Hypergraph Theory: Applications in 5G Heterogeneous Ultra-Dense Networks

Heterogeneous ultra-dense networks (HUDNs) can significantly increase the spectral efficiency of cellular networks and cater for the explosive growth of data traffic in 5G communications. Due to the dense deployment of small cells, interference among neighboring cells becomes severe. As a result, effective resource allocation and user association algorithms are essential to minimize inter-cell interference and optimize network performance. However, optimizing network resources in an HUDN is extremely complicated as resource allocation and user association are coupled. Therefore, an HUDN requires low-complexity but effective resource allocation schemes to address these issues. Hypergraph theory has been recognized as a useful mathematical tool to model the complex relations among multiple entities. In this article, we show how the hypergraph models can be used to effectively tackle resource allocation problems in an HUDN. We also discuss several potential research issues in this field.