## 4 Algorithmic Approaches
This is because the solution found will increasingly approach the optimal solution found by model \(M_{2}\) and with shorter CPU times. This can be observed, for example, in the results of random networks with 400 and 500 nodes for the scenario using 40% controller density. ## 6 Conclusions

In this study, we focused on reducing latency density in software-defined networks, which is crucial for enhancing user experience and operational efficiency for network administrators. Lowering latency density in SDNs provides significant benefits for users, such as faster response times, improved connection reliability, and better resource utilization. For network decision-makers, this translates into more efficient traffic management and an enhanced ability to meet service-level agreements. In order to tackle this challenge, we introduced two novel mathematical models, \(M_{1}\) and \(M_{2}\). These models are specifically designed to optimize resource distribution and management in SDNs, aiming to minimize latency and enhance overall network performance. Our evaluations consistently highlight that the \(M_{2}\) model outperforms \(M_{1}\) in terms of CPU times and MipGaps across all studied instances, demonstrating its effectiveness and robustness in various network configurations. In addition to theoretical modeling, we conducted comprehensive analyses using real benchmark instances, including randomly generated ones. This approach validated the practical effectiveness and applicability of our models. As a complement to our mathematical models, we developed a meta-heuristic localization algorithm to compare with the model \(M_{2}\). The results indicate that this algorithm offers competitive solutions in terms of efficiency and accuracy and is particularly recommended for large-scale networks where resource optimization is critical. Throughout our study, we explored different controller density scenarios in networks, each representing unique conditions impacting network optimization and efficiency. Our findings show that increasing controller density tends to simplify the problem, as it enables more efficient traffic management, reducing latency and improving resource distribution. Furthermore, we introduced a sensitivity model similar to \(M_{2}\), emphasizing that prioritizing connections between switches and controllers over controller-to-controller links significantly reduces CPU times. This strategic approach allows for more effective resource allocation and precise network optimization, which is particularly crucial in environments requiring scalability and efficiency. These insights highlight the importance of considering controller density as a key factor in SDN design and management. By adjusting controller density according to specific network needs, we can simplify problem resolution and significantly enhance overall network performance and responsiveness. This adaptive and strategic approach is essential for addressing emerging challenges in modern network management and preparing networks for continued growth and increasing demands for digital services. In conclusion, this study not only advances the theoretical understanding of SDN optimization but also provides a robust framework for the practical implementation of solutions that enhance performance and efficiency in these critical digital networks. Our findings suggest that deploying the model \(M_{2}\) and the proposed algorithm represents a significant step toward more efficient and adaptive networks capable of meeting escalating connectivity and performance demands in enterprise and telecommunications settings. In future work, we aim to explore the relationship between latency density and the distribution of network components, along with how this relates to service quality and the costs associated with the deployment and maintenance of the network by service operators. It is important to address multiple issues simultaneously because there are different stakeholders with various challenges that require analysis and solutions.