Nearest neighbor queries in spatial network databases

A very frequent type of query in Geographical Information Systems is to find the K-nearest neighbors (KNN) of a query object. Majority of the current studies on KNN in spatial databases are aimed at Euclidean spaces/distances. However, the distances between objects in spatial network databases, SNDB (e.g., road networks), are usually defined as the length of the shortest path between them, rendering the current solutions impractical. In this dissertation, we propose solutions for variations of KNN queries in SNDB. We propose two approaches to address regular KNN queries. The first approach is based on transforming the two dimensional (road) networks to a higher dimensional space and utilizing computationally simple Minkowski distance metrics for distance measurement to provide a better approximate result set for a KNN query as compared to the current solutions. This approach is appropriate only where small percentage of false results is tolerable. The second proposed approach, termed VN3, provides an exact result set for the KNN queries by utilizing network Voronoi diagrams (NVD). The solution is based on an iterative process that contains filter and refinement steps. In the filter step, objects are added to a candidate set by utilizing the properties introduced in VN3. In the refinement step, the next nearest neighbor of the query is selected by utilizing some pre-computed shortest path distances. We also propose two solutions for continuous KNN queries of a path. The first solution finds the KNNs of each node on the path and then determines the locations of split points between every two adjacent nodes. The second solution eliminates the need for finding KNN queries of some nodes on the path by determining the minimum distance that the KNNs of a moving query object remain the same. We also address group NN queries by concurrently finding the next NN of all query objects and maintaining a sorted list of the points based on their aggregate distances to the objects. Finally, we show how the properties of VN3 can be utilized to address shortest path queries as well as reverse NN queries in SNDB.