Benchmarking Spatial Join Operations with Spatial Output

The spatial join operation is benchmarked using variants of well-known spatial data structures such as the R-tree, R -tree, R-tree, and the PMR quadtree. The focus is on a spatial join with spatial output because the result of the spatial join frequently serves as input to subsequent spatial operations (i.e., a cascaded spatial join as would be common in a spatial spreadsheet). Thus, in addition to the time required to perform the spatial join itself (whose output is not always required to be spatial), the time to build the spatial data structure also plays an important role in the benchmark. The studied quantities are the time to build the data structure and the time to do the spatial join in an application domain consisting of planar line segment data. Experiments reveal that spatial data structures based on a disjoint decomposition of space and bounding boxes (i.e., the R-tree and the PMR quadtree with bounding boxes) outperform the other structures that are based upon a non-disjoint decomposition (i.e., the R-tree and R -tree). As the size of the output of the spatial join increases with respect to the larger of the two inputs, the advantage of the bounding boxes used in methods based on a disjoint non-regular decomposition is no longer a factor and methods based on a disjoint regular decomposition (i.e., the PMR quadtree regardless of the presence of bounding boxes) perform signi cantly better. When the output of the spatial join is not required to be spatial (i.e., it is a list or table of tuples), then the performance of the best methods based on a non-disjoint decomposition (i.e., the R -tree) is comparable to those with a disjoint decomposition (i.e., the R-tree and the PMR quadtree with and without bounding boxes) as long as the size of the output is considerably smaller than that of the larger of the two inputs (e.g., 10%). However, as the output gets larger, the methods based on a regular decomposition (i.e., the PMR quadtree with and without bounding boxes) are much better than those based on an irregular decomposition (i.e, the R -tree and the R-tree) which have comparable performance in this case regardless of whether or not they are based on a disjoint or non-disjoint decomposition of space.