## 1 Introduction
### Literature Review on the Inter-Satellite Routing Algorithm  
Although the inter-satellite routing problem has been a research topic and challenge in low-orbit satellite networks, which has led to many related studies [5; 6], it still has received less attention compared to other types of satellite scheduling such as satellite imaging and measurement scheduling [7; 8; 9]. Based on the routing characteristics, the existing satellite network routing algorithms can be divided into centralized and distributed routing algorithms, static routing, and dynamic routing algorithms. According to the constellation topology dynamic processing method, it can be further divided into routing algorithms based on the virtual topology method and the virtual node method. Some representative routing schemes are discussed below. The main idea of the centralized routing algorithm is to compute the optimal route solution for all tasks uniformly while avoiding constraint violations. [PERSON] et al. [10] established software-defined networking (SDN) to handle multi-route TCP for Low Earth Orbit (LEO) satellite constellations. The SDN framework with a centralized method enhances system scalability but also increases system complexity making it difficult to solve large-scale routing problems. The advantage of distributed routing algorithms is that each satellite node in the constellation network calculates its route individually [11], reducing the transmission cost of a large number of messages in the network [12] and eliminating the  
Figure 1: Task transmission process of low-orbit constellation network. requirement for a centralized control center [13]. Utilizing a distributed framework, [PERSON] et al. [14] proposed a datagram routing algorithm to solve the LEO satellite network problem. Moreover, to improve the system flexibility and facilitate the management of ground facilities, [PERSON] et al. [15] developed a location-assisted on-demand routing protocol (LAOR), and the LAOR protocol showed better results in comparison with centralized routing protocols. However, some situations where the topology of the satellite network is constantly changing [16] also greatly increase the difficulty of studying inter-satellite routing algorithms. Therefore, many researchers classified routing characteristics into static and dynamic routing. [PERSON] et al. [17] considered the LEO satellite network as a finite-state automaton (FSA), where the FSA framework converted a link assignment problem in a satellite network into a set of link assignment problems in a fixed topology network. Their simulation results showed that a static routing algorithm performed better than a dynamic routing algorithm for the same link assignment scenario. However, [PERSON] et al. [18] argued that dynamic routing algorithms must be used in dynamic satellite networks. Compared to static routing algorithms, dynamic routing algorithms were better suited to deal with unexpected situations such as node and link changes and network congestion. Therefore, [PERSON] et al. proposed a simple distributed GomHop autonomous routing algorithm for a low-orbit mega constellation. Later, [PERSON] et al. [19] proposed a novel Temporal Netgrid Model (TNM) for the problem of traditional routing algorithms that cannot handle satellite trajectories, and they developed an efficient Netgrid-based Shortestroute Routing (NSR) algorithm based on the TNM. Nevertheless, inter-satellite routing problems have become more and more complex as user requirements have increased. The shortcomings of dynamic routing algorithms in dealing with inter-satellite routing problems have gradually emerged. Therefore, some researchers have adopted a \"divide and conquer\" approach to the inter-satellite routing problem. The specific idea is to use the proposed virtual topology method [20] to deal with the satellite topology change problems. Then, some congestion avoidance and load-balancing routing algorithms [21; 22] were designed to solve the routing problems.