Super edge-connectivity and matching preclusion of data center networks

Edge-connectivity is a classic measure for reliability of a network in the presence of edge failures. $k$-restricted edge-connectivity is one of the refined indicators for fault tolerance of large networks. Matching preclusion and conditional matching preclusion are two important measures for the robustness of networks in edge fault scenario. In this paper, we show that the DCell network $D_{k,n}$ is super-$\lambda$ for $k\geq2$ and $n\geq2$, super-$\lambda_2$ for $k\geq3$ and $n\geq2$, or $k=2$ and $n=2$, and super-$\lambda_3$ for $k\geq4$ and $n\geq3$. Moreover, as an application of $k$-restricted edge-connectivity, we study the matching preclusion number and conditional matching preclusion number, and characterize the corresponding optimal solutions of $D_{k,n}$. In particular, we have shown that $D_{1,n}$ is isomorphic to the $(n,k)$-star graph $S_{n+1,2}$ for $n\geq2$.Comment: 20 pages, 1 figur

The structure connectivity of Data Center Networks

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 $\kappa(G; H)$ (resp. $H$-substructure connectivity $\kappa^{s}(G; H)$) 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 $\kappa (D_{m,n}; K_{1,t})=\kappa^s (D_{m,n}; K_{1,t})=\lceil \frac{n-1}{1+t}\rceil+m$ for $1\leq t\leq m+n-2$ and $\kappa (D_{m,n}; K_s)= \lceil\frac{n-1}{s}\rceil+m$ for $3\leq s\leq n-1$ by analyzing the structural properties of $D_{m,n}$. We also compute $\kappa(B_n; H)$ and $\kappa^s(B_n; H)$ 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 $B_n$

Packing internally disjoint Steiner paths of data center networks

Let $S\subseteq V(G)$ and $\pi_{G}(S)$ denote the maximum number $t$ of edge-disjoint paths $P_{1},P_{2},\ldots,P_{t}$ in a graph $G$ such that $V(P_{i})\cap V(P_{j})=S$ for any $i,j\in\{1,2,\ldots,t\}$ and $i\neq j$. If $S=V(G)$, then $\pi_{G}(S)$ is the maximum number of edge-disjoint spanning paths in $G$. It is proved [Graphs Combin., 37 (2021) 2521-2533] that deciding whether $\pi_G(S)\geq r$ is NP-complete for a given $S\subseteq V(G)$. For an integer $r$ with $2\leq r\leq n$, the $r$-path connectivity of a graph $G$ is defined as $\pi_{r}(G)=$min$\{\pi_{G}(S)|S\subseteq V(G)$ and $|S|=r\}$, which is a generalization of tree connectivity. In this paper, we study the $3$-path connectivity of the $k$-dimensional data center network with $n$-port switches $D_{k,n}$ which has significate role in the cloud computing, and prove that $\pi_{3}(D_{k,n})=\lfloor\frac{2n+3k}{4}\rfloor$ with $k\geq 1$ and $n\geq 6$

A Power Efficient Server-to-Server Wireless Data Center Network Architecture Using 60 GHz Links

Data Centers have become the digital backbone of the modern society with the advent of cloud computing, social networking, big data analytics etc. They play a vital role in processing a large amount of information generated. The number of data centers and the servers present in them have been on the rise over the last decade. This has eventually led to the increase in the power consumption of the data center due to the power-hungry interconnect fabric which consists of switches, routers and switching fabric necessary for communication in the data center. Moreover, a major portion of the power consumed in a data center belongs to cooling infrastructure. The data center’s complex cabling prevents the heat dissipation by obstructing the air flow resulting in the need for a cooling infrastructure. Additionally, the complex cabling in traditional data centers poses design and maintenance challenges. In this work, these problems of traditional data centers are addressed by designing a unique new server-to-server wireless Data Center Network (DCN) architecture. The proposed design methodology uses 60GHz unlicensed millimeter-wave bands to establish direct communication links between servers in a DCN without the need for a conventional fabric. This will reduce the power consumption of the DCN significantly by getting rid of the power-hungry switches along with an increase in the independency in communication between servers. In this work, the previous traffic models of a data center network are studied and a new traffic model very similar to the actual traffic in a data center is modeled and used for simulating the DCN environment. It is estimated that the proposed DCN architecture’s power consumption is lowered by six to ten times in comparison to the existing conventional DCN architecture. Having established the power model of a server-to-server wireless DCN in terms of its power consumption, we demonstrate that such a power-efficient wireless DCN can sustain the traffic requirements encountered and provide data rates that are comparable to traditional DCNs. We have also compared the efficiency and performance of the proposed DCN architecture with some of the other novel DCN architectures like DCell, BCube with the same traffic

Torii: Multipath Distributed Ethernet Fabric Protocol for Data Centers with Zero-Loss Path Repair

This paper describes and evaluates Torii, a layer-two data center network fabric protocol. The main features of Torii are being fully distributed, scalable, fault-tolerant and with automatic setup. Torii is based on multiple, tree-based, topological MAC addresses that are used for table-free forwarding over multiple equal-cost paths, and it is capable of rerouting frames around failed links on the fly without needing a central fabric manager for any function. To the best of our knowledge, it is the first protocol that does not require the exchange of periodic messages to work under normal conditions and to recover from link failures, as Torii exchanges messages just once. Moreover, another important characteristic of Torii is that it is compatible with a wide range of data center topologies. Simulation results show an excellent distribution of traffic load and latencies, similar to shortest path protocols