A variant of k-d trees, the divided k-d tree, is described that has some important advantages over ordinary k-d trees. The divided k-d tree is fully dynamic and allows for the insertion and deletion of points in O(log n) worst-case time. Moreover, divided k-d trees allow for split and concatenate

Abstract. We modify the k-d tree on [0, 1] d by always cutting the longest edge instead of rotating through the coordinates. This modification makes the expected time behavior of lower-dimensional partial match queries behave as for perfectly balanced complete k-d trees on n nodes

In this paper we present a generalization of the k-d tree data structure suitable for an efficient management and querying in a distributed framework. We present optimal searching algorithm for exact, partial, and range search queries. Optimality is in the sense that (1) only servers that could

A hierarchical search structure for ray tracing based on k-d trees is introduced. This data

A method is presented that uses an Approximate Nearest Neighbor method for determining correspondences within the Iterative Closest Point Algorithm. The method is based upon the k-d tree. The standard k-d tree uses a tentative backtracking search to identify nearest neighbors. In contrast

The k-D tree is a well-studied acceleration data structure for ray tracing. It is used to organize primitives in a scene to allow efficient execution of intersection operations between rays and the primitives. The highest quality k-D tree can be obtained using greedy cost optimization based on a

The ICP (Iterative Closest Point) algorithm is the de facto standard for geometric alignment of threedimensional models when an initial relative pose estimate is available. The basis of ICP is the search for closest points. Since the development of ICP, k-d trees have been used to accelerate

K-d trees have been widely studied, yet their complete advantages are often not realized due to ineffective search implementations and degrading performance in high dimensional spaces. We outline an effective search algorithm for k-d trees that combines an optimal depth-first branch and bound (DFBB

There are certain problems in machine learning which desire special attention when we scale up the size of the data or move towards data mining. One of them is the problem of searching nearest neighbours of a given point in k dimensional space. If the space is ! k than k-d trees can solve

. We analyze the expected time complexity of range searching with k-d trees in all dimensions when the data points are uniformly distributed in the unit hypercube. The partial match results of Flajolet and Puech are reproved using elementary probabilistic methods. In addition, we give asymptotic