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.

翻译：空间交集连接是一种重要的空间查询操作，因其普及性和高复杂度而备受关注。空间连接流程以两个空间对象（如多边形）集合作为输入。在过滤阶段，识别出相交的对象最小外接矩形（MBR）对，并将其传递至精化阶段，以基于精确对象几何验证连接谓词。空间连接评估的瓶颈在于精化阶段。我们提出APRIL，一种基于对象几何栅格区间近似的强大中间步骤。该技术通过对“区间化”的对象近似执行一系列区间连接，以判断对象是否相交。与先前工作相比，APRIL近似更简洁、占用空间更少，且在更高速度下实现相近的剪枝效果。除多边形间交集连接外，APRIL可直接应用于多边形范围查询、包含连接及多边形与线串连接，并具有高效性。通过轻量级压缩技术，APRIL近似所需空间甚至小于对象MBR。此外，APRIL可定制化应用于分区数据及不同大小的多边形，并以不同粒度进行栅格化。我们的最后贡献是一种新算法，无需完全栅格化即可计算多边形的APRIL近似，其速度比其他栅格近似计算快数个数量级。真实数据实验证明了APRIL的有效性与效率；与最先进的中间过滤器相比，APRIL占用空间减少2至8倍，时间效率提升3.5至8.5倍，并降低端到端连接成本高达3倍。