KDtrær

KD-trær, an abbreviation for k-d trees, are space-partitioning data structures in computer science used for organizing points in a k-dimensional space. They are binary trees where each non-leaf node represents a splitting hyperplane that divides the space into two half-spaces. The splitting hyperplanes are axis-aligned, meaning they are parallel to one of the coordinate axes.

The construction of a k-d tree typically involves recursively partitioning the set of points. At each step, a dimension is chosen, and the points are sorted along that dimension. The median point is then selected as the current node, and the remaining points are divided into two subsets based on whether they lie on one side or the other of the median point along the chosen dimension. This process is repeated for the two subsets, with the splitting dimension often cycling through the available dimensions to ensure a balanced tree.

KD-trær are particularly useful for a variety of applications, including nearest neighbor searches, range searches, and spatial indexing. In a nearest neighbor search, given a query point, the algorithm efficiently finds the point in the dataset that is closest to the query point. Range searches involve finding all points within a specified region of the k-dimensional space. The efficiency of these operations in k-d trees depends on the dimensionality of the space and the distribution of the data. While effective in lower dimensions, their performance can degrade in very high-dimensional spaces due to the "curse of dimensionality."