## 2 Literature Review
### Spatio-Temporal Graph Neural Networks  
In recent years, Graph Neural Networks (GNNs) have been widely used in traffic prediction, utilizing graph theory to filter signals on local subgraphs. The graph convolution in GNN models combines the central node representation with neighboring node representations to create a new representation for the node, exploring spatio-temporal correlations in traffic data. GNNs can handle non-Euclidean structured data, using graphs to model parking networks and capture spatial dependencies, which is particularly suitable for irregularly distributed parking lots.  
[PERSON] et al. [29] enhanced the modeling capability of dynamic spatio-temporal correlations in traffic data by proposing an attention-based spatio-temporal graph convolutional network (ASTGCN) model for traffic flow forecasting. Leveraging the robustness of neural controlled differential equations (NCDEs) to irregular time series, [PERSON] et al. [30] combined NCDEs with graph neural networks for spatio-temporal processing of traffic data. Furthermore, [PERSON] et al. [31] introduced a latent network for extracting spatio-temporal features and proposed a dynamic graph convolutional network that adaptively constructs the dynamic road network graph matrix for traffic prediction.  
In the field of parking prediction, researchers have gradually started using graph neural networks. For example, [PERSON] et al. [32] used an Elman neural network to predict short-term available parking spaces. [PERSON] et al. [33] employed a genetic algorithm optimized multilayer perceptron (MLP) to predict the occupancy rates of regional parking lots for the next 30 min. [PERSON] et al. [34] also proposed an APS prediction algorithm based on a CNN-LSTM model, which considered both spatial and temporal correlations, although it only accounted for roadside parking directly affected by traffic flow. With technological advancements, [PERSON] et al. [35] proposed a residual spatio-temporal graph convolutional neural network prediction model, which uses GNNs and temporal convolutional networks to capture spatial and temporal features, respectively, improving the accuracy and efficiency of the prediction process. [PERSON] et al. [36] introduced a parking prediction model named DWT-ConvGRU-BRC, which uses discrete wavelet transform (DWT) to denoise historical parking data and then employs a convolutional gated recurrent unit network (ConvGRU) to extract temporal correlations of the parking lot itself and spatial correlations between different parking lots. [PERSON] et al. [4] utilized graph convolutional neural networks (GCNNs) to extract spatial relationships in parking data from a large-scale network and used long short-term memory (LSTM) networks to capture temporal features. [PERSON] et al. [25] extracted discriminative features from multisource data and combined multigraph convolutional neural networks (MGCNs) with LSTM networks to capture complex spatio-temporal correlations. [PERSON] et al. [37] proposed a hierarchical graph convolution module to capture local and global spatial dependencies and then used a hierarchical attentional recurrent network module to capture dynamic short-term and long-term temporal dependencies in each parking lot.  
However, the aforementioned GCN-based approaches require predefining connection graphs through similarity or distance measures [38] to capture spatial correlations. The graphs generated in this way are often intuitive, incomplete, and not directly tailored to the prediction task [39]. To fill this gap, this paper proposes a novel method called the dynamic spatio-temporal adaptive graph convolutional recurrent network (DSTAGCRN), which integrates dynamic graphs, GRUs, and attention mechanisms to create an accurate and efficient VPS prediction model.