# Navigating the Maps: Euclidean vs. Road Network Distances in Spatial Queries
## 5 Discussion  
The primary objective of this research was to evaluate the accuracy of the Euclidean distance method compared to the road network distance method. The Open Source Routing Machine (OSRM) was utilized to extract the road network distances, which served as the benchmark for comparison with the Euclidean distance method. OSRM provided a reliable and efficient means of calculating the actual distances based on the road network topology. By using OSRM as the benchmark, we were able to assess the accuracy of the Euclidean distance method in capturing the actual distances along the road network. Furthermore, the study aimed to comprehensively examine the unique characteristics associated with each classification of query points and to rigorously evaluate the accuracy of each category. Our analysis disclosed the accuracy rates of each query method when measured against the Euclidean and road network distances, with the latter serving as the established benchmark. In kNN queries, we observed a correlation between the accuracy and the number of k. Specifically, we found that as the number of k increased, the accuracy for each class of query points consistently decreased. This observation could be attributed to the intricate road structure within the city. As the value of k rises, the algorithm considers a higher number of nearby points, thus potentially leading to a greater diversity in road structures and terrain. This diversity might introduce variations in the distances calculated, thereby impacting the accuracy of the Euclidean distance method. The road network's complexity, including factors like one-way streets, intersections, and irregularities, could also contribute to this phenomenon. This finding highlights the impact of the chosen value of k on the accuracy of the Euclidean distance method. Regarding the range query, we identified a consistent pattern across different classes, with each class exhibiting a similar trend except for the turning point in the range value. The turning point, which represents the threshold where the accuracy starts to increase, is influenced by the density of the POIs. Class Five showed the earliest increase in accuracy, followed by Class Four, thus suggesting a relationship between the class and the point at which accuracy begins to improve. Figure 20: Line graph plot with the different datasets (hospital, ambulance, and hospital and ambulance for range queries). (**a**) Class 1—line graph plot with the different datasets. (**b**) Class 2—line graph plot with the different datasets. (**c**) Class 3—line graph plot with the different datasets. (**d**) Class 4—line graph plot with the different datasets. (**e**) Class 5—line graph plot with the different datasets. However, the increased accuracy in this context may suggest that the distance range adequately covers all surrounding points of interest (POIs). As previously mentioned in the kNN case, where road structure influenced the decrease in accuracy, we saw a correlated phenomenon here. The high-density class experienced a reduction in accuracy when the range distance was less, thus indicating a potential interplay between road structure, density, and range distance that impacts accuracy trends. Another insight gained from this research is that many POIs do not necessarily guarantee high accuracy. Despite the hospital dataset having fewer POIs than the ambulance dataset, the accuracy of the hospital dataset was found to be higher. This observation suggests that when there are limited choices (few POIs), the retrieved results using the Euclidean distance method may closely align with those obtained from the road network. Nevertheless, as the number of available choices increases, there is a likelihood of encountering slight differences in distances, thereby potentially influencing the final results and impacting the overall accuracy.