The trip graph, which can model the residents’ taxi demands, consists of vertices used to indicate trips and edges used to indicate the follow-up relationships between trips. A trip $$v_j$$v j is a tight follow-up trip of another trip $$v_i$$v i , if a taxi can arrive at the departure location of $$v_j$$v j within a time threshold $$\delta$$δ after it finishes $$v_i$$v i . However, for big cities, there are a large amount of trips every day and it is time consuming to construct a trip graph. In this paper, we propose efficient algorithms to construct trip graphs for big cities. When constructing a trip graph, the most expensive step is to connect the vertices if the tight follow-up relationships exist. To find out the tight follow-up trips fast, we design an index considering both spatial and temporal constraints. To designate appropriate search areas, we propose efficient methods to determine the distance-based search areas and the traffic-based search areas. We conduct experiments on real datasets, i.e., the taxi trajectories of Shanghai in 2015. The experimental results show that our algorithm can construct the trip graph about 40 times faster than the straightforward method. We also demonstrate the usages of the trip graph in green transportation applications, i.e., the minimum fleet analysis and the minimum total “idle” mileage analysis.

Molecular properties play a crucial role in material discovery, protein interaction and drug development. The appearance of Graph Neural Network(GNN) significantly improved the performance of molecular property prediction. However, nodes in GNN only update the features of neighbor nodes, resulting in insufficient ability to encode global feature information. The self attention mechanism in transformer encodes the global information of molecules, while its spatial information is insufficient. Since molecules are three-dimensional spatial structures, spatial geometry information is an important attribute of molecules. Therefore, a transformer based geometric enhanced graph neural network (TG-GNN) is proposed to combine global and local molecule information with three-dimensional spatial structures to predict molecular properties. In this network, Graph neural network Geometric Feature Fusion Module (GGFF) and Transformer Geometric Feature Enhancement Module (TGF) are proposed to enhance the spatial geometry learning ability of the network. The GGFF module constructs a parallel graph neural network using bond and bond angle. The introduction of bond angle effectively complements the spatial information of the network. The TGF module introduces the coordinates and centrality degree features into the transformer to enhance the geometric expression ability of the module. GGFF module and TGF module encode local information and global information of molecules at the same time on the QM9 and OMDB dataset.