Range Searching.

Range searching is one of the central problems in computational geometry, because it arises in many applications and a wide variety of geometric problems can be formulated as a range-searching problem. Range counting and range reporting are just two instances of range-searching queries. Typically, the canonical subsets are organized in a tree-like data structure, each of whose node V is associated with a canonical subset A V stores the weight wA and some auxiliary information. A query is answered by searching the tree in a top-down fashion, using the auxiliary information to guide the search.