## 1 Introduction  
Due to the advantage of large coverage and little limitation of ground geographical conditions, a micro-satellite network has become an effective means to provide communication service in areas where ground communication facilities are difficult to cover. In recent years, many countries and companies have put forward plans to build a new generation of micro-satellite networks, setting off a boom in satellite network research [1]. For instance, the commercial rocket company SpaceX launched a star-link project to provide Internet service to remote areas [2]. What is more, Tsinghua University has proposed the plan of GRID (Gammy Ray Integrated Detectors) to explore astrophysics.  
Different from the ground network, the constant motion of satellites will inevitably bring about frequent switching of links between satellites. These switches result in the constant changes in the topology of the whole satellite network, and the routing information needs to be updated accordingly. Therefore, routing algorithms have a great influence on the efficiency of inter-satellite communication and have become one of the hot topics [3, 4]. In satellite networks, the transmission cost of a path is mainly determined by propagation delay and waiting delay. Compared with the ground network, the distance between satellite nodes is longer, so the propagation delay occupies a larger proportion of the total delay. This paper focuses on the end-to-end shortest delay routing algorithm.  
At present, mainstream inter-satellite routing algorithms still have their limitations. Current real-time dynamic routing algorithms mainly include flooding and backtrackingalgorithm and the greedy algorithm. The principle of the flooding and backtracking algorithm is to traverse every inter-satellite node and compare the length of each path to find the shortest path [5]. This algorithm needs to backtrack to find out which one of these paths goes through fewer inter-satellite nodes or if more than two paths have the same path length. Hence, its advantage is that the routing path calculated must be the optimal path. On the other hand, the algorithm has too much calculation and poor scalability. The routing strategy of the greedy algorithm is to find the nearest node under the condition of a local optimal path. The greedy algorithm has a small amount of calculation while the path calculated is usually not the globally optimal path. Both the flooding algorithm and the greedy algorithm have major drawbacks. For these two algorithms, the calculation of the routing path must be completed by a single star node at a time. This means that the computational burden cannot be shared by multiple nodes. When the actual system is running, the inter-star traffic cannot be evenly distributed to each star node, and the calculation pressure of some star nodes is too high. However, it is not known in advance which star nodes will have high computational pressure, so redundancy design can only be carried out to ensure reliability. We know that satellites are powered by solar energy to perform all kinds of calculations in space, and more satellites need to install larger solar panels, which will greatly increase the cost of satellite hardware [6; 7; 8].  
This paper has the following structure: Section 2 presents related work on academic achievements of predecessors and the main contribution of the paper; Section 3 provides a mathematical analysis of the inter-satellite routing algorithm; two optimization directions of the balanced partition routing algorithm are discussed in Section 4; lastly, Section 5 summarizes the work.