For 20 points, name this hierarchical structure often used for representing two-dimensional data, a type of tree where internal nodes have up to four children.
One type of this data structure has a depth known as its resolution, and can contain a lower bound of 2 to the negative of the resolution number of side lengths.  An extensive analysis of these data structures is given by Samet, who notes that the amortized neighbor finding in them can be done in Big O of 1 time.  Several types of these data structures are differentiated by their handling of q-edges, although they all have the property that their leaf nodes are maximal.  Another variety of this data structure draws a line through the center of a node and recursively divides the node until each node contains at most one endpoint.  The general form of these data structures was first formulated by Finkel and Bentley in a paper on "A Data Structure for Retrieval on Composite Keys", and they come in varieties like Point Region and Polygonal Map, or PR and PM, respectively.  For 20 points, name this hierarchical structure often used for representing two-dimensional data, a type of tree where internal nodes have up to four children.
One type of this data structure has a depth known as its resolution, and can contain a lower bound of 2 to the negative of the resolution number of side lengths.  
{Quadtree} [accept {PM Quadtree} or {PR Quadtree} before mentioned; prompt on "{Tree}"]