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.
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