## 2 Materials and Methods
### Developing the Improved Federated RHLP Algorithm for Efficient Client Selection
It selects a focused and diverse group of clients for training using a dual-biased strategy, considering factors such as dataset size, label variety, and local model performance. The goal is to optimize both data diversity and the quality of the global model, aligning with the approach in [35]. The Oort algorithm also tackles the participant selection challenge by considering data and system diversity to choose suitable participants. A key feature of the enhanced version of the Fed-RHLP algorithm is the prioritization of high-performing clients while still allowing lower-performing clients to contribute. Focusing on high-performing clients during model aggregation improves global model accuracy, while including lower-performing clients ensures fairness and maintains data diversity. The equilibrium between clients with high and low performance fosters convergence and enhances the model's ability to generalize effectively across varied data distributions. As noted in [36], it is crucial to maintain fairness in FL by carefully selecting high-quality clients and equitably distributing incentives. This assessment may involve considerations of data quality, data volume, and advancements in the model. To realize this objective, it is imperative to engage multiple clients in collaboration, rather than depending solely on a single source for the training dataset [37]. Additionally, this method reduces the computational cost of federated learning by selectively choosing clients based on dataset characteristics and local model performance. By minimizing the number of clients required for each aggregation round, execution time is reduced, which is especially beneficial in resource-constrained or large-scale scenarios. As outlined in [38], the approach improves computational efficiency and addressescommunication overhead by dynamically selecting the best client models to share. This reduces unnecessary communication, lowers costs, and accelerates aggregation, making it especially valuable in federated settings with limited network bandwidth. The result is a more efficient FL framework with reduced computational load and faster model updates. The process of aggregating the global model during each communication round of the enhanced Fed-RHLP algorithm entails computing the average of the local model parameters derived from the chosen optimal clients. This methodology significantly strengthens the robustness of global model aggregation. This strategy is consistent with the results presented in [39], which indicate that the WFA (Distance-weighted FedAvg aggregation) function achieved markedly superior accuracy and recall compared to other algorithms. While the accuracy and recall of the proposed function may experience a minor decline when faced with attacks, it still demonstrates considerable resilience against such threats. In conclusion, the enhanced Fed-RHLP algorithm improves both accuracy and convergence, especially in Non-IID environments with significant data heterogeneity. By balancing the involvement of high- and low-performing clients, the algorithm ensures fairness and increases the diversity of contributions to the global model. This balance accelerates convergence and reduces computational costs, making it an effective solution for federated learning in diverse data environments. ## 5 Future Works

In future work, we aim to improve the Fed-RHLP algorithm by incorporating hierarchical FL structures. As the client pool expands, the central server faces heightened computational demands. To alleviate this, we propose dividing clients into smaller subgroups for localized aggregation before transmitting the results to the central server. This strategy will help reduce the computational load and enhance scalability, as well as decrease communication overhead and speed up the aggregation process. Additionally, we plan to adapt this hierarchical framework to handle various data distributions and model types, ensuring its effectiveness in diverse environments.