论文标题
数据中心网络的结构连通性
The structure connectivity of Data Center Networks
论文作者
论文摘要
最近十年，构建了许多巨型数据中心网络，以提供越来越时尚的Web应用程序。对于两个整数，$ m \ geq 0 $和$ n \ geq 2 $，$ n $ - port switches $ d_ {m，n} $和$ n $ diemensional bcdc网络$ b_ {n} $已提议。连接性是测量网络的故障耐受性的基本参数。随着连通性的概括，最近提出了结构（子结构）连通性。令$ g $和$ h $为两个连接的图。令$ \ mathcal {f} $为元素是$ g $的子图的集合，$ \ Mathcal {f} $的每个成员都是同构至$ h $的（分别是连接的$ h $）。然后，$ h $ - 结构连接性$κ（g; h）$（$ h $ h $ -subtructure $κ^{s}（g; h）$的$ g $是$ \ nathcal {f} $最小的大小。然后，在某些公共结构上计算数据中心网络的结构连接是有意义的，例如star $ k_ {1，t} $，路径$ p_k $，cycle $ c_k $，完整的图形$ k_s $等。在本文中，我们获得了$κ（d_ {m，n}; k_ {1，t}）=κ^s（d_ {m，n}; k_ {1，t}）= \ lceil \ lceil \ frac {n-1} $κ（d_ {m，n}; k_s）= \ lceil \ frac {n-1} {s} {s} \ rceil+m $，$ 3 \ leq s \ leq s \ leq n-1 $，通过分析$ d_ {m {m {m {m，n} $的结构属性。 We also compute $κ(B_n; H)$ and $κ^s(B_n; H)$ for $H\in \{K_{1,t}, P_{k}, C_{k}|1\leq t\leq 2n-3, 6\leq k\leq 2n-1 \}$ and $n\geq 5$ by using $g$-extra connectivity $ b_n $。
Last decade, numerous giant data center networks are built to provide increasingly fashionable web applications. For two integers $m\geq 0$ and $n\geq 2$, the $m$-dimensional DCell network with $n$-port switches $D_{m,n}$ and $n$-dimensional BCDC network $B_{n}$ have been proposed. Connectivity is a basic parameter to measure fault-tolerance of networks. As generalizations of connectivity, structure (substructure) connectivity was recently proposed. Let $G$ and $H$ be two connected graphs. Let $\mathcal{F}$ be a set whose elements are subgraphs of $G$, and every member of $\mathcal{F}$ is isomorphic to $H$ (resp. a connected subgraph of $H$). Then $H$-structure connectivity $κ(G; H)$ (resp. $H$-substructure connectivity $κ^{s}(G; H)$) of $G$ is the size of a smallest set of $\mathcal{F}$ such that the rest of $G$ is disconnected or the singleton when removing $\mathcal{F}$. Then it is meaningful to calculate the structure connectivity of data center networks on some common structures, such as star $K_{1,t}$, path $P_k$, cycle $C_k$, complete graph $K_s$ and so on. In this paper, we obtain that $κ(D_{m,n}; K_{1,t})=κ^s (D_{m,n}; K_{1,t})=\lceil \frac{n-1}{1+t}\rceil+m$ for $1\leq t\leq m+n-2$ and $κ(D_{m,n}; K_s)= \lceil\frac{n-1}{s}\rceil+m$ for $3\leq s\leq n-1$ by analyzing the structural properties of $D_{m,n}$. We also compute $κ(B_n; H)$ and $κ^s(B_n; H)$ for $H\in \{K_{1,t}, P_{k}, C_{k}|1\leq t\leq 2n-3, 6\leq k\leq 2n-1 \}$ and $n\geq 5$ by using $g$-extra connectivity of $B_n$.
