Description
A range tree on a set of 1-dimensional points is a balanced binary search tree on those points. The points stored in the tree are stored in the leaves of the tree; each internal node stores the largest value contained in its left subtree. A range tree on a set of points in d-dimensions is a recursively defined multi-level binary search tree. Each level of the data structure is a binary search tree on one of the d-dimensions. The first level is a binary search tree on the first of the d-coordinates. Each vertex v of this tree contains an associated structure that is a (d−1)-dimensional range tree on the last (d−1)-coordinates of the points stored in the subtree of v.
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