## 1 Introduction
However, due to the nature of FANETs, the FANET routing algorithms need to consider factors such as the location, speed, and direction of the UAVs to adjust the routing path in a timely manner. In addition, the rejoining of nodes and re-establishment of routes due to the loss of UAVs need to be taken into account. Finally, communication quality needs to be guaranteed within energy consumption limits while meeting the individual needs of users and operators. We have investigated the latest reviews in FANET-related fields, and several researchers have surveyed and summarized aspects of UAV-related fields in recent years. [PERSON] et al. [15] in 2020 proposed a graph-classification-based classification method for the UAV routing problem and summarized the latest research progress on existing UAV routing and scheduling problems, which is more complete but has a different focus from this paper. In October of the same year, [PERSON] et al. [16] addressed the UAV routing problem but focused on UAV safety with extensive research on UAV collision avoidance and connectivity. [PERSON] et al. [17] reviewed various routing protocols for wireless sensor networks and summarized the challenges facing the UAV sensor network industry. [PERSON] et al. [18] discussed UAV communication network characteristics, design, applications, and routing protocols, focusing on the quality of service (QoS) and power aspects of the study. In addition, [PERSON] et al. 's [19] survey was based on four communication architectures under FANET. The above studies all differed in the direction and focus of their investigations. Our main objective is to gain insight into current research trends in UAV self-assembled network routing algorithms for the application of air-space integrated networks and to outline possible future research directions. Specifically, this paper makes the following contributions:  
* In this paper, we review 48 relevant articles, which were published in the past five years and represent the latest research advancements in routing algorithms. We conduct an in-depth analysis of the limitations of these routing algorithms. * We categorize existing routing algorithms into eight major classes and discuss the optimization directions for each class. Additionally, we provide insights into the research directions for FANET routing algorithms in the context of future SAGINs. * To provide foundational experimental ideas for future researchers, we summarize the existing research's experimental methodologies from multiple aspects, including network scale, UAV types, and simulation platforms. Moreover, we present the trends and shortcomings of the experimental designs in the form of statistical charts to provide a visual analysis of experimental methodologies. The structure of the paper is linked to the sections as shown in Figure 1. The remainder of the paper is organized as follows: Section 2 introduces the basic architecture of FANETs under SAGINs and provides a categorical review of the routing protocols. Section 3 discusses the latest research progress in FANET routing algorithms over the last five years. Section 4 provides a comparative analysis of recent research. In addition, future research directions are foreseen at the end of Section 4 based on this analysis. Finally, Section 5 concludes the paper.