, the running time of the routing algorithm designed in this study is compared with the classical shortest path multicast tree algorithm DijkstraSPT, and its running time is lower than that of the algorithm DijkstraSPT by about 5ms on different server nodes, which shows that the routing algorithm designed in this study according to HCN and BCN structure operate efficiently.

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Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (61672209, 61701170, 62102196), Science and technology development plan of Henan Province (192102210282, 202102210327), Special project for key R &D and promotion of Henan Province (222102210052, 222102210007, 222102210062, 222102210272), Natural Science Foundation of Jiangsu Province (No. BK20200753), Jiangsu Postdoctoral Science Foundation Funded Project (No. 2021K096A), the Future Network Scientific Research Fund Project (No FNSRFP-2021-YB-60), the Natural Science Fund for Colleges and Universities in Jiangsu Province (No 21KJB520026), in the Acknowledgements. The Fundamental Research Funds for the Central Universities of Jilin University (No. 93K172020K25).

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Authors and Affiliations

  1. School of Computer and Information Engineering, Henan University, Longting District, Kaifeng, 475004, Henan, China

    Xiaoyu Du, Cheng Cheng & Shuai Ding

  2. School of Software, Henan University, Longting District, Kaifeng, 475004, Henan, China

    Zhijie Han

  3. Henan Engineering Laboratory of Spatial Information Processing, Henan University, Longting District, Kaifeng, 475004, Henan, China

    Xiaoyu Du

  4. College of Computer, Nanjing University of Posts and Telecommunications, Qixia District, Nanjing, 210000, Jiangsu, China

    Weibei Fan

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  1. Xiaoyu Du
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Correspondence to Weibei Fan.

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Du, X., Cheng, C., Han, Z. et al. Hamiltonian properties of HCN and BCN networks. J Supercomput 79, 1622–1653 (2023). https://doi.org/10.1007/s11227-022-04723-w

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