The multidimensional binary search tree (or <italic>k-d tree) as a data structure for storage of information to be retrieved by associative searches is developed and it is shown to be quite efficient in its storage requirements.Expand

An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record.… Expand

An optimized tree is defined and an algorithm to accomplish optimization in n log n time is presented, guaranteeing that Searching is guaranteed to be fast in optimized trees.Expand

Algorithms that count the number of pairwise intersections among a set of N objects in the plane and algorithms that report all such intersections are given.Expand

Three techniques in computational geometry are explored: scaling solves a problem by viewing it at increasing levels of numerical precision; activation is a restricted type of update operation, useful in sweep algorithms; the Cartesian tree is a data structure for problems involving maximums and minimums.Expand

This work presents theoretical algorithms for sorting and searching multikey data, and derive from them practical C implementations for applications in which keys are character strings, and presents extensions to more complex string problems, such as partial-match searching.Expand

Multidimensional divide-and-conquer is discussed, an algorithmic paradigm that can be instantiated in many different ways to yield a number of algorithms and data structures for multidimensional problems.Expand

Other new techniques can be applied to general K-d trees, leading to a data structure that is significantly faster and less vulnerable to pathological inputs than ordinary <italic>K—d trees.Expand

Three classes of transformations based on a different counting scheme for representing the integers are exhibited, and a combinatorial model is used to show the optimality of many of the transformations.Expand

Transforms for converting a static structure into a dynamic structure, for adding 'range variables' to queries, and for making preprocessing/query time tradeoffs are presented.Expand