## 2 Related Works
### Main Algorithm Ideas and Contributions of the Paper  
In this paper, the constellation is assumed to consist of N satellite nodes.  
\[\text{Topo}=\begin{bmatrix}a_{11}&\cdots&a_{1N}\\ \vdots&\ddots&\vdots\\ a_{N1}&\cdots&a_{NN}\end{bmatrix}\]  
The Topo table represents the direct distance between two star nodes. For instance, \(a_{11}\) represents the distance from the No. 1 satellite to the No. 1 satellite, and the distance of course is 0. \(a_{ij}\) represents the direct distance from the No. i satellite to the No. j satellite [12; 13].  
Inspired by the above research, we propose a balanced routing algorithm based on the partition routing idea. In the original partition routing algorithm, as long as the communication nodes between two partitions have problems, the mutual communication will be affected [14] and the balanced partition routing algorithm determines the external communication nodes between partitions in a dynamic way. If the original optimal communication nodes have problems, our algorithm will consider the distance between the original communication nodes to be infinite. Then, the algorithm will immediately update and calculate the new communication node, so that the destruction resistance will be greatly enhanced [15].  
In this paper, N star nodes are divided into three groups. Star nodes in group A are numbered 1 through \(\frac{\text{N}}{3}\). By parity of reasoning, nodes in group B are numbered \(\frac{\text{N}}{3}+1\) through \(\frac{\text{2N}}{3}\) and nodes in group C are numbered \(\frac{\text{2N}}{3}+1\) through N. The direct communication distance and the variance of the distance between star nodes in the same group are smaller. \(a_{ij}\) approximately satisfies the following relation:  
\[\left\{\begin{array}{c}a_{ij}\sim N\big{(}\mu_{1},\;\sigma_{1}^{2}\big{)},\; i,\;j\subseteq\varphi\\ a_{ij}\sim N\big{(}\mu_{2},\;\sigma_{2}^{2}\big{)},\;i\subseteq\varphi,\;j \
subseteq\varphi\end{array}\right.\]  
In the above formula, \(\mu_{1}>\mu_{2},\;\sigma_{1}^{2}>\sigma_{2}^{2}\), \(\varphi\) refers to one group [16]. The algorithm first calculates the two nearest star nodes between each group, and these two star nodes serve as the gateway communication nodes between each group. For instance, the routing path between node No. i and node No. j needs to be calculated. The specific algorithm is as follows:  
1. If node No. i and node No. j belong to the same group, then we only need to address the route within the group. The routing algorithm within the group performs the partial flooding and greedy algorithm at the same time and selects the shorter one as the final routing path.
2. In the other case where node No. i and node No. j do not belong to the same group, then we need to calculate the two nearest communication nodes between the two groups that node No. i and node No. j belong to. It is assumed that these two star nodes are node No. i + m and node No. j + n. Finally, the algorithm needs to calculate the shortest routing paths from node No. i to node No. i + m and from node No. j + n to node No. j. Therefore, our final routing path is No. i ->No. i + m ->No. j + n ->No. j.  
The simulation results reveal that compared with other algorithms, the proposed balanced partition routing algorithm achieves better performance.  
In the latter part of this paper, the balanced partition routing algorithm was further explored. We have yet to explore two different optimization directions on the premise of further reducing the computational pressure of a single node. One way is to divide a large group into smaller groups (which can be interpreted as smaller groups belonging to a larger group), and the other way is to divide nodes into more groups directly. Experimental results show that these two optimization methods can further reduce the complexity of the algorithm. What is more, the hardware cost of nodes is greatly reduced. Finally, thesetwo optimization ideas can make the algorithm adapt to various application scenarios and have better flexibility.