APRIL: Approximating Polygons as Raster Interval Lists
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The spatial intersection join an important spatial query operation, due to its popularity and high complexity. The spatial join pipeline takes as input two collections of spatial objects (e.g., polygons). In the filter step, pairs of object MBRs that intersect are identified and passed to the refinement step for verification of the join predicate on the exact object geometries. The bottleneck of spatial join evaluation is in the refinement step. We introduce APRIL, a powerful intermediate step in the pipeline, which is based on raster interval approximations of object geometries. Our technique applies a sequence of interval joins on 'intervalized' object approximations to determine whether the objects intersect or not. Compared to previous work, APRIL approximations are simpler, occupy much less space, and achieve similar pruning effectiveness at a much higher speed. Besides intersection joins between polygons, APRIL can directly be applied and has high effectiveness for polygonal range queries, within joins, and polygon-linestring joins. By applying a lightweight compression technique, APRIL approximations may occupy even less space than object MBRs. Furthermore, APRIL can be customized to apply on partitioned data and on polygons of varying sizes, rasterized at different granularities. Our last contribution is a novel algorithm that computes the APRIL approximation of a polygon without having to rasterize it in full, which is orders of magnitude faster than the computation of other raster approximations. Experiments on real data demonstrate the effectiveness and efficiency of APRIL; compared to the state-of-the-art intermediate filter, APRIL occupies 2x-8x less space, is 3.5x-8.5x more time-efficient, and reduces the end-to-end join cost up to 3 times.
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