## 1 Introduction  
The field of network technologies is rapidly evolving to meet the growing demands for speed, reliability, and ubiquitous connectivity. Historically, a new generation of wireless communication systems has emerged approximately every decade, each aiming to address the limitations of its predecessor [1]. From the analog 1G systems of the 1980s to the digital GSM-based 2G networks of the 1990s, and onward to 3G, 4G LTE, and the currently deployed 5G, each generation has introduced substantial enhancements in data rates, latency, and user capacity [2; 3; 4; 5]. The commercial launch of 5G in 2019 brought significant improvements, such as ultra-reliable low-latency communication (URLLC), enhanced mobile broadband (eMBB), and massive machine-type communication (mMTC) [1]. However, the escalating demands from emerging applications now highlight several critical limitations of 5G. Applications such as immersive extended reality (XR), holographic communication, autonomous systems, and brain-computer interfaces require latency on the order of microseconds and data rates approaching terabits per second (Tbps), which are beyond the capabilities of 5G [6; 7; 8]. Furthermore, the exponential increase in the number of connected devices, particularly in Internet of Everything (IoE) scenarios, demands extremely high connection density, energy efficiency, and intelligent resource management. These limitations have accelerated the need for sixth-generation (6G) networks. 6G, expected to be realized around 2030, aims to support ultra-low latency (<0.1 ms), Tbps-level throughput, extreme reliability, and pervasive global connectivity [6; 9; 10]. Figure 1 summarizes latency requirements across different 5G and 6G application domains, illustrating the stringent demands placed on future network designs. This vision is underpinned by key enabling technologies such as terahertz (THz) communication, visible light communication (VLC), integrated terrestrial and non-terrestrial networks (NTNs), reconfigurable intelligent surfaces (RISs), and advanced artificial intelligence (AI)-driven network control [11; 12; 13; 14; 15; 16; 17; 18]. For example, THz bands (0.1-10 THz) offer unprecedented bandwidth, but their high propagation loss and line-of-sight constraints demand new signal processing and routing strategies. Simultaneously, AI and machine learning (ML) are poised to transform network optimization and decision-making, providing adaptive and context-aware management across diverse, dynamic environments [19; 20; 21]. One of the most significant shifts in 6G is the seamless integration of terrestrial, aerial, maritime, and satellite segments--often referred to as the 3+ paradigm--to ensure truly global coverage. Satellite networks, particularly low Earth orbit (LEO) constellations, play a vital role in achieving ubiquitous broadband access, especially in underserved and remote areas [22; 23; 24; 25]. However, this integration introduces new challenges in network architecture, mobility management, and, most notably, routing. Routing in 6G and integrated satellite-terrestrial networks becomes increasingly complex due to the heterogeneous, dynamic, and large-scale nature of these environments. Traditional routing protocols, designed for static or slowly changing networks, are inadequate to ensure low latency and reliable communication in such settings. AI-enabled routing methods, including deep reinforcement learning (DRL), genetic algorithms (GAs),  
Figure 1: Latency tolerance thresholds (average) for different services in 5G and beyond 5G (comparison for different apps). and neural networks, have been proposed to address these issues. These techniques offer adaptability, scalability, and real-time optimization capabilities necessary for 6G routing demands [26; 27; 28; 29; 30; 31; 32]. Despite the growing body of literature on 6G and routing, there remains a lack of comprehensive analysis that bridges the domains of AI-driven routing and integrated satellite-terrestrial networks.