## 3 Algorithmic Mathematical Analysis
### Analysis of Hardware Architecture Cost  
The inter-star model is composed of nine star nodes. We randomly conducted 1000 communication missions among these star nodes. We only considered the calculation power consumption of these nodes in calculating the routing path, and the energy consumption of the nodes is positively correlated with the calculation amount. In the actual space environment, the payload of the satellite relies on solar panels to collect solar energy to provide energy. Table 1 shows the calculation amount for the routing calculation for each node under different algorithms in a simulation experiment. Something that looks like \(10^{12}\) or \(10^{5}\) is an order of magnitude. The amount of computation here is expressed only in numbers, not in units. The larger the value is here, the greater the amount of computation performed on this node. This means that this node will consume more power and require higher hardware costs. According to the principle of reliability, since we do not know the calculation pressure of each node in advance, the design index of each node should refer to the node with the largest calculation pressure. For example, in this experiment, the design index of the satellite nodes should refer to the No. 1 star under the flooding algorithm, and the No. 6 star under the greedy algorithm. In other words, the actual hardware design cost of satellite nodes is mainly determined by which node bears the most computational pressure. In order to increase the reliability of the experiment, we conducted a total of 10 experiments. In Table 2, we omit the computation amount of each star node under various algorithms and only show the numerical value of the node with the most computation in each experiment. It can be seen from this table that the computing capacity requirements of the flooding algorithm for the nodes are not in the same order of magnitude as those of the other three \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Types of Algorithms** & **Gredy** & **Flooding** & **Partition Routing** & **Balanced** \\
**Flooding** (\(10^{12}\)) & 13.04 & 1.75 & 2.89 & 1.28 & 5.38 & 8.57 & 2.25 & 4.11 & 9.51 \\ \hline
**Greedy** (\(10^{4}\)) & 0.09 & 2.73 & 1.00 & 1.99 & 1.34 & 21.9 & 12.8 & 2.37 & 2.62 \\ \hline
**Partition routing** (\(10^{5}\)) & 6.11 & 6.36 & 5.22 & 7.31 & 5.45 & 6.26 & 6.21 & 6.32 & 6.25 \\ \hline
**Balanced partition routing** (\(10^{5}\)) & 7.62 & 7.70 & 7.71 & 7.67 & 7.88 & 7.63 & 7.67 & 7.64 & 7.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Amount of computation for each node. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sequence** & **Greedy** & **Flooding** & **Partition Routing** & **Balanced** \\
**Partition** & **Partition** \\
**Routing** (\(10^{5}\)) \\ \hline
1 & 2.19 & 13.04 & 7.31 & 7.88 \\ \hline
2 & 1.21 & 9.63 & 6.29 & 7.99 \\ \hline
3 & 7.41 & 9.99 & 6.38 & 8.06 \\ \hline
4 & 3.53 & 3.92 & 6.72 & 8.09 \\ \hline
5 & 1.75 & 1.26 & 6.02 & 8.08 \\ \hline
6 & 6.44 & 2.57 & 5.98 & 8.16 \\ \hline
7 & 5.32 & 19.9 & 5.68 & 8.14 \\ \hline
8 & 8.01 & 3.78 & 6.48 & 8.18 \\ \hline
9 & 2.11 & 2.82 & 6.46 & 8.28 \\ \hline
10 & 1.07 & 6.11 & 6.18 & 8.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Largest amount of computation for single node in each experiment. algorithms. If the flooding algorithm is used, the hardware cost for the star nodes will be very large. In theory, the average calculation pressure of each node of the greedy algorithm should be far less than that of the partition routing algorithm and balanced partition routing algorithm. However, each route calculation of the greedy algorithm can only be completed by one node independently and cannot be dispersed to multiple nodes. It leads to great calculation pressure on some nodes. According to our simulation results, the node with the greatest computational pressure of the greedy algorithm is the same order of magnitude as that of the two partition routing algorithms, and the hardware cost among them is also close.