## 4 Experimental Results
### Computation Time  
Figure 16 presents the computation times for the MDP and greedy algorithms as functions of the total number of targets, with the data displayed on a logarithmic scale. This visualization underscores the correlation between increased computation times and the rising numbers of both targets and satellites. It specifically highlights the exponential growth in computational demand as the number of satellites increases, a factor that is precisely plotted to illustrate its impact on computational time. Upon detailed analysis, it becomes apparent that the volume of targets exerts a more substantial impact on the computational complexity than does the satellite count. This augmented complexity primarily arises from the intricacies of generating sub-problems. Specifically, as the target  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Statistic** & **MDP (Hour)** & **Greedy (Hour)** \\ \hline Mean & **6.08** & 7.80 \\ Standard deviation & **3.77** & 6.00 \\ Minimum & 1.48 & **0.78** \\
25 th percentile & **3.20** & 3.48 \\ Median & **5.13** & 6.25 \\
75 th percentile & **8.23** & 9.49 \\ Maximum & **17.84** & 23.56 \\ \hline \hline \end{tabular} The bold text indicates the best parameter values for the two algorithms.  
\end{table}
Table 4: Statistics of mean revisit time.  
Figure 15: Box plot of mean revisit time.  
count increases, the task of calculating each target's visibility window and the intervals between them necessitates a significant escalation in computational resources.  
A comparative assessment reveals that, across all tested scenarios, the greedy algorithm outperforms the MDP algorithm in computation time, especially in complex scenarios involving 1000 targets, where greedy's computation time is merely 101 s compared to MDP's 998 s. This efficiency of greedy stems from its strategy of optimizing each sub-problem individually for immediate results, in contrast to MDP, which assesses the overall benefit pathway, leading to a more thorough optimization at the cost of longer computation times. However, despite its DP-based nature, MDP manages to complete even the most computationally demanding scenarios within a reasonable timeframe. With advancements in computing powers such as CPU and RAM, it is feasible to significantly reduce computation times, establishing the MDP algorithm's suitability for satellite constellation mission planning by providing higher objective function outcomes efficiently. This underscores the need to balance algorithmic efficiency with optimization potential in computational resource allocation for complex tasks.  
Furthermore, an interesting aspect of the computation times for both the MDP and greedy algorithms emerges when considering the interplay between the number of targets and satellites. While the computation time for the greedy algorithm increases directly with the number of targets and satellites, the MDP algorithm displays a more complex pattern of behavior. Specifically, scenarios with a lower count of satellites have occasionally demanded more computational time than those with a higher count. This observation is tied to the mission success rates discussed in Section 4.3. For example, an MDP scenario with 40 satellites and 1000 targets reaches a 100% mission success rate by 3 January, whereas, with only 8 satellites, a 95% success rate is only achieved by 7 January. This indicates that scenarios with fewer satellites, despite their reduced satellite count, incur greater computational demands due to the prolonged duration required to achieve mission success. In contrast, scenarios employing the greedy algorithm for 1000 targets fail to reach a 100% mission success rate by 7 January, regardless of the satellite count, necessitating ongoing mission planning throughout the seven-day period. This scenario accounts for the relatively shorter computation times observed in situations with fewer satellites.  
Figure 16: Computation time comparison of MDP and greedy algorithms under all test cases.