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Neural Networks (GNNs) have recently emerged as a promising approach totackling power allocation problems in wireless networks. Since unpairedtransmitters and receivers are often spatially distant, the distanced-basedthreshold is proposed to reduce the computation time by excluding or includingthe channel state information in GNNs. In this paper, we are the first tointroduce a neighbour-based threshold approach to GNNs to reduce the timecomplexity. Furthermore, we conduct a comprehensive analysis of bothdistance-based and neighbour-based thresholds and provide recommendations forselecting the appropriate value in different communication channel scenarios.We design the corresponding distance-based and neighbour-based Graph NeuralNetworks with the aim of allocating transmit powers to maximise the networkthroughput. Our results show that our proposed GNNs offer significantadvantages in terms of reducing time complexity while preserving strongperformance. Besides, we show that by choosing a suitable threshold, the timecomplexity is reduced from O(|V|^2) to O(|V|), where |V| is the total number oftransceiver pairs.

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