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 distanced-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 distance-based and neighbour-based Graph Neural Networks with the aim of allocating transmit powers to maximise the network throughput. Our results show that our proposed GNNs offer significant advantages in terms of reducing time complexity while preserving strong performance. 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）近期已成为解决无线网络功率分配问题的一种有前景的方法。由于未配对发射机与接收机通常空间距离较远，基于距离的阈值被提出用于通过排除或包含信道状态信息来降低GNN的计算时间。本文首次提出将基于邻居的阈值方法引入GNN以降低时间复杂度。此外，我们对基于距离和基于邻居的阈值进行了全面分析，并针对不同通信信道场景下如何选择合适阈值给出了建议。我们设计了相应的基于距离和基于邻居的图神经网络，以分配发射功率从而最大化网络吞吐量。结果表明，我们提出的GNN在降低时间复杂度的同时保持了优异的性能。此外，通过选择合适阈值，时间复杂度可从O(|V|^2)降至O(|V|)，其中|V|为收发机对的总数。