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 introduce 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 advantages 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 O(|V|^2) to O(|V|), where |V| is the total number of transceiver pairs.

翻译：图神经网络（GNNs）近年来已成为解决无线网络中功率分配问题的一种有前景的方法。由于未配对的发射机与接收机通常在空间上距离较远，基于距离的阈值方法被提出，通过在图神经网络中排除或纳入信道状态信息来减少计算时间。本文首次将基于邻居数量的阈值方法引入图神经网络以降低时间复杂度。此外，我们对基于距离和基于邻居的两种阈值策略进行了全面分析，并为不同通信信道场景下的阈值选取提供了建议。我们设计了相应的基于邻居的图神经网络（N-GNN），旨在通过分配发射功率以最大化网络吞吐量。实验结果表明，所提出的N-GNN在保持优异性能与泛化能力的同时，能显著降低时间复杂度。此外，我们证明通过选择合适的阈值，可将时间复杂度从O(|V|^2)降低至O(|V|)，其中|V|表示收发器对的总数。