# An Accelerated Maximum Flow Algorithm with Prediction Enhancement in Dynamic LEO Networks
## 5 Evaluations
As shown in Figure 6, the running time of all four algorithms increases as the number of time slots rises. However, the proposed warm-starting Ford-Fulkerson algorithm  
Figure 6: Running time comparison of warm-starting FF. Figure 7: Running time comparison of predictive LEO maximum flow. consistently exhibits the smallest running time compared to the other algorithms. This is mainly because the warm-starting Ford-Fulkerson algorithm leverages previously computed flow information from earlier time slots, significantly reducing the time needed for flow calculations in subsequent iterations. In contrast, the e-TEG algorithm performs worse than [PERSON]'s for a smaller number of time slots because it requires additional overhead to update and maintain the time-expanded graph, leading to longer computation times. However, as the number of time slots increases, e-TEG benefits from its energy constraints and dynamic topology adaptation, allowing it to outperform [PERSON]'s algorithm in more complex scenarios. We further calculated the acceleration percentage of the warm-starting Ford-Fulkerson algorithm, shown in Table 2, where it reached a peak of 32.24%. Figure 7 presents a comparative analysis of the acceleration performance between the existing algorithms and the predictive LEO maximum flow algorithm. Notably, the predictive LEO maximum flow algorithm demonstrates a significant reduction in overall running time. This is primarily because predictive LEO maximum flow not only leverages predictive flow acquisition (that is, estimating flow based on past network states) but also incorporates dynamic adaptability to changing network conditions, allowing it to make more efficient routing decisions and minimize the need for recalculations. However, it is slightly less efficient than warm-starting FF in some cases because warm-starting FF directly utilizes historical flow data from earlier time slots, leading to faster convergence and fewer recalculations when network topology changes incrementally. In contrast, predictive LEO maximum flow, while highly efficient, sometimes needs to adjust more dynamically in response to more substantial changes in the network. Table 2 further provides the acceleration percentages achieved by the predictive LEO maximum flow algorithm across varying numbers of time slots. As shown in Table 2, the predictive LEO maximum flow algorithm consistently improves in performance, reaching a peak acceleration of 23.36%. We also considered the impact of satellite storage capacity on algorithm performance, as well as the effect of network scalability in terms of the number of satellites, as shown in Figure 8 and Figure 9, respectively. Figure 8 presents the acceleration percentage of predictive LEO maximum flow for different storage configurations (500 GB, 600 GB, and 700 GB) as the number of time slots varies from 25 to 40. As observed in Figure 8, when available storage capacity decreases, the predictive LEO maximum flow algorithm achieves a higher acceleration percentage. This is because lower storage capacity imposes stricter resource constraints, compelling the algorithm to more effectively utilize its predictive capabilities. With less storage available, the algorithm must make better decisions about data flow management, ensuring more efficient use of computational resources while maintaining high flow throughput. This trend suggests that stricter resource constraints incentivize the algorithm to focus on the \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Time Slots**} & \multicolumn{3}{c}{**Acceleration Percentage**} \\ \cline{2-3}  & **Warm-Starting FF** & **Predictive LEO Maximum Flow** \\ \hline
25 & 16.67\% & 7.64\% \\
30 & 26.15\% & 25.13\% \\
35 & 18.55\% & 12.22\% \\
40 & 23.13\% & 14.55\% \\
45 & 28.62\% & 17.54\% \\
50 & 31.51\% & 20.10\% \\
55 & 32.24\% & 23.36\% \\
60 & 28.00\% & 23.00\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Acceleration percentage of warm-starting FF and predictive LEO maximum flow compared to e-TEG.