k-d tree
k-dimensional tree

He is credited with the invention of the k-d tree.

Note that Octrees are not the same as k-d trees.

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

It is also possible to define a k-d tree with points stored solely in leaves.

Implicit k-d trees as defined here have recently been introduced, with applications in computer graphics.

Implicit k-d trees are in general not constructed explicitly.

Instead of points, a k-d tree can also contain rectangles or hyperrectangles.

Building a static k-d tree from n points takes:

Removing a point from a balanced k-d tree takes O(log n) time.

The canonical method of k-d tree construction has the following constraints:

Many of these variants are adaptive k-d trees.

This method leads to a balanced k-d tree, in which each leaf node is about the same distance from the root.

Searching for a nearest neighbour in a k-d tree proceeds as follows:

These guidelines will simplify creation of k-d trees:

Several variants of balanced k-d trees exist.

Finding 1 nearest neighbour in a balanced k-d tree with randomly distributed points takes O(log n) time on average.

An obvious advantage of implicit k-d trees is that their split plane's orientations and positions need not to be stored explicitly.

Given an implicit k-d tree spanned over an k-dimensional grid with n gridcells.

An adaptive k-d tree is a tree for multidimensional points where successive levels may be split along different dimensions.

The k-d tree is a binary tree in which every node is a k-dimensional point.

This form of k-d tree allows a variety of split mechanics other than the standard median split.

Given a list of n points, the following algorithm uses a median-finding sort to construct a balanced k-d tree containing those points.

One adds a new point to a k-d tree in the same way as one adds an element to any other search tree.

Perhaps the simplest is the k-d tree, which iteratively bisects the search space into two regions containing half of the points of the parent region.

As a complete implicit k-d tree has one inner node less than grid cells, it is known in advance how many attributes need to be stored.

In computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space.

A Kd-tree (k-dimensional tree) is a space-partitioning data structure that stores a set of k-dimensional points in a tree structure that enables efficient range searches and nearest neighbor searches.