A frequent type of query in spatial networks (e.g., road networks) is to find the K nearest neighbors (KNN) of a given query object. With these networks, the distances between objects depend on their network connectivity and it is computationally expensive to compute the distances (e.g., shortest paths) between objects. In this paper, we propose a novel approach to efficiently and accurately evaluate KNN queries in spatial network databases using first order Voronoi diagram. This approach is based on partitioning a large network to small Voronoi regions, and then pre-computing distances both within and across the regions. By localizing the precomputation within the regions, we save on both storage and computation and by performing across-the-network computation for only the border points of the neighboring regions, we avoid global pre-computation between every node-pair. Our empirical experiments with several real-world data sets show that our proposed solution outperforms approaches that are based on on-line distance computation by up to one order of magnitude, and provides a factor of four improvement in the selectivity of the filter step as compared to the index-based approaches.
Several variations of nearest neighbor (NN) query have been investigated by the database community. However, realworld applications often result in the formulation of new variations of the NN problem demanding new solutions. In this paper, we study an unexploited and novel form of NN queries named Optimal Sequenced Route (OSR) query in both vector and metric spaces. OSR strives to find a route of minimum length starting from a given source location and passing through a number of typed locations in a specific sequence imposed on the types of the locations. We first transform the OSR problem into a shortest path problem on a large planar graph. We show that a classic shortest path algorithm such as Dijkstra's is impractical for most real-world scenarios. Therefore, we propose LORD, a light thresholdbased iterative algorithm, that utilizes various thresholds to filter out the locations that cannot be in the optimal route. Then we propose R-LORD, an extension of LORD which uses R-tree to examine the threshold values more efficiently. Finally, LORD and R-LORD are not applicable in metric spaces, hence we propose another approach that progressively issues NN queries on different point types to construct the optimal route for the OSR query. Our extensive experiments using both real-world and synthetic datasets verify that our algorithms significantly outperform the Dijkstrabased approach in terms of processing time (up to two orders of magnitude) and required workspace (up to 90% reduction on average).
A very important class of queries in GIS applications is the class of K-nearest neighbor queries. Most of the current studies on the K-nearest neighbor queries utilize spatial index structures and hence are based on the Euclidean distances between the points. In real-world road networks, however, the shortest distance between two points depends on the actual path connecting the points and cannot be computed accurately using one of the Minkowski metrics. Thus, the Euclidean distance may not properly approximate the real distance. In this paper, we apply an embedding technique to transform a road network to a high dimensional space in order to utilize computationally simple Minkowski metrics for distance measurement. Subsequently, we extend our approach to dynamically transform new points into the embedding space. Finally, we propose an ef®cient technique that can ®nd the actual shortest path between two points in the original road network using only the embedding space. Our empirical experiments indicate that the Chessboard distance metric L ? in the embedding space preserves the ordering of the distances between a point and its neighbors more precisely as compared to the Euclidean distance in the original road network.
Continuous K nearest neighbor queries (C-KNN) are defined as finding the nearest points of interest along an entire path (e.g., finding the three nearest gas stations to a moving car on any point of a pre-specified path). The result of this type of query is a set of intervals (or split points) and their corresponding KNNs, such that the KNNs of all points within each interval are the same. The current studies on C-KNN focus on vector spaces where the distance between two objects is a function of their spatial attributes (e.g., Euclidean distance metric). These studies are not applicable to spatial network databases (SNDB) where the distance between two objects is a function of the network connectivity (e.g., shortest path between two objects). In this paper, we propose two techniques to address C-KNN queries in SNDB: Intersection Examination (IE) and Upper Bound Algorithm (UBA). With IE, we first find the KNNs of all nodes on a path and then, for those adjacent nodes whose nearest neighbors are different, we find the intermediate split points. Finally, we compute the KNNs of the split points using the KNNs of the surrounding nodes. The intuition behind UBA is that the performance of IE can be improved by determining the adjacent nodes that cannot have any split points in between, and consequently eliminating the computation of KNN queries for those nodes. Our empirical experiments show that the UBA approach outperforms IE, specially when the points of interest are sparsely distributed in the network.
A very important class of queries in GIS applications is the class of K-nearest neighbor queries. Most of the current studies on the K-nearest neighbor queries utilize spatial index structures and hence are based on the Euclidean distances between the points. In real-world road networks, however, the shortest distance between two points depends on the actual path connecting the points and cannot be computed accurately using one of the Minkowski metrics. Thus, the Euclidean distance may not properly approximate the real distance. In this paper, we apply an embedding technique to transform a road network to a high dimensional space in order to utilize computationally simple Minkowski metrics for distance measurement. Subsequently, we extend our approach to dynamically transform new points into the embedding space. Finally, we propose an ef®cient technique that can ®nd the actual shortest path between two points in the original road network using only the embedding space. Our empirical experiments indicate that the Chessboard distance metric L ? in the embedding space preserves the ordering of the distances between a point and its neighbors more precisely as compared to the Euclidean distance in the original road network.
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