Generalization For Higher Dimensions
The segment tree can be generalized to higher dimension spaces, in the form of multi-level segment trees. In higher dimension versions, the segment tree stores a collection of axis-parallel (hyper-)rectangles, and can retrieve the rectangles that contain a given query point. The structure uses O(nlogd-1n) storage, and answers queries in O(logdn).
The use of fractional cascading lowers the query time bound by a logarithmic factor. The use of the interval tree on the deepest level of associated structures lowers the storage bound with a logarithmic factor.
Read more about this topic: Segment Tree
Famous quotes containing the words higher and/or dimensions:
“Slavery can only be abolished by raising the character of the people who compose the nation; and that can be done only by showing them a higher one.”
—Maria Weston Chapman (1806–1885)
“Why is it that many contemporary male thinkers, especially men of color, repudiate the imperialist legacy of Columbus but affirm dimensions of that legacy by their refusal to repudiate patriarchy?”
—bell hooks (b. c. 1955)