Scalable Query Processing on Spatial Networks
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Spatial networks (e.g., road networks) are general graphs with spatial information (e.g., latitude/longitude) information associated with the vertices and/or the edges of the graph. Techniques are presented for query processing on spatial networks that are based on the observed coherence between the spatial positions of the vertices and the shortest paths between them. This facilitates aggregation of the vertices into coherent regions that share vertices on the shortest paths between them. Using this observation, a framework, termed SILC, is introduced that precomputes and compactly encodes the N^2 shortest path and network distances between every pair of vertices on a spatial network containing N vertices. The compactness of the shortest paths from source vertex V is achieved by partitioning the destination vertices into subsets based on the identity of the first edge to them from V. The spatial coherence of these subsets is captured by using a quadtree representation whose dimension-reducing property enables the storage requirements of each subset to be reduced to be proportional to the perimeter of the spatially coherent regions, instead of to the number of vertices in the spatial network. In particular, experiments on a number of large road networks as well as a theoretical analysis have shown that the total storage for the shortest paths has been reduced from O(N^3) to O(N^1.5). In addition to SILC, another framework, termed PCP, is proposed that also takes advantage of the spatial coherence of the source vertices and makes use of the Well Separated Pair decomposition to further reduce the storage, under suitably defined conditions, to O(N).
Using these frameworks, scalable algorithms are presented to implement a wide variety of operations such as nearest neighbor finding and distance joins on large datasets of locations residing on a spatial network. These frameworks essentially decouple the process of computing shortest paths from that of spatial query processing as well as also decouple the domain of the participating objects from the domain 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.