## 2 Materials and Methods
### Developing the Improved Federated RHLP Algorithm for Efficient Client Selection
Setting Up Hardware Component Specifications

This experiment prepares the hardware specifications for setting up and executing the algorithms, as outlined in Table 1.

#### 2.3.3 Algorithm Performance Evaluation

The global model of the algorithms was evaluated 3 times over 200 communication rounds to ensure the stable reporting of its performance, using 10,000 global test samples from the MNIST and FMNIST datasets. The formula for evaluating the Improved RFLP algorithm, compared with other benchmark algorithms, involves measuring prediction accuracy, convergence speed, and reduced execution time [11]. The calculation methods for these three performance metrics are shown in Equations (5)-(7). \[\text{Accuracy }(\%)=\frac{(\text{Total number of test samples }-\text{ Number of incorrectly predicted samples})\times 100}{\text{Total number of test samples}} \tag{5}\]

\[\text{Convergence speed }(\%)=\frac{(\text{Higher round }-\text{ Lower round})\times 100}{\text{Higher round}} \tag{6}\]

\[\text{Educed execution time }(\%)=\frac{(\text{Higher execution time }-\text{ Lower execution time})\times 100}{\text{Higher execution time}} \tag{7}\]

## 3 Results

The Improved Fed-RFLP was assessed for its overall model accuracy and benchmarked against various algorithms across different ratios of selected clients. This evaluation was conducted using the MNIST and FMNIST datasets, which respectively represent high and low degrees of Non-IID challenges. The results are shown below. The data depicted in Figure 6 demonstrate that the improved Fed-RFLP exhibits superior global model accuracy compared to alternative client selection algorithms, irrespective of the severity of Non-IID challenges, as substantiated by the results derived from the MNIST and FMNIST datasets. In scenarios characterized by high Non-IID issues, the improved Fed-RFLP significantly outperforms its competitors across all client selection proportions. Conversely, under conditions of low Non-IID challenges, the algorithm provides a modest advantage over alternative approaches. In scenarios characterized by high Non-IID challenges within the MNIST dataset, the improved Fed-RFLP achieves a peak global model accuracy of 96.49% when employing a selection proportion of 10%. This performance demonstrates notable improvements: 10.31% higher than FedAvg (highest accuracy: 86.18% at a 10% selection proportion), 3.06% higher than PoC (highest accuracy: 93.43% at a 2% selection proportion), and 6.27% higher than FedChoice (highest accuracy: 90.22% at a 2% selection proportion). Similarly, in the context of high Non-IID issues within the FMNIST dataset, the improved Fed-RFLP attains a global model accuracy of 89.06% at a selection proportion of 10%. This represents performance improvements of 4.02% higher than FedAvg (highest accuracy: 85.04% at an 8% selection proportion), 3.27% higher than PoC (highest accuracy: 85.79% at a 10% selection proportion), and 1.16% higher than FedChoice (highest accuracy: 87.90% at a 10% selection proportion). \begin{table}
\begin{tabular}{c c} \hline
**Device** & **Specification** \\ \hline Central Processing Unit & 11 th Gen Intel(R) Core(TM) i5-11400F 2.59 \\ GHz \\ Graphics Processing Unit & Radeon (TM) RX 480 Graphics \\ Random Access Memory & 32.0 GB \\ Operating System & Windows 11 \\ Software Environment & Python 3.7.2 with the Pytorch framework \\ \hline \end{tabular}
\end{table} 
Table 1: Hardware specifications for executing the algorithms. In scenarios characterized by low Non-IID challenges within the MNIST dataset, the improved Fed-RHLP achieves a peak global model accuracy of 98.91% with a selection proportion of 4%. This performance demonstrates marginal improvements: 0.44% higher than FedAvg (highest accuracy: 98.47% at a 10% selection proportion), 0.08% higher than PoC (highest accuracy: 98.83% at a 10% selection proportion), and 0.14% higher than FedChoice (highest accuracy: 98.78% with a 4% selection proportion).