Input: A set of possibly overlapping regions (polygons with and without interior rings) and a set of points.

Output: Pair each input point with one or more of the input polygons such that a given spatial condition is satisfied between the polygon and the point.

Description: A region can be any polygon (with or without interior rings) that is made up of straight line segments. A set of these regions that can possibly overlap with each other are provided as part of the input. The number of the regions will be no more than a 500. Additionally, a set of input points are given. The number of these points will be no more than 1 Million. The objective is to match each of these points with one or more of the polygons from the input based on a spatial predicate. We have two spatial predicates, explained as follows:

• INSIDE: which evaluates to TRUE if a point is inside the polygon. Notice that the point can be associated with one or more polygons (i.e., two overlapping polygons can contain the same point). A point can be INSIDE any polygon with a sequence number (i.e., timestamp) less than the sequence number of the point where only the latest position of each polygon (up to that sequence number) is considered.

• WITHIN n (e.g., WITHIN a distance of 1000 units): which evaluates to true if the point is at less than 1000 units distance from the polygon. Notice that each point may be associated with one or more of the polygons, as the same point can be within 1000 units distance from several polygons.

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