An algorithm is presented for finding the k nearest neighbors in a spatial network in a best-first manner using network distance. The algorithm is based on precomputing the shortest paths between all possible vertices in the network and then making use of an encoding that takes advantage of the fact that the shortest paths from vertex u to all of the remaining vertices can be decomposed into subsets based on the first edges on the shortest paths to them from u. Thus, in the worst case, the amount of work depends on the number of objects that are examined and the number of links on the shortest paths to them from q, rather than depending on the number of vertices in the network. The amount of storage required to keep track of the subsets is reduced by taking advantage of their spatial coherence which is captured by the aid of a shortest path quadtree. In particular, experiments on a number of large road networks as well as a theoretical analysis have shown that the storage has been reduced from O(N 3 ) to O(N 1.5 ) (i.e., by an order of magnitude equal to the square root). The precomputation of the shortest paths along the network essentially decouples the process of computing shortest paths along the network from that of finding the neighbors, and thereby also decouples the domain S of the query objects and that of the objects from which the neighbors are drawn from the domain V of the vertices of the spatial network. This means that as long as the spatial network is unchanged, the algorithm and underlying representation of the shortest paths in the spatial network can be used with different sets of objects.

A framework for determining the shortest path and the distance between every pair of vertices on a spatial network is presented. The framework, termed SILC, uses path coherence between the shortest path and the spatial positions of vertices on the spatial network, thereby, resulting in an encoding that is compact in representation and fast in path and distance retrievals. Using this framework, a wide variety of spatial queries such as incremental nearest neighbor searches and spatial distance joins can be shown to work on datasets of locations residing on a spatial network of sufficiently large size. The suggested framework is suitable for both main memory and disk-resident datasets.

The advent of location-based services has led to an increased demand for performing operations on spatial networks in real time. The challenge lies in being able to cast operations on spatial networks in terms of relational operators so that they can be performed in the context of a database. A linear-sized construct termed a path oracle is introduced that compactly encodes the n 2 shortest paths between every pair of vertices in a spatial network having n vertices thereby reducing each of the paths to a single tuple in a relational database and enables finding shortest paths by repeated application of a single SQL SELECT operator. The construction of the path oracle is based on the observed coherence between the spatial positions of both source and destination vertices and the shortest paths between them which facilitates the aggregation of source and destination vertices into groups that share common vertices or edges on the shortest paths between them. With the aid of the Well-Separated Pair (WSP) technique, which has been applied to spatial networks using the network distance measure, a path oracle is proposed that takes O(s d n) space, where s is empirically estimated to be around 12 for road networks, but that can retrieve an intermediate link in a shortest path in O(log n) time using a B-tree. An additional construct termed the path-distance oracle of size O(n · max(s d ,(empirically (n · max(12 2 , 2.5 ε 2 ))) is proposed that can retrieve an intermediate vertex as well as an ε-approximation of the network distances in O(log n) time using a B-tree. Experimental results indicate that the proposed oracles are linear in n which means that they are scalable and can enable complicated query processing scenarios on massive spatial network datasets.

Numerous federal agencies produce official statistics made accessible to ordinary citizens for searching and data retrieval. This is frequently done via the Internet through a Web browser interface. If this data is presented in textual formatT T he SAND Spatial Browser is part of the SAND System whose server side contains a spatial database system that facilitates organization (that is, indexing) of spatial and nonspatial data [1] to support efficient query processing. This database system handles any two or higher dimensional data with extent (for example, country boundaries, river paths), as well as point data (for example, city locations). It facilitates the response to queries involving this data such as finding the closest hazardous waste site to the border of a particular state.Users access and manipulate spatial and nonspatial data using the SAND Spatial Browser in a manner similar to that used in spreadsheets where the map plays the same as a relation in a relational database management system. In particular, operations can be specified as compositions of maps with the output of one or more operations serving as input to other operations that can be saved for use as input to

The result of a distance join operation on two sets of objects R, S on a spatial network G is a set P of object pairs , p ∈ R, q ∈ S such that the distance of an object pair is the shortest distance from p to q in G. Several variations to the distance join operation such as UnOrdered, Incremental, Top-k, Semi-Join impose additional constraints on the distance between the object pairs in P , the ordering of object pairs in P , and on the cardinality of P. A distance join algorithm on spatial networks is proposed that works in conjunction with the SILC framework, which is a new approach to query processing on spatial networks. Experimental results demonstrate up to an order of magnitude speed up when compared with a prominent existing technique.