Optimal Bounds-Only Pruning for Spatial AkNN Joins

We propose a bounds-only pruning test for exact Euclidean AkNN joins on partitioned spatial datasets. Data warehouses commonly partition large tables and store row group statistics for them to accelerate searches and joins, rather than maintaining indexes. AkNN joins can benefit from such statistics by constructing bounds and localizing join evaluations to a few partitions before loading them to build spatial indexes. Existing pruning methods are overly conservative for bounds-only spatial data because they do not fully capture its directional semantics, thereby missing opportunities to skip unneeded partitions at the earliest stages of a join. We propose a three-bound proximity test to determine whether all points within a partition have a closer neighbor in one partition than in another, potentially occluded partition. We show that our algorithm is both optimal and efficient.