## 3 Dynamic Link Establishment of Mega-Constellations
### Simulation Analysis  
The simulation commenced at 04:00:00 UTCG on 29 January 2024 and concluded at 05:35:39 UTCG on 29 January 2024. The simulation time step was set to 3 s.  
Initially, based on the general graph maximum weight-matching algorithm, the solution was derived to calculate the continuous connection duration for each satellite. According to the graphical representation shown in Figure 14, the average maximum link duration computed by the maximum weighted matching algorithm for general graphs is 1870.4 s (approximately 31.17 min), whereas the average minimum link duration is 11.92 s, and the overall average link duration stands at 216.00 s. The minimum link duration determines the frequency of link switches, and while comparing with the results from the greedy algorithm, it is evident that the solution provided by the maximum weighted matching algorithm significantly improves upon it, yet an average link duration of 11.92 s remains excessively short for normal link switching operations. Subsequently, we proceed to solve for the number of topological changes, as shown in Figure 15.  
After calculating an average of 250 topological changes, we determined the average topological stability time to be approximately 23.0678 s using Formula (8). Comparing this with the previously found average link duration of 216.00 s, we observe a significant difference, indicating that satellite connections typically last much longer. This suggests that the maximum weighted matching algorithm for general graphs tends to result in longer durations of unconnected dynamic links for satellites. M  
Figure 13: Maximum weight-matching algorithm flowchart with the elite retention strategy. a variant of this algorithm incorporating an elite retention strategy and present the resulting satellite connection durations in Figure 16.  
Upon processing the data, the application of the elite retention strategy within the maximum weighted matching algorithm for general graphs resulted in an average maximum link duration of 1252.8 s (approximately 20.88 min), with an average minimum link duration of 62.69 s and an overall average link duration of 429.0628 s. In comparison with the outcomes of the conventional maximum weighted matching algorithm for general graphs, the improved version notably enhances the minimum average duration, which now falls within a reasonable range for low-Earth-orbit satellite connections. Consequently, this modification contributes to enhanced system performance. We conducted a qualitative analysis of the number of topological changes and average link duration under the elite retention variant of the maximum weighted matching algorithm for general graphs, as shown in Figure 17.  
Figure 14: Satellite persistent connection time with the maximum weight-matching algorithm for general graphs. Figure 15: Topology change count and average stability time with the maximum weight-matching algorithm for general graphs. The average number of topological changes in the maximum weighted matching algorithm for general graphs employing an elite retention strategy was computed to be 39 occurrences. This represents a significant improvement over both the greedy algorithm and the standard maximum weighted matching algorithm, highlighting the advanced nature of the improved algorithm. Subsequently, a comprehensive horizontal and vertical comparative analysis of the data from both algorithms will be conducted. In the horizontal comparison, we focus on the performance of two algorithms in each time slice. By counting the number of satellites without dynamic links in each time slice, we can assess the immediate efficiency of the algorithms. Figure 18 presents the count of satellites without dynamic links in each time slot, determined by the general graph maximum weight-matching algorithm and the same algorithm incorporating an elite retention strategy. The blue line represents the general graph maximum weight-matching algorithm, showing significant performance variability across different time intervals.