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The hierarchical Petersen network: a new interconnection network with fixed degree

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Abstract

Network cost and fixed-degree characteristic for the graph are important factors to evaluate interconnection networks. In this paper, we propose hierarchical Petersen network (HPN) that is constructed in recursive and hierarchical structure based on a Petersen graph as a basic module. The degree of HPN(n) is 5, and HPN(n) has \(10^n\) nodes and \(2.5 \times 10^n\) edges. And we analyze its basic topological properties, routing algorithm, diameter, spanning tree, broadcasting algorithm and embedding. From the analysis, we prove that the diameter and network cost of HPN(n) are \(3\log _{10}N-1\) and \(15 \log _{10}N-1\), respectively, and it contains a spanning tree with the degree of 4. In addition, we propose link-disjoint one-to-all broadcasting algorithm and show that HPN(n) can be embedded into FP\(_k\) with expansion 1, dilation 2k and congestion 4. For most of the fixed-degree networks proposed, network cost and diameter require \(O(\sqrt{N})\) and the degree of the graph requires O(N). However, HPN(n) requires O(1) for the degree and \(O(\log _{10}N)\) for both diameter and network cost. As a result, the suggested interconnection network in this paper is superior to current fixed-degree and hierarchical networks in terms of network cost, diameter and the degree of the graph.

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Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A3B03032173). We are grateful to the anonymous referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Computer Engineering, Sunchon National University, Suncheon, Jeonnam, 57922, South Korea

    Jung-Hyun Seo

  2. Department of Mathematics and Physics, North Carolina Central University, Durham, NC, 27707, USA

    Jong-Seok Kim

  3. Department of Computer Science, Troy University - Montgomery, Montgomery, AL, 36104, USA

    Hyung Jae Chang

  4. Department of Computer Education, Sunchon National University, Sunchon, Jeonnam, 57922, South Korea

    Hyeong-Ok Lee

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  1. Jung-Hyun Seo
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Correspondence to Hyeong-Ok Lee.

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Seo, JH., Kim, JS., Chang, H.J. et al. The hierarchical Petersen network: a new interconnection network with fixed degree. J Supercomput 74, 1636–1654 (2018). https://doi.org/10.1007/s11227-017-2186-4

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