Hamiltonian Properties of the Data Center Network HSDC with Faulty Elements
Hui Dong, Jianxi Fan, Baolei Cheng, Yan Wang, Li Wen Xu · The Computer Journal · 2022
Abstract The data center network HSDC is a superior candidate for building large-scale data centers, and strikes a good balance among diameter, bisection width, incremental scalability and other important characteristics in contrast to the state-of-the-art data center network architectures. The Hamiltonian property is an important indicator to measure the reliability of a network. In this paper, we study the Hamiltonian properties of HSDC’s logic graph $H_n$. Firstly, we prove that $H_n$ is Hamiltonian-connected for $n\geq 3$. Secondly, we propose an $O(NlogN)$ algorithm for finding a Hamiltonian path between any two distinct nodes in $H_n$, where $N$ is the number of nodes in $H_n$. Furthermore, we consider the Hamiltonian properties of $H_n$ with faulty elements, and prove that $H_n$ is $(n-3)$-fault-tolerant Hamiltonian-connected and $(n-2)$-fault-tolerant Hamiltonian for $n\geq 3$.