## 2 Literature Review  
Due to the dynamic topology of networks, the limited resources of satellites, and the imbalanced demands of users, ground routing strategies are deemed unsuitable for satellite networks. Consequently, extensive studies had been conducted in the routing of LEO satellite constellations. In this section, we review the recent works in LEO satellite routing. Existing studies have extensively researched routing in satellite networks, and the mainstream routing algorithms can be divided into two types: static routing and dynamic routing. The static routing algorithm discretizes the network topology in time and space and then makes routing decisions, e.g., the \"snapshot\"-based routing algorithm [27] and the Contact Graph Routing (CGR) algorithm [28]. However, the static routing algorithm cannot be changed in real time according to network status, resulting in a lack of flexibility and fault tolerance [37]. Dynamic routing algorithms make routing decisions by obtaining real-time state information about the satellite network [29; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58  
tables based on network information, reducing the routing calculation overhead. In [31], [PERSON] et al. proposed a status and reputation-adaptive-based dynamic routing (SRADR) algorithm that introduces security attributes expressed in terms of node reputation, which guarantees the security of the path while deciding the path with the shortest delay. The above algorithms are mainly based on the shortest path, which selects a path with the least forwarding nodes during traffic transmission. However, as the amount of traffic in the network increases, the satellite nodes on the shortest path will carry a large amount of traffic flow, which results in an unbalanced network load. Because of this, a series of load balancing routing algorithms have been proposed. The segmentation routing-based load balancing algorithm [32] dynamically divides the light- and heavy-traffic-load areas, adopting the snapshot routing algorithm in the light-traffic-load areas and adopting the minimum weight path defined by the congestion index as the routing rule in the heavy-traffic-load areas. The QoS routing algorithm considers energy consumption (QER) [33] and adjusts the next-hop forwarding node according to the node cache queue size and remaining energy to control the link traffic. Distributed routing algorithms based on neighbor satellite load status [39] alleviate the network condition of satellite congestion by introducing mechanisms such as adjacent satellite load state updating, load balancing, and route adjudication, obtaining low-latency and low-packet-drop rate paths. However, the above algorithms do not take into account the SFC constraints for traffic transmission and are not suitable under the new network architecture. There have been few efforts to investigate the routing strategy satisfying SFC constraints in the LEO-MSN. In [33], the joint optimization of NFV deployment and routing strategy in the space-air-ground integrated network was studied without considering the time-varying characteristics of this network. In [26], the routing problem in LEO-MSN was studied by considering the SFC constraints; however, there is a lack of consideration of factors such as end-to-end link, channel modeling, and network node load. In [34], [PERSON] et al. introduce an effective Deep Reinforcement Learning (DRL) approach to effectively tackle the SFC routing problem in LEO-MSN. Previous studies have explored the routing problem in LEO-MSN from several angles, which has laid a good foundation for the study of routing strategies. However, considering the new network architecture, there is still room for improvement in the current study.