K-d tree

One -dimensional tree, or-d tree is a un - balanced search tree for storing points from the. It offers similar to the range tree the ability to perform orthogonal range queries. The request complexity is indeed higher, but the memory overhead is held.

Definition

There are homogeneous and inhomogeneous k- d- trees. In homogeneous kd - trees, each node stores a record. In the inhomogeneous variant, the internal nodes contain only keys that leaves contain references to records.

In an inhomogeneous kd-tree is the paraxial -dimensional hyperplane in place. For the root dividing the points by the hyperplane into two equal as possible point sets and carries the one in the root, the left of which all points are stored, which are smaller than the right of the root of all major. For the left child node, the points are divided again by a new split level and stored in the internal nodes. To the left of all points are stored, which is less than. This will now be continued recursively on all dimensions. Then it returns to the first dimension, to each point can be uniquely identified by hyperplanes.

A k- d- tree can be divided into construct. Orthogonal range queries can be answered in, the size of the response indicated. The memory requirements for the tree itself is in.

Example 2-d tree

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