## 5 Discussion  
Overlay analysis is one of the basic functions of GIS spatial analysis. When faced with a large amount of data, traditional serial algorithms take too much time. Parallelization after a reasonable division of data is an effective way to improve computational efficiency. Based on this idea, this paper designs a multicore parallelization method based on shape complexity-based data partitioning, which considers the influence of polygon structure, size, and other factors. By establishing a shape complexity model and applying it to divide the vector data, the grouped data can be distributed among multiple cores to execute polygon overlay analysis in parallel. Compared with the traditional multicore parallelization method based on dividing data by the number of polygons, the effectiveness of the proposed method in optimizing the execution of polygon overlay analysis algorithms is verified from three perspectives: the running time, the acceleration ratio, and the load balancing index.  
Figure 7: Multicore parallel difference operator calculation results achieved with different methods for different amounts of data.  
The running speed of the method proposed in this study is greatly improved compared to that of the serial algorithm. Moreover, compared with those achieved with the traditional data partitioning method, the running speed and load balancing are both improved. In particular, when processing large-scale data, the speed is significantly improved, and the load balancing index is also significantly reduced. The running time of the multicore parallel algorithm depends on the running time of the slowest thread. Because the data partitioning method in this paper is more balanced, the running time of each thread is less different, which can effectively save the overall running time. Therefore, when the shape complexity of the data increases, the task time of each thread increases so that a higher speedup and a lower load balancing index can be obtained. The research results are beneficial for improving the efficiency of large-scale spatial overlay analysis and have certain reference values for the optimization of GIS spatial algorithms. Nevertheless, although the polygon shape complexity models proposed in this article accurately reflect the impact of polygon shape characteristics on the computational efficiency of overlay analysis, these models can still be improved because the structures of polygons can greatly differ. In this paper, the proposed multicore parallelization method based on shape complexity partitioning has been verified only for the intersection operator and difference operator of the Vatti algorithm, and additional in-depth research must be conducted to verify its broader applicability. In the future, we will consider calculating additional indicators that may affect the efficiency of polygon overlay analysis based on the shape characteristics and spatial characteristics of polygons and establish a shape complexity model that can better explain the observed algorithm performance. Moreover, this approach will be applied to data partitioning for various operators of other algorithms. Applying the data partitioning method based on the shape complexity model to applications for distributed parallel computing in a cloud environment and the cluster processing of large-scale vector data will also effectively improve the computing efficiency of spatial data.