Extending Rectangle Join Algorithms for Rectilinear Polygons

Spatial joins are very important but costly operations in spatial databases. A typical evaluation strategy of spatial joins is to perform the join on approximations of spatial objects and then evaluate the join of the real objects based on the results. The common approximation is the minimum bounding rectangle. Minimum bounding rectangles are coarse approximations of spatial objects and may cause a large number of "false hits". In this paper, we consider a more general form of approximation with rectilinear polygons for spatial objects in the context of spatial join evaluation. A naive approach is to decompose rectilinear polygons into rectangles and use an exisiting rectangle join algorithm. This may require additional cost for sorting, index construction, and decomposition and prohibits the join evaluation to be pipelined. The main contribution of the paper is a technique for extending plane sweeping based rectangle join algorithms to perform a spatial join on rectilinear polygons directly. We show that the join of two sets of rectilinear polygons can be computed in O(bN logb N/b + l2k) IOs directly, where N is the total number of boundary points in each input set, l the maximum number of boundary points of a rectilinear polygon, b the page size, and k the number of rectilinear polygon intersections. When the rectilinear polygons are y-monotone, the IO complexity becomes O(bN logb N/b + lk.