## 2 Materials and Methods
### Developing the Improved Federated RHLP Algorithm for Efficient Client Selection
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Algorithm**} & \multirow{3}{*}{**Issue Level**} & \multirow{3}{*}{
\begin{tabular}{c} **Accuracy** \\ **of Global** \\ **Model** \\ \end{tabular} } & \multicolumn{6}{c}{**Convergence Rounds and Time (Seconds) with Different Accuracy**} \\ \cline{3-10}  & & & \multicolumn{2}{c}{**60\%**} & \multicolumn{2}{c}{**70\%**} & \multicolumn{2}{c}{**80\%**} & \multicolumn{2}{c}{**90\%**} \\ \cline{3-10}  & & & **Round** & **Time** & **Round** & **Time** & **Round** & **Time** & **Round** & **Time** \\ \hline improved & High & 89.06\% & 6 & 1288.8 & 11 & 2362.8 & 15 & 3222 & - & - \\ \cline{2-10} Fed-RILP & Low & 90.97\% & 1 & 328.2 & 2 & 656.4 & 7 & 2297.4 & 48 & 15,753.6 \\ \hline FedAvg & High & 83.68\% & 13 & 2386.8 & 23 & 4222.8 & 55 & 10,098 & - & - \\ \cline{2-10}  & Low & 90.59\% & 3 & 747 & 3 & 747 & 3 & 747 & 83 & 20,667 \\ \hline \multirow{2}{*}{PoC} & High & 85.97\% & 8 & 1929.6 & 9 & 2170.8 & 39 & 9406.8 & - & - \\ \cline{2-10}  & Low & 90.77\% & 3 & 1072.8 & 5 & 1788 & 6 & 2145.6 & 85 & 30,396 \\ \hline \multirow{2}{*}{FedChoice} & High & 87.90\% & 8 & 1934.4 & 12 & 2901.6 & 21 & 5077.8 & - & - \\ \cline{2-10}  & Low & 90.63\% & 2 & 714 & 4 & 1428 & 6 & 2142 & 59 & 21,063 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance metrics for the global model on the Non-IID FMNIST dataset. Figure 7: Accuracy of the global model based on the proportion of selected clients that achieve the highest global model accuracy. (**a**) Accuracy of global model in high-level Non-IID issue in MNIST. (**b**) Accuracy of global model in low-level Non-IID issue in MNIST. (**c**) Accuracy of global model in high-level Non-IID issue in FMNIST. (**d**) Accuracy of global model in low-level Non-IID issue in FMNIST. From Tables 2 and 3, the testing results on the MNIST and FMNIST datasets demonstrate that the improved Fed-RHLP exhibits significant advantages in addressing high Non-IID levels compared to other algorithms. In the context of the MNIST dataset characterized by high Non-IID challenges, the improved Fed-RHLP demonstrates exceptional performance, achieving an accuracy of 96.49%. This result surpasses that of FedAvg, PoC, and FedChoice by margins of 10.31%, 6.18%, and 8.69%, respectively. At an accuracy level of 80%, Fed-RHLP exhibits both faster convergence and reduced execution time compared to all other algorithms. Most notably, it reaches 90% accuracy within merely 41 communication rounds, which represents a 77.84% improvement over PoC, accompanied by a 74.51% reduction in execution time. In scenarios with low Non-IID levels, Fed-RHLP significantly outperforms FedAvg, achieving an 80.77% enhancement in convergence speed and a 58.79% decrease in execution time. Additionally, the algorithm marginally exceeds the performance of PoC and FedChoice. In the context of the FMNIST dataset characterized by high Non-IID challenges, the improved Fed-RHLP demonstrates a peak accuracy of 89.06%. This performance exceeds that of FedAvg, PoC, and FedChoice by margins of 5.38%, 3.27%, and 1.16%, respectively. When achieving an accuracy of 80%, Fed-RHLP exhibits remarkable convergence characteristics: 72.73% more rapid convergence than FedAvg, 61.54% faster than PoC, and 28.57% quicker than FedChoice. Correspondingly, the algorithm achieves significant reductions in execution time: a 68.09% reduction compared to FedAvg, a 65.75% reduction compared to PoC, and a 36.55% reduction compared to FedChoice. In scenarios with low levels of Non-IID, Fed-RHLP demonstrates a marginal advantage over FedAvg, PoC, and FedChoice. In summary, the improved Fed-RHLP exhibits greater efficiency and precision in managing elevated Non-IID levels across both datasets, showing notable advancements in convergence speed and execution duration when compared to alternative algorithms. ## 4 Discussion and Conclusions

This paper presents an enhanced version of the Fed-RHLP algorithm designed to address challenges posed by Non-IID data distributions.