Optimizing within-distance queries by approximating shapes with maximal bounded boxes

Background: In geospatial query processing, spatial containment and intersection queries can be efficiently answered from the index. There is, however, a class of queries (such as within-distance) with a semantics that implies that every shape in the database is a potential match and should, in principle, be compared with the threshold. Naturally, this is impractical and optimizations have been developed that efficiently refine the set of candidate shapes before starting to actually compute distances and apply the threshold. In the case of the within-distance queries, many instances can be discarded in advance as too distant. Since geospatial databases organize data as a hierarchy of bounding boxes, this already provided the first direct optimization as the actual distance cannot be smaller than the distance between the bounding boxes. One can easily understand that there are shape configurations that give bounding boxes that are not very selective for near-by shapes. That is, configurations where there are shapes outside the requested distance but within the request distance from the bounding box. Methods: In this article, we investigate a further optimization in addition to and after comparing the bounding boxes, but before computing precise distances. We describe the distance optimizer operation currently used by PostGIS and show how the existing implementation prevails over approaches that use additional approximations. We implement a recursive algorithm to calculate the minimal possible largest inner rectangles of geometries. Results: We observe that the performance of the distance operation cannot be improved by using the inner approximations instead of the actual shapes. The overheads of the inner rectangles would not be recovered from calculating the distance between simpler geometries. Conclusions: The execution time of the distance operator has a small dependence on polygon complexity. Conclusively, an inner approximation for complex polygons cannot out-perform the standard PostGIS implementation.