# An Algorithm to Generate a Weighted Network Voronoi Diagram Based on Improved PCNN
## 5 Experiment Studies and Discussion
### Discussion  
It can be seen in Figures 9d and 10 that: (1) the ordinary weighted Voronoi diagram cut the network planar smoothly, and the weighted network Voronoi diagram cut the network planar unevenly, for the road network is usually unevenly distributed and there is a slight chance to connect original facility points by a straight line. (2) The ordinary weighted Voronoi diagram ignores the influence of the road network where the point cluster is located; thus, the final results would be the same even if the point cluster were put into different road networks. However, the weighted network Voronoi diagram is constructed while fully considering the attributes of road networks, and the importance of points, which ends up providing results more suitable to real life. (3) The weighted network Voronoi diagram is close to the ordinary weighted Voronoi diagram when the road network around the point is dense enough. For instance, the shaded areas (\(A\) in Figure 9d and \(A^{\prime}\) in Figure 10), which represent the impacting regions of the same points calculated by the two methods, are similar in both shape and size, due to the large density of the road network related to the point. If the following three assumptions stand--(1) the road network density is large enough and any two facility points can be connected by roads similar to straight lines, (2) all the roads in road network are of the same weight and (3) all the roads in road network are two-way--it can be inferred that the weighted network Voronoi diagram will be nearly the same as the ordinary weighted Voronoi diagram. However, in fact, the road networks are usually unevenly distributed, and different roads in road network always have different attributes, such as grades and directions. Therefore, it is doubtless that the weighted network Voronoi diagram is a better choice for the representation of the impact scope of a point cluster rather than the ordinary weighted Voronoi diagram.  
A comparison experiment based on the idea of the shortest path was performed on the same data. The weighted network Voronoi diagram was constructed using the tool SANET ([[http://sanet.csis.u-tokyo.ac.jp/](http://sanet.csis.u-tokyo.ac.jp/)]([http://sanet.csis.u-tokyo.ac.jp/](http://sanet.csis.u-tokyo.ac.jp/))), as shown in Figure 11b. It can be deducted that the method based on the idea of the shortest path ignores some of influence factors, such as the attributes of the related road networks. For instance, the road segments next to the points \(P_{1}\) and \(P_{2}\) are of higher grade in Figure 11a, so the auto-waves transmit faster along them, resulting in larger impacting regions of \(P_{1}\) and \(P_{2}\) than in Figure 11b. In addition, as shown in Table 1, experiments with different unit speed were performed, and performance parameters of the proposed algorithm for constructing weighted network Voronoi diagrams are described in Table 1. It can be seen that the iteration number is directly related to the transmission speed of the auto-wave, which can be adjusted according to the practical situation. It can be seen that the time complexity of the algorithm mainly depends on the transmission speed of the auto-wave in the improved PCNN, which is able to be adjusted  
Figure 10: Weighted Voronoi diagram of points in the study area.  
**Acknowledgments:** The authors are grateful to anonymous reviewers, whose comments and suggestions have helped us to improve the context and presentation of the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.