# Graph-Based Resource Allocation for Integrated Space and Terrestrial Communications
###### Abstract  
Resource allocation (RA) has always had a prominent place in wireless communications research due to its significance for network throughput maximization, and its inherent complexity. Concurrently, graph-based solutions for RA have also grown in importance, providing opportunities for higher throughput and efficiency due to their representational capabilities, as well as challenges for realizing scalable algorithms. This article presents a comprehensive review and analysis of graph-based RA methods in three major wireless network types: cellular homogeneous and heterogeneous, device-to-device, and cognitive radio networks. The main design characteristics, as well as directions for future research, are provided for each of these categories. On the basis of this review, the concept of Graph-based Resource allocation for Integrated Space and Terrestrial communications (GRIST) is proposed. It describes the inter-connectivity and coexistence of various terrestrial and non-terrestrial networks via a hypergraph and its attributes. In addition, the implementation challenges of GRIST are explained in detail. Finally, to complement GRIST, a scheme for determining the appropriate balance between different design considerations is introduced. It is described via a simplified complete graph-based design process for resource management algorithms. 6G; device-to-device networks; cellular networks; cognitive radio; graph; heterogeneous networks; resource allocation; wireless communications +
Footnote †: journal: Sensors  
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The RA procedure is responsible for adequate distribution of the network's very limited resources (frequency channels and/or transmission power) in a complex radio propagation environment, and with the increasing number of UEs, in view of reducing the interference, which is usually unavoidable. Furthermore, the densification of the network's nodes creates potential for considerable overhead that would result in intolerable delays [4]. Consequently, the RA scheme has to actively minimize it during the network's operation, while providing optimal spectral efficiency (maximizing the throughput gains on the available spectrum) at the same time. Due to the various nodes deployment densities in different networks, the RA procedures differ in requirements and complexity. It is notable that the RA functionality is usually applied for one (or a combination) of the following three wireless network scenarios (they are also considered in recent, more general surveys in the field [4; 5; 6; 7; 8], which review machine learning and heuristic methods for RA) within the context of 5G and beyond:  
* Homogeneous and heterogeneous networks (Het-Nets). Most current wireless communication systems are of this type. Traditionally, terrestrial Het-Nets consist of cells with various ranges that serve multiple mobile UEs within their area of coverage. With the advent of integrated space and terrestrial networks (ISTNs) [2], Het-Nets expand to incorporate multiple ground-based licensed/license-free cellular networks, cell-less ultra-dense networks, as well as communications between unmanned aerial vehicle (UAV) based, marine, and satellite nodes. When only one communication standard is used in the network's nodes, it is homogeneous. The base stations (BSs) are usually stationary, but they can also be mobile. Users are often characterized by bandwidth-intensive applications, and attach to the cell (or cells) which provides the most favorable throughput. RA is predominantly focused on providing inter-cell interference (ICI) coordination. * Device-to-Device (D2D) Networks. They are characterized by the fact that the UEs themselves provide radio access for each other, and their communication exchanges are not intermediated by the BSs/Access Points (APs). Accordingly, low delays and high throughputs can be achieved, which makes D2D communications more prevalent in modern networks.