Accelerating Graph Neural Networks via Edge Pruning for Power Allocation in Wireless Networks

Graph Neural Networks (GNNs) have recently emerged as a promising approach to tackling power allocation problems in wireless networks. Since unpaired transmitters and receivers are often spatially distant, the distance-based threshold is proposed to reduce the computation time by excluding or including the channel state information in GNNs. In this paper, we are the first to intro-duce a neighbour-based threshold approach to GNNs to reduce the time complexity. Furthermore, we conduct a comprehensive analysis of both distance-based and neighbour-based thresholds and provide recommendations for selecting the appropriate value in different communication channel scenarios. We design the corresponding neighbour-based Graph Neural Networks (N-GNN) with the aim of allocating transmit powers to maximise the network throughput. Our results show that our proposed N-GNN offer significant advan-tages in terms of reducing time complexity while preserving strong performance and generalisation capacity. Besides, we show that by choosing a suitable threshold, the time complexity is reduced from $\mathcal{O}(\vert \mathcal{V}\vert ^{2})$ to $\mathcal{O}(\vert \mathcal{V}\vert)$, where $\vert \mathcal{V}\vert$ is the total number of transceiver pairs.