## 3 Dynamic Link Establishment of Mega-Constellations
### Simulation Analysis
These fluctuations may reflect changes in the spatial configuration of the satellites and variations in the resource availability. In certain time slots, the blue line indicates a noticeable increase in the number of satellites without dynamic links, suggesting a lower resource allocation efficiency during these periods. Figure 16: Satellite persistent connection time with the maximum weight-matching algorithm for general graphs with the elite retention strategy. Figure 17: Topology change count and average stability time with the maximum weight-matching algorithm for general graphs with the elite retention strategy. In contrast, the red line represents the algorithm augmented with the elite retention strategy. The red line demonstrates that this algorithm maintains a consistently lower and relatively stable number of satellites without dynamic links throughout most time intervals. This indicates that the elite retention strategy effectively reduces satellite disconnections and significantly enhances the resource allocation efficiency and stability. Regardless of high- or low-resource-demand periods, the red line consistently exhibits superior performance, showing that this strategy is more flexible and effective in handling varying conditions. The vertical comparison focuses on the overall performance of the algorithms throughout an entire orbital period. By calculating the total time each satellite is without dynamic links during the orbital period, we can evaluate the long-term efficiency of the algorithms. Figure 19 is a graph showing the total time for each satellite without dynamic links calculated by the general graph maximum weight-matching algorithm and the total time for each satellite without dynamic links calculated by the general graph maximum weight-matching algorithm with an elite retention strategy. The blue line in this picture shows that the average total time without dynamic links for the general graph maximum weight-matching algorithm is 3.5773 min within the orbital period, which, although improved, still has room for enhancement. In contrast, the red line in this picture indicates that the algorithm with the elite retention strategy reduces this time to 5.0804 min, further optimizing the connection efficiency. Data computations show that, on average, each satellite lacks dynamic links for 5.0804 min when employing the maximum weighted matching algorithm for general  
Figure 19: Vertical comparison results. Figure 18: Horizontal comparison results. graphs with an elite retention strategy. Subsequently, a summary of the outcomes for the three algorithms under consideration is presented in Figure 13:0  
Comparing the results of the greedy algorithm, the general graph maximum weight-matching algorithm, and the general graph maximum weight-matching algorithm with the elite retention strategy, we can draw the following conclusions: Firstly, in terms of average maximum link duration, the greedy algorithm yields the shortest duration. This is because the greedy algorithm only considers the current satellite being traversed, which can lead to subsequent satellites being unable to connect with those that could potentially yield longer connections. In contrast, the general graph maximum weight-matching algorithm may encounter scenarios where most satellites have relatively short remaining connection times with other satellites, while a few have significantly longer periods, causing these satellites to remain connected until the end. However, the general graph maximum weight-matching algorithm with the elite retention strategy ensures that each satellite connects to others in its best possible state, which might slightly reduce the maximum connection time but still outperforms the greedy algorithm. In terms of the average minimum link duration, the performance improves progressively from the greedy algorithm to the general graph maximum weight-matching algorithm, and further to the one with the elite retention strategy, with durations extending accordingly.