# Graph-Based Resource Allocation for Integrated Space and Terrestrial Communications
## 6 Graph-Based RA in CR Networks
### Lessons Learned and Trends in Development
The hypergraph illustration of the relationships between the sub-networks in Figure 7 gives the following information that can be utilized in formulating and solving the RA problem:  
* Hypervertex attributes:
* Available/unutilized channels. They may be shared with sub-networks of the same type or via CRs. In addition, CPs in nearby sub-networks can use this information to regulate their power and channel allocation. * Resource demands to meet the sub-network's QoS requirements. A supplementary attribute that provides greater agility in SSh pairing between sub-networks. It also establishes priority in resource distribution due to the requirements (for example, groups of users requesting the same high-throughput streaming content, holographic telepresence, etc.) of certain sub-networks. * Sub-network EE gain. Its purpose is to describe the sub-network's overall performance to notify its neighbors of the need for channel/power allocation readjustment. Furthermore, some operator infrastructure nodes (BSs/APs) may be switched to idle mode so as to reduce the power consumption. Achieving high EE will be the main optimization goal of the GRIST. * User data characteristics. Cooperative caching between sub-networks (both terrestrial and non-terrestrial) is facilitated by information about which data (_type, amount_, and _period of time_ to be cached at a particular node) are required in a sub-network (or a set of sub-networks). This information is acquired through ML. * Hyperedge attributes:
* Distance between sub-networks. Determines the viability of frequency reuse and communication quality due to path loss. Unused channels can also be shared within a distance such that the potential interference is avoided. In addition, path loss is a significant consideration in communications between terrestrial and air/space nodes, so their association is dependent on the distance. * Carrier frequency of the connected sub-networks. It is an additional factor, together with the path loss, for association, resource sharing and information
exchange between two sub-networks, especially considering the frequency range expansion with mmWave and terahertz in beyond 5G. Through these features, the resulting optimization problems for a set of sub-networks within a hypergraph consider the results of their individual RA procedures for the overall resource management. Thus, they present a strong incentive for developing global solutions through GNNs based on message passing and vertex aggregation [11; 18; 95]. Hereby, the limitations of the proposed GRIST concept are identified as follows:  
* The implementation of the RA procedures in ISTNs naturally involves a large number of nodes, sub-networks, and the optimization of the relevant parameters. Therefore, defining and solving graph-based RA algorithms in such scenarios is limited by the number of communication nodes that will ensure feasible computational complexity for the devices' processing capabilities. This also poses the question of the optimization method's scalability for realistic scenarios. * Consequently, the implementation of RA will be limited by the requirements for EE of the sub-networks' nodes. * The RA algorithm for GRIST is unlikely to employ a unified graph model to describe the sub-problems that need to be solved due to the variety of the design parameters and radio environments in the different layers. As a consequence, the design process will be overburdened. Following these limitations, several open challenges and research directions for the design and implementation of graph-based RA procedures are expanded in a greater detail:  
* **Modeling coexistence and communications between sub-networks on different layers of GRIST. ** As it has been explored in various studies [90; 91; 93; 96; 97], the realization of the coexistence and reliable information exchange between contemporary and future networks is non-trivial.