## 1 Introduction  
Space-air-ground integrated networks (SAGINs) are multi-domain dynamic networks that comprise satellite networks for communication, navigation, and meteorology; unmanned aerial vehicle networks; and ground-based wired and wireless network facilities. These networks can be flexibly deployed to provide wide coverage and high applicability. As such, SAGINs have the potential to enable a range of critical applications, including disaster response, search and rescue, and remote sensing, among others [1, 2]. Unmanned aerial vehicle networks play a bridging role, enabling the interconnection of satellite and ground-based networks by undertaking data transmission and communication relay tasks to achieve goals such as information sharing and collaborative work [3]. The rapid development of integrated air-space networks is therefore partly due to research related to unmanned aerial vehicles (UAVs) [4]. UAVs are often referred to as drones [5], and in recent years, with the development of automation and radio technology, UAVs have been used in a wide range of applications, including but not limited to field rescue, cargo transportation, industrial monitoring, and communication relay operations. In SAGINs,flying ad hoc networks (FANETs) are formed by the collaboration of multiple UAVs, at least one of which is connected to a ground station or satellite. FANETs can perform complex and variable missions at a lower cost, with greater efficiency, and in a more hostile environment. In the context of SAGINs, FANETs find broader applications in assisting communication and improving communication efficiency. A FANET can serve as an aerial base station to provide communication services for users in cellular networks [6]. Additionally, FANETs can assist edge computing by offloading computational tasks when IoT devices exceed their computational capacity. Failure to process tasks promptly may result in significant response latency, which the FANET can alleviate by supporting local devices such as vehicular networks through computation offloading [7]. Furthermore, with the development of the sixth-generation mobile communication system (6G) in the era of ubiquitous connectivity [8], there is a demand for higher quality and more precise communication links. UAVs can integrate with intelligent computing to achieve communication awareness through resource allocation and route planning [9]. Although the participation of FANETs effectively expands the network dimensions of SAGINs and enhances network resilience, whether it is assisting ground cellular network communication, task offloading, or achieving communication awareness, a set of excellent routing strategies is essential to support these functionalities. FANETs have the following characteristics due to the unique physical characteristics of the UAVs:  
* High dynamics: The stability of the routing path is greatly affected by the rapid speed of the drone's movement through the air [10]. * High loss of connection rate: Due to the flight height, terrain, and weather of the UAV, there will be situations where the UAV loses connection with ground nodes or other UAVs [11]. * Low bandwidth and high latency: Due to the long communication distance between UAVs, the communication signal is affected by factors such as atmosphere and terrain. The communication bandwidth is low, and the communication latency is high [12]. * Energy consumption limitation: The energy consumption of UAVs is limited by the fact that the batteries or fuel that sustain them and communicate with them cannot be replenished in real time in the same way as the ground network [13; 14]. Efficient and reliable routing algorithms can effectively improve the efficiency and reliability of packet transmission in the FANETs and reduce network congestion and service interruptions. The routing algorithm is also the key link to ensuring proper communication in FANETs.