# Navigating the Maps: Euclidean vs. Road Network Distances in Spatial Queries
## 2 Related Work
### Existing Research  
One research study explored the relationship between transport costs and road distance. The researchers employed a correlation factor to estimate the actual road distance by considering the Euclidean distance. They evaluated the accuracy of this approximation by calculating the average difference between the estimated and actual distances [28]. The conclusion highlights the development of a linear regression model for Euclidean distances, thereby demonstrating its superior reliability compared to existing literature models. Two adjustment methods are discussed: one based on mean ratios and another utilizing regression equations. While more computationally intensive, the latter provides closer-to-reality results, but caution is urged regarding its constant, particularly for smaller distances. Notably, the study did not provide explicit information regarding the precision of the Euclidean distance. Instead, it introduced a regression model to approximate the road distance and compared it with the actual distance. In another research study, the accuracy of the Euclidean distance was compared with the road network distance. The study investigated the performance of two query processing methods: the benchmark method, which utilized the road network distance, and the Euclidean decider, which employs the Euclidean distance [29]. The paper suggests using Euclidean distance as a fast and computationally less intensive alternative for estimatingroad network distance. The authors argue that, despite potential differences, Euclidean distance-based solutions can provide acceptable accuracy for specific queries, such as group nearest neighbor (GNN) queries. Experiments involved comparing two GNN query processing methods using road network distance as a benchmark and Euclidean decoder (using Euclidean distance). Actual road network graphs from cities were utilized, thereby creating scenarios with scattered or clustered query points and points of interest (POIs). Parameters such as the number of query points, POI density, the value of k, and road network were varied to assess performance. Euclidean decider's accuracy was evaluated by comparing distances with the benchmark results. The experiments aimed to determine the effectiveness of Euclidean distance in achieving a balance between accuracy and computational efficiency for GNN queries in transportation services. The study's results [29] indicate that the Euclidean metric achieved an accuracy level exceeding 74.7% for kNN queries and exhibited even higher accuracy for general group nearest neighbor (GNN) queries, which ranged from 86% to 95% when considering two query points. In a related work, [PERSON], [PERSON], [PERSON], and [PERSON] proposed the Hilbert-order based star expansion cloaking algorithm (H-star) [30]. This algorithm is designed to optimize query processing cost by considering cloaking regions for a group of queries, thereby reducing the number of boundary points and, consequently, the query processing cost. The proposed H-Star algorithm has been extended to include query processing algorithms for k-nearest neighbor (kNN) and range queries. Another research study proposed a method for road network extraction from high-resolution synthetic aperture radar (SAR) images. The approach involved constructing road networks using smooth, crosslinked curves with determined functions, thereby enabling mathematical descriptions for road segments. The method employed a multiplicative Duda operation for line feature responses, and nonroad detection techniques were introduced to reduce false positives. Binary image decomposition and polynomial curve fitting were then used to linearize road segments, and network optimization was achieved through geometric constraints [31].