interval tree
range tree

See also interval tree, which is a 1-dimensional special case.

Each interval tree also needs an addition for higher dimensions.

A much simpler solution is to use nested interval trees.

A similar data structure is the interval tree.

In computer science, an interval tree is an ordered tree data structure to hold intervals.

Interval trees are dynamic, i.e., they allow insertion and deletion of intervals.

Interval tree - A degenerate R-tree for one dimension (usually time).

Interval trees solve this problem.

To find these overlaps, N interval trees are created, and one axis intersecting R is queried for each.

The use of the interval tree on the deepest level of associated structures lowers the storage bound with a logarithmic factor.

Likewise, the left (or any other vertical line intersecting R) would be queried against the interval tree constructed on the vertical axis.

Interval Tree (an augmented self balancing avl tree implementation)

This mechanism can depict scalability problems in some settings, but can be replaced by Interval Tree Clocks.

Interval Tree Clocks generalize version vectors and vector clocks and allows dynamic numbers of replicas/processes.

This article describes two alternative designs for an interval tree, dubbed the centered interval tree and the augmented tree.

The interval tree data structure can be generalized to a higher dimension N with identical query and construction time and O(n log n) space.

Now, for each node in the tree, add another interval tree on the x ranges, for all elements whose y range intersect that node's y range.

This algorithm is expected to be faster than traditional Interval Tree (Augmented tree) in search operation, adding is just a little bit slower (order of growth is the same).

Edelsbrunner has also made important contributions to algorithms for intersections of line segments, construction of K-sets, the ham sandwich theorem, Delaunay triangulation, point location, interval trees, fractional cascading, and protein docking.

A version for higher dimensions of the interval tree and the priority search tree does not exist, that is, there is no clear extension of these structures that solves the analogous problem in higher dimensions.

The segment tree is less efficient than the interval tree for range queries in one dimension, due to its higher storage requirement: O(nlogn) against the O(n) of the interval tree.

Range trees can be used to find the set of points that lie inside a given interval.

In computer science, a range tree is an ordered tree data structure to hold a list of points.

The range tree is an alternative to the k-d tree.

Continue searching for x in the range tree.

Instead of two sorted lists of points as was used in the one-dimensional case, a range tree is constructed.

Range trees were introduced by Jon Louis Bentley in 1979.

A range tree on a set of 1-dimensional points is a balanced binary search tree on those points.

This can be improved by noticing that a range tree on a set 2-dimensional points can be constructed in O(n log n) time.

Since the range tree is a balanced binary tree, the search paths to x and x have length O(log n).

Lecture 8: Range Trees, Marc van Kreveld.

Index (database), Quadtree, Kd-tree, UB-tree, R-tree, range tree as alternatives.

Otherwise, construct the associated structure of S, a 1-dimensional range tree on the y-coordinates of the points in S. Let x be the median x-coordinate of the points.

Using (k 1)-dimensional range trees to store and query coordinates, Felsner's algorithms for chromatic number, maximum clique, and maximum independent set can be applied to k-trapezoid graphs in time.

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.

This reduces the time to construct a 2-dimensional range tree to O(n log n), which also reduces the time to construct a d-dimensional range tree to O(n logn).

First, a range tree in N dimensions is constructed that allows efficient retrieval of all intervals with beginning and end points inside the query region R. Once the corresponding ranges are found, the only thing that is left are those ranges that enclose the region in some dimension.

Most algorithms and data structures for searching a dataset are based on the classical binary search algorithm, and generalizations such as the k-d tree or range tree work by interleaving the binary search algorithm over the separate coordinates and treating each spatial coordinate as an independent search constraint.