# Graph-Based Resource Allocation for Integrated Space and Terrestrial Communications
## 6 Graph-Based RA in CR Networks
### Lessons Learned and Trends in Development
This section aims to facilitate the RA for these communication networks by considering (1) the existing 6G ISTN concepts; (2) graph-based algorithms for RA for different types of networks, and (3) their mutual coexistence on a large scale on the ground, in the air, underwater, and in space. Challenges for algorithm design within the proposed resource management framework are also described. Architectures for 6G global inter-connectivity and network coexistence have considered multiple kinds of connected devices that are categorized by the environment they operate in. Sixth-generation integrated communications consist of a multi-layered structure containing marine, terrestrial, air, and space environments (some of them can contain several tiers; for example, different satellites operate on predetermined heights [92]), as illustrated in Figure 7.  
This demonstrates the proposed concept for GRIST, depicted as a set of hypergraphs composed of different sub-networks on every layer, and the connections between those of them that interact with each other for the provision of their required services. A sub-network may be formed from communications nodes of the same type, i.e., terrestrial/aerial/space, or a combination of these, to describe the integration of TNs and NTNs conceptualized in [93]. The sub-networks are described by separate graphs (for simplicity, only their vertices are shown, as white circles containing example communication nodes), and may be formed around a coordination point (CP) that determines the sub-network's range of operation. This CP is a network infrastructure unit that incorporates the communication flows within the sub-network so as to facilitate a specific application scenario. Hence, it may be realized as an AP that provides access to all wireless nodes within a home, or as  
Figure 7: The GRIST concept. an RRH/UAV-based AP/cellular macro BS/satellite-based node that covers a particular area with its UEs, BSs, ground-based APs, and others (such as V2V nodes, IoT devices, or patches of large intelligent surfaces). In coexisting incumbent and cognitive sub-networks, the CPs may be implemented in the Spectrum Access Control units that are responsible for RA and network self-organization, as described in [74]. As illustrated in the GRIST concept (Figure 7), the sub-networks (the ellipses within each layer containing the communication nodes) are represented by the hypergraph's hypervertices. While individual sub-networks may resolve their UA and RA autonomously, most of them will collaborate/share spectra with each other, which is described via the hyperedges between them. The management of resources and their allocation is determined within the span of a single hypergraph that connects sub-networks covering a particular volume of space during the time of a communication exchange which requires the sub-networks' mutual collaboration (Other communications tasks, such as user data processing, channel estimation, and signal and traffic flow classification, may be more efficient if they are realized via distributed learning methods [94]). A conceptual example of this cooperation within GRIST is given on the right side of Figure 7, which illustrates an enlarged version (in light yellow) of one hypervertex. It shows the modeling of the sub-network cooperation by the vertices (nodes of a TN and a NTN) and the edges that connect them. These connections are depicted in green (model of the RA in TN), violet (model of the RA in NTN), and blue (sharing of the available resources of the TN and the NTN, performed by the CPs of the two sub-networks). The edges within the TN and the NTN are determined by the physical and social relationships between the nodes (such as channel/power allocation, SSh, EE). Additional RA problems that are solved separately (often being the distribution of available channels) for each sub-network may be performed via a bipartite graph, as is common in the literature. They are defined for the sub-network's set of nodes and the set of respective resource units.