# Graph-Based Resource Allocation for Integrated Space and Terrestrial Communications
## 6 Graph-Based RA in CR Networks
### Lessons Learned and Trends in Development
By finding the path  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **General/Complete** & **Bipartite** & **Star** & **Path** & **GSP/GNN** & **References** \\  & **Graph** & **Graph** & **Graph** & **Graph** & **GSP/GNN** & **References** \\ \hline RA methods in OFDM & ✗ & ✗ & & & [19; 20; 21] \\ Systems & & & & & [19; 20; 21] \\ \hline RA Methods with user and & & ✗ & ✗ & & [22; 23; 24; 25; 26; 27] \\ cell clustering & & & & & \\ \hline RA methods With belief & ✗ & ✗ & & [28; 29] \\ propagation & & & & & [30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53] \\ \hline RA Methods based on GSP & ✗ & ✗ & & ✗ & [30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53] \\ Joint power and channel & & & & & [51; 52; 53] \\ allocation methods & & & & & [54; 55; 56; 57] \\ \hline Hypergraph-based RA & ✗ & ✗ & & [54; 55; 57] \\ methods & & & & & [58; 59; 60; 61] \\ \hline Graph-coloring-based RA & ✗ & & & & [58; 59; 60; 61] \\ methods & & & & & \\ \hline RA methods in NOMA & & & & [62; 63; 64] \\ systems & & & & & [75; 76; 77] \\ RA methods in underlay CR & ✗ & ✗ & & & [78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89] \\ networks & & & & & & [78; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 98; 99; 98; 99; 90; 99; 91; 99; 92; 93; 95; 97; 99; 98; 9 with the best utility-to-cost ratio on the graph in Figure 9, the most important design considerations (so as to decrease the algorithm's complexity) can be determined. The graph on Figure 9 connects all design aspects that are directly dependent on each other, and the design process will require a suitable trade-off between them, so as to adapt the algorithm's complexity and applicability according to a particular scenario. This model is a complete graph, although some relationships between the aspects and functionalities are too broadly related to each other, and the edges they constitute can be neglected. The edges coming out of each vertex are colored in a combination of the connected vertices' colors (denoting the vertex attribute), so as to illustrate the weight of each edge. The design graph's vertex concerning the RA (the leading problem that concerns spectral efficiency, and thus related to all the rest) have been sufficiently clarified, so only the remaining aspects are hereby described. * Spectrum sharing. Generally, it is considered a requirement for: (1) achieving the efficient utilization of the allocated spectrum of a particular communication system by sharing it with other wireless standards (it has been established by multiple measurement campaigns, such as [109; 110], that the spectrum of many modern communication systems, especially those operating in the sub-6 GHz range, is poorly utilized for most of the time. Therefore, the coexistence between different wireless technologies is presently considered as a major research topic); and (2) integration of communication systems operating in different (especially, adjacent) frequency bands [111]. In other words, SSh is performed: (1) between the incumbent (primary) and non-licensed (or secondary) users; and (2) between the primary users of different wireless technologies. This aspect is applicable mostly for CR networks, and related to all other aspects apart from Data Caching, because that is directly associated with EE and RA. * User association. The upcoming and future networks are multi-tiered, i.e., users communicate via multiple types of cells or access points (APs), and they do not associate with them in the same way. In some applications, the users are attached to multiple macro cells, while for others, numerous APs serve a single user (especially in scenarios where they are much more densely deployed than the UEs). Thus, UA is generally relevant for EE, SSh, Security, RA, and Delay. * EE and conservation.