Structure connectivity and substructure connectivity of data center network

Bo Zhu; Shumin Zhang; Jinyu Zou; Chengfu Ye; Bo Zhu; Shumin Zhang; Jinyu Zou; Chengfu Ye

doi:10.3934/math.2023499

AIMS Mathematics

2023, Volume 8, Issue 4: 9877-9889. doi: 10.3934/math.2023499

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Structure connectivity and substructure connectivity of data center network

1.
Department of Computer, Qinghai Normal University, Xining, Qinghai 810008, China
2.
School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, China
3.
Department of Basic Research, Qinghai University, Xining, Qinghai 810016, China
4.
Academy of Plateau Science and Sustainability, People's Government of Qinghai Province and Beijing Normal University

Received: 06 December 2022 Revised: 05 February 2023 Accepted: 16 February 2023 Published: 22 February 2023
MSC : 05C40, 05C07

The structure connectivity $ \kappa(G; H) $ and substructure connectivity $ \kappa^s(G; H) $ are important indicators to measure interconnection network's fault tolerance and reliability. The data center network, denoted by $ D_{k, n} $, have been proposed for data centers as a server-centric interconnection network structure, which can support millions of servers with high network capacity by only using commodity switches. In this paper, we obtain $ \kappa(D_{k, n}; S_m) $ and $ \kappa^s(D_{k, n}; S_m) $ when $ k\geq2 $, $ n\geq4 $ and $ 1\leq m\leq n+k-2 $. Furthermore, we obtain both $ \kappa(D_{k, n}; S_{23}) $ and $ \kappa^s(D_{k, n}; S_{23}) $ for $ k\geq8 $ and $ n\geq8 $.
- structure connectivity,
- substructure connectivity,
- data center network
Citation: Bo Zhu, Shumin Zhang, Jinyu Zou, Chengfu Ye. Structure connectivity and substructure connectivity of data center network[J]. AIMS Mathematics, 2023, 8(4): 9877-9889. doi: 10.3934/math.2023499

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Abstract

The structure connectivity $ \kappa(G; H) $ and substructure connectivity $ \kappa^s(G; H) $ are important indicators to measure interconnection network's fault tolerance and reliability. The data center network, denoted by $ D_{k, n} $, have been proposed for data centers as a server-centric interconnection network structure, which can support millions of servers with high network capacity by only using commodity switches. In this paper, we obtain $ \kappa(D_{k, n}; S_m) $ and $ \kappa^s(D_{k, n}; S_m) $ when $ k\geq2 $, $ n\geq4 $ and $ 1\leq m\leq n+k-2 $. Furthermore, we obtain both $ \kappa(D_{k, n}; S_{23}) $ and $ \kappa^s(D_{k, n}; S_{23}) $ for $ k\geq8 $ and $ n\geq8 $.

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