# Arithmetic Study about Efficiency in Network Topologies for Data Centers
## 3 Related Work  
After having presented some of the main network topologies being used in data centers, it is time to report some of the related work among them. There are some papers comparing the main features of the most typically used topologies. For instance, [PERSON] et al. [56] undertake an analysis of reliability and survivability of data center network topologies where Fat Tree, BCube and DCell are compared, which concludes that BCube is the most robust to link failures, whilst DCell isthe most robust regarding switch failures, and that robustness is related to the number of interfaces per node. [PERSON] et al. [57] compare BCube and DCell, obtaining better speed in data transmission for the latter, although the former has better security and integrity because it is able to forward data completely without any failures. [PERSON] et al. [58] confront Fat Tree and BCube,with the outcome indicating that the latter obtains better results than the former.Al [PERSON] et al. [59] state that data center networks may be classified into two broad groups, such as switch-centric and server-centric, where switches are mainly responsible for routing and networking in the former, whilst servers aremainly accountable in the latter, which allows the use of commodity switches [60]. Examples of the former are fat tree and leaf and spine, whereas instances of the latter are FiConn, DCell and BCube. [PERSON] et al. [61] carry out a comparative analysis among several well-known data center network topologies, such as Multi-tiered, Fat Tree, Flattened Butterfly, Camcube and BCube, regarding a variety of metrics, such as scalability, path diversity, hop count, throughput and cost, finding that different topologies scale differently for various metrics and concluding that designers must consider maximizing certain features whilst minimizing cost and power. [PERSON] et al. [62] propose a camcube design (\(k\)-ary \(n\)-cube) following the SDN paradigm such that the control plane is hosted in an SDN controller and including QoS into the decision-making process. After running several simulations using Mininet software, the results obtained are better than those attained with the shortest-path approach regarding packet error rate and latency. [PERSON] et al. [63] undertake a comparison among diverse topologies for InfiniBand networks, such as tori, hypercube, Dragonfly, Flattened Butterfly and Slim Fly, and their results seem interesting in the field of data center networks. After having executed the necessary simulations, they conclude that the best outcome is obtained by Flattened Butterfly and a combination of this with Slim Fly.Rao et al. [64] carry out a comparison among different topologies for Network-on-Chip (NoC), such as Dragon Fly, Flattened Butterfly, Torus topology and Mesh topology; their results may be extrapolated to data center networks. Those comparisons were made with diverse figures of trade-offs, such as packet latency, network latency, throughput change and hop average; the authors concluded that Torus topology is the most efficient one for being adaptive in nature as well as for having less latency and time complexity. [PERSON] et al. [65] compare a novel DCCube design with fat tree, Flattened Butterfly, BCube and SWCube, where the former achieves both higher performance and lower cost consideringthe number of switches, server NICs, server CPUs and cabling. Furthermore, [PERSON] et al. [66] propose a greedy forwarding strategy that is independent of the network topology in place and obtains acceptable results,whilst [PERSON] et al. [67] present average networking equipment power consumption for different topologies, showing that fat tree, leaf and spine, BCube and DCell obtain the highest outcome.In terms of creating a specific coefficient to measure performance in a data center, most efforts have been focused on energy efficiency. For instance, [PERSON] et al. [68] come up with a metric called Data Center Energy Productivity (DCeP) as the ratio of useful work produced to the energy consumed to get that work done.