# Graph-Based Resource Allocation for Integrated Space and Terrestrial Communications
## 6 Graph-Based RA in CR Networks
### Lessons Learned and Trends in Development
Depending on the optimization method's complexity (contributed primarily by the nodes' density, the number of their links (i.e., whether they implement MC), the number of frequency channels, the social relationships between the nodes, etc. ), an edge reduction mechanism will likely be necessary to increase the algorithm's convergence speed. Overhead exchange for resource availability between sub-networks, as well as the management of resources for multiple sub-networks, may be modeled via star graphs, as they can describe the consolidation of the overhead in a single node (such as the CP). The current advancements in deep learning and its prominence in wireless communications research [12] point to the potential for RA algorithms within GRIST to be trained using GSP/GNN. In general, path graphs are not appropriate for modeling of RA methods for GRIST due to their linear, non-hierarchical nature. Figure 8: Illustrations for sub-networks for communication exchange over terrestrial, marine, aerial and space layers. (**a**) Sub-network comprised of terrestrial and aerial nodes. (**b**) Sub-network comprised of marine, aerial, and space nodes. * **Solving algorithm. ** As seen in the review in the previous sections, heuristic algorithms based on logical sequence of procedures are prevalent in graph-based solutions for wireless communications. In addition, complex RA algorithms are often decomposed into sub-graphs or a combination of graph-based and traditional optimization methods. It is questionable to what extend such approaches will be practical, in terms of efficiency and performance, for implementing GRIST on a wide-scale. Therefore, scalability as the number of connected vertices grows substantially, even within a small area in a single layer of the ISTN, is a primary research direction for the development of GNN-based learning methods for RA between sub-networks. Although not a universal solution, graph encoding and compression [102] may be appropriate alternatives for application in GRIST. Furthermore, a recent method for sequential graph construction and aggregation [103] for GNNs has shown significant reduction in memory usage and processing time. * **GNN-based solutions for sub-network functionalities. ** Deep learning on graphs has shown potential for not just RA, but also for cognitive functionalities such as cooperative spectrum sensing, spectrum database construction, localization, modulation recognition, and spectrum decision [79; 104; 105], due to its ability for feature (SNR, distance, achievable throughput, QoS requirements) extraction from the network's nodes. The impact of deep learning on graphs for these functionalities depends on the sub-network's application, density, and throughput requirements. For the implementation of some of them, it may be more feasible to use a combination of probabilistic and deep learning methods, or the employment of the same type of data (such as received signal samples or statistics of various performance indicators) to train multi-purpose neural networks. Accordingly, multiple tasks (such as transmitter detection and recognition) may be performed both by the CP, or distributively (by sensors/APs/UEs) via the same deep learning model, while the achieved results can yield the information parameters (spectrum occupancy, user density, etc.) that form the hypergraph attributes described above. Then, the RA problem may be solved through reinforcement/supervised learning of a neural network on a graph. * **Applying FL for RA between sub-networks. ** The novel FL concept allows for decentralized learning of a global model by multiple devices in the network that perform training on their local datasets and transmit only the resulting parameters to the aggregation unit (usually a cloud server) [106]. In this way, the overhead exchange is reduced and the protection of the users' private data is increased. Thus, the CSI and other traffic information can be provided from the sub-network's UEs to their serving CPs, which perform continuous learning of their local models.