# Arithmetic Study about Efficiency in Network Topologies for Data Centers
## 1 Introduction  
Data center deployments are ever growing because of the increase in IoT environments [1]. In order to improve performance, it is convenient to optimize the allocation strategy of virtual resources [2], with the target of minimizing the number of hops among nodes, which results in shorter migration times [3] and decreases energy consumption [4]. Diverse proposals in the literature have been made to reach efficiency in data centers, such as deploying an online mechanism design for demand response [5], implementing a mobility-based strategy [6] or using a specific query engine [7]. Furthermore, holistic approaches have been proposed, such as a sustainability-based [8], security-based [9] or federated learning-based [10]. It is to be noted that data centersin the cloud are composed ofmultiple nodes with greater processing and storage resources, as their scope is usually global in order for them to be accessed anywhere and anytime by many users [11]. However, data centerson the edge have a restricted scope to the network where they are located, although they oftentimes employ cloud servers as backup solutions [12]. This limited scope establishes a reduced number of users in an edge environment, thus requiring a small number of servers to deal with traffic flows [13].Anyway, there are some general strategies to be followed when trying to optimize data center performance [14], such as employing the right cooling system so as to dissipate heat faster, monitoring the environment by using data center infrastructure management (DCIM) solutions so as to facilitate decision making, taking advantage of automation to respond faster to management and maintenance tasks, maximizing flexibility and scalability to be able to adapt to dynamic environments and aligning budgets with business requirements to enhance innovation in the organization [15]. Performance is also often related to energy consumption, as energy sources deliver power to data center components such as switchgears, generators, panels, uninterruptedpower systems (UPS) and power distribution units (PDU) [16]. In turn, that power goes to either ICT or non-ICT equipment, where the former refers to servers, storage or networking, whilst the latterrefers to cooling, lightning or security [17].Regarding large data centers, performance is related to data distribution analysis to support big data analysis across geo-distributed data centers [18].An appropriate replication scheme is necessary to store replicas whilst satisfying quality-of-service (QoS) requirements and storage capacity constraints [19]. In those cases, measurements are made through profiling-based evaluation methods along with an approach based on multiview comparative workload trace analysis to properly assess efficiency [20]. Hyperscale data centers (HDC) require huge demands in terms of scale and quantity related to data storage and processing [21]. In this sense, network technologies employed in supercomputers and data centers have many common points [22], leading to convergence at multiple layers, which may result in the emergence of smart networking solutions to accelerate such a convergence [23]. Furthermore, high-density data centers are catching on due to the ever-growing demands of remote computation power, which is achieved by the use of ultra-high-performance hardware, such as NVRAM and GPUs [24]. Traditional data centers have issues related to bandwidth bottlenecks and failures of critical links and critical switches; thus, high-density data centers need larger bandwidth and better fault tolerance [25]. In order to properly utilize that bandwidth and robustness, different techniques need be employed, such as implementing multipath TCP for different flows to take different paths [26] or the development of optimal row-based cooling systems [27].