## 2 Review of the Improved Clustering Algorithm  
The authors approached the task clustering model and algorithm early in their research using three parts: clustering constraints, the task clustering graph theory model, and the model solving algorithm [1]. The clustering preprocessing is the important part for space mission planning, which could enhance the efficiency of space missions.  
Aiming to clearly demonstrate a two-phase scheduling strategy, here, a brief review of clustering preprocessing is given.  
In the present paper, the practical constraints from the sensors, time window, observation duration, maximum observation time, slewing angle, and pitching angle were considered in building the clustering model. According to the constraints of the satellite clustering task, graph theory was adopted to build the clustering model. A graph \(G=\langle V,E\rangle\) consists of the set of vertices \(V\) and the set of edges \(E\). \(V(G_{i})\) represents the set of tasks that can be observed in the ith orbit of the satellite. \(E(G_{i})\) represents the connecting line of points that meet the clustering constraint in the ith orbit. If \(task_{u}\) and \(task_{v}\) meet the constraint condition, then points \(v_{u}\) and \(v_{v}\) are connected by edge \(e_{uv}\). All the edges satisfy the clustering constraints that comprise \(E(G_{i})\). Thus, the undirected graph model \(G=\langle V,E\rangle\) can be used to represent the satellite clustering in the ith orbit among the observable original tasks.  
Next, the task clustering in the graph model needs to be divided into independent cliques, as shown in Figure 2[1]. Each independent clique represents a clustering task. In order to complete as many tasks as possible without violating the constraint conditions and improve the efficiency of satellite task completion under limited resources, the total number of clustering tasks should be as small as possible after cluster partitioning. This is a minimum clique partitioning problem, which is difficult to solve by a deterministic algorithm, but a heuristic algorithm or intelligent algorithm is generally used to solve it.  
In our earlier research, the classic clique partitioning algorithm was improved, where task priority and minimum slew angle were considered as follows:  
* In the cluster graph, select the edge with the largest number of common neighbors in the edge set.
* If the edge is not unique, select the edge that needs to delete the least number of edges after merging.  
* If the edge is still not unique, select two vertices with higher priority and smaller clustering task slew angle to form the edge.
* Combine the two vertices of the edge into a new virtual vertex and delete the edges associated with the merged vertex to create a new edge. Update the vertex and edge collections.  
Simulation results showed that the improved clique partitioning algorithm based on the graph model is an effective task clustering algorithm that can simultaneously and effectively reduce the task number size, save resources, and improve the observation efficiency [1]. Compared with the graph algorithms [2; 5], the improved clique partition algorithm is relatively simple and more suitable for practical problems.  
The clustering task generated by the above improved clique partitioning algorithm was taken as the input of the following task planning to carry out the optimization design.