# Graph-Based Resource Allocation for Integrated Space and Terrestrial Communications
## 6 Graph-Based RA in CR Networks
### Lessons Learned and Trends in Development
In order to provide ubiquitous and saleable networks that ensure seamless communications on all four layers [93; 96], the integration of TN and NTNs can be facilitated by graph-based algorithms for RA, energy conservation, data offloading, localization, and dynamic spectrum access in the unlicensed bands (that are suitable for upcoming aerial communication nodes [97]). Such solutions will need to consider the physical parameters (speed, direction, weight, altitude of operation, size, available power supply/battery, etc.) of the communication node, which, together with the environmental aspects (such as fading, shadowing, wind, rain, and distance-dependent path loss) affect the communications. These aspects will then define the graphs' structures and attributes within GRIST. The following two examples are given: (1) RA for a sub-network that includes terrestrial and aerial nodes (Figure 8a), is dependent on the physical parameters of the UAVs mentioned above, as well as on the movement speed and the spectrum access scheme (fixed/dynamic) of the ground users [96; 97]. Together with the traditional RA problems in a terrestrial network, the graph-based solutions within GRIST will need to solve the problems of user and UAV mobility, determined by the aerial nodes' battery limitation, transmission power, and available channels (incumbent or shared), which can also be described as vertex attributes. (2) The most essential parameters that concern the RA for a sub-network comprised of terrestrial/marine/aerial and space nodes (Figure 8b) are the link delay, achievable data rate, and the duration of direct visibility between the nodes [98]. They can be used as edge attributes, while physical parameters (such as longitude, latitude, speed, and capacity) serve as vertex attributes for graph-based RA algorithms for ISTNs. The optimization problem can be solved using deep neural networks and reinforcement learning (RL)-based training procedures, which have shown promising performance gains (such as fast convergence and short processing time) [99]. Different learning procedures may be utilized depending on the operations for service provision in the sub-networks. Supervised learning has widely been used for functions such as signal decoding, spectrum sensing, and multiple access, while reinforcement learning has been applied for RA on a sub-network level, and for radio access technology selection for ISTN [100; 101]. * **Modeling of graphs for RA methods in GRIST sub-networks**. The relevant types of graphs, including GSP (Section 3), which is used for the modeling of the reviewed RA methods in each sub-category (comprising Sections 4-6), are highlighted in Table 9 that matches them with the sub-categories. _The table illustrates which of them are most commonly applied, as well as those appropriate for application in GRIST_. Firstly, as noted in Table 9, applying a graph-based RA approach will likely model both the sub-network's nodes as a general/complete graph, and connect the available channel and/or power resources and users as a bipartite/tripartite graph. The general/complete graph type is the most intuitive for modeling the physical relationships between the network's nodes, as their parameters (power level, channel gain, distance, interference, etc.) are aptly considered. In this way, the optimization method will also be updated at each iteration with inputs that reflect the influence of the nodes' movement and the changes in their radio environment. The main limitation of this type is the significant increase in complexity with the number of nodes. Bipartite/tripartite graphs allow for resource distribution that also considers the environment's influence, and they are easier to define. Nevertheless, they are viable for a fixed set of resources that are only available to a particular sub-network. Thus, these two types of graphs are near-universally applied in RA methods, as exemplified by the review in the previous Sections.