Abstract: Methods for cascade elimination of candidates in spatial relation operations are performed by systems, devices, and apparatuses. Spatial relation operations include counts of geometric objects against geographies/geometries, and data points associated with vertices of shapes representing the geographies/geometries are reduced to form smaller sets of data points that represent the initial shapes. Elimination of geometric objects for operations is performed using inner- and outer-reductions in cascade. Data points are reduced until a representation of the original shape with a specified area or number of data points is generated. Multi-polygon geometries are joined by union based on preservation of area and data points of the polygons therein prior to reducing data points. Cascade reductions are also performed at specified times during spatial operations based on costs associated therewith.

Abstract: Methods for cascade elimination of candidates in spatial relation operations are performed by systems, devices, and apparatuses. Spatial relation operations include counts of geometric objects against geographies/geometries, and data points associated with vertices of shapes representing the geographies/geometries are reduced to form smaller sets of data points that represent the initial shapes. Elimination of geometric objects for operations is performed using inner- and outer-reductions in cascade. Data points are reduced until a representation of the original shape with a specified area or number of data points is generated. Multi-polygon geometries are joined by union based on preservation of area and data points of the polygons therein prior to reducing data points. Cascade reductions are also performed at specified times during spatial operations based on costs associated therewith.