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.

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Sensor networks are unattended deeply distributed systems whose schema can be conceptualized using the relational model. Aggregation queries on the data sampled at each sensor node are the main means to extract the abstract characteristics of the surrounding environment. However, the non-uniform distribution of the sensor nodes in the environment leads to inaccurate results generated by the aggregation queries. In this paper, we introduce "spatial aggregations" that take into consideration the distribution of the values generated by the sensor nodes. We propose the use of spatial interpolation methods derived from the fields of spatial statistics and computational geometry to answer spatial aggregations. In particular, we study Spatial Moving Average (SMA), Voronoi Diagram and Triangulated Irregular Network (TIN). Investigating these methods for answering spatial average queries, we show that the average value on the data samples weighted by the area of the Voronoi cell of the corresponding sensor node, provides the best precision. Consequently, we introduce an incremental algorithm to compute and maintain the Voronoi cell at each sensor node. To demonstrate the performance of in-network implementation of our algorithm, we have developed prototypes of two different approaches to distributed spatial aggregate processing.

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.