## 3 Dynamic Link Establishment of Mega-Constellations
### Simulation Analysis
The latter significantly outperforms the former two, being 20 times better than the greedy algorithm and 6 times better than the standard general graph maximum weight-matching algorithm, demonstrating the superiority of this strategy. Additionally, the algorithm with the elite retention strategy exhibits the longest average link duration, being 20 times that of the greedy algorithm and 2 times that of the standard general graph maximum weight-matching algorithm. Moreover, it performs best in terms of the average number of topological changes, showing fewer changes compared to the standard algorithm, which requires optimal matching at all times, potentially leading to premature disconnections and an increased frequency of topological changes. In summary, although in some cases the standard general graph maximum weight-matching algorithm surpasses the version with the elite retention strategy, when the latter performs better, its superiority is far more pronounced, sometimes demonstrating an order-of-magnitude improvement in effectiveness, thus proving its superiority in dynamic link matching. Therefore, the elite retention strategy remains a proven effective and applicable method for dynamic link matching. The above content compares the algorithms [24; 25]. Next, this study validates the superior performance of the satellite-to-satellite topology structure established by the proposed algorithm in terms of its configuration compared to the traditional Manhattan configuration. Taking the communication delay between Los Angeles, United States, and \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Heading Level**} & \multirow{2}{*}{**Greedy Algorithm**} & \begin{tabular}{c} **Maximum Weight-Matching** \\ **Algorithm for General** \\ **Graphs** \\ \end{tabular} & \begin{tabular}{c} **Maximum Weight-Matching** \\ **Algorithm for General** \\ **Graphs with Elite Strategy** \\ \end{tabular} \\ \hline \begin{tabular}{c} Average Duration of Maximum \\ Links/min \\ Average Duration of Maximum \\ Links/s \\ Average Duration of Links/s \\ Average Topology Change Count \\ Number of Satellites with No \\ Dynamic Links per Time Slice \\ (maximum/minimum) \\ Average Time with No Dynamic \\ Links per Satellite/min \\ \end{tabular} & 7.51 & 31.17 & 20.88 \\ \begin{tabular}{c} Average Duration of Maximum \\ Links/s \\ \end{tabular} & 3.08 & 11.92 & 62.69 \\ \
\begin{tabular}{c} Average Duration of Links/s \\ Average Topology Change Count \\ Number of Satellites with No \\ Dynamic Links per Time Slice \\ (maximum/minimum) \\ Average Time with No Dynamic \\ Links per Satellite/min \\ \end{tabular} & 23.95 & 216.01 & 429.06 \\
\begin{tabular}{c} Number of Satellites with No \\ Dynamic Links per Time Slice \\ (maximum/minimum) \\ 55.05 \\ \end{tabular} & 25.0 & 39 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the three algorithms. Xiamen, China, as an example, only the propagation delay (not the transmission delay) is considered, and the Dijkstra algorithm is used to calculate the shortest path. Due to space limitations, this paper does not present the specific implementation of the Dijkstra algorithm, but directly presents the propagation delay results based on this algorithm for the Los Angeles-Xiamen route. Table 4 lists the latitude and longitude data for Los Angeles and Xiamen. Before calculating the communication delay, it is essential to determine the satellite connections directly above the coordinates of both cities at each moment. In this study, the proximity principle is adopted, assuming that, at each moment, both Xiamen and Los Angeles establish connections with the nearest satellite directly above them. The dynamic links obtained using the general graph maximum weight-matching algorithm proposed in this research, which incorporates an elite retention strategy, serve as the configuration for the \"3 + 1\" topology scheme. This configuration is then compared to the traditional Manhattan configuration, which does not utilize dynamic links. The simulation results are shown in the figure below.