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- Jon Louis Bentley
- Commun. ACM
- 1975

This paper develops the multidimensional binary search tree (or <italic>k</italic>-d tree, where <italic>k</italic> is the dimensionality of the search space) as a data structure for storage of information to be retrieved by associative searches. The <italic>k</italic>-d tree is defined and examples are given. It is shown to be quite efficient in its… (More)

- Jerome H. Friedman, Jon Louis Bentley, Raphael A. Finkel
- ACM Trans. Math. Softw.
- 1977

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. The computation required to organize the file is proportional to kN log N. The expected number of records examined in each search is independent of the file… (More)

- Jon Louis Bentley, Thomas Ottmann
- IEEE Trans. Computers
- 1979

- Raphael A. Finkel, Jon Louis Bentley
- Acta Informatica
- 1974

The quad tree is a data structure appropriate for storing information to be retrieved on composite keys. We discuss the specific case of two-dimensional retrieval, although the structure is easily generalised to arbitrary dimensions. Algorithms are given both for staightforward insertion and for a type of balanced insertion into quad trees. Empirical… (More)

- Jon Louis Bentley
- INFORMS Journal on Computing
- 1992

- Jon Louis Bentley
- Commun. ACM
- 1980

Most results in the field of algorithm design are single algorithms that solve single problems. In this paper we discuss <italic>multidimensional divide-and-conquer</italic>, an algorithmic <italic>paradigm</italic> that can be instantiated in many different ways to yield a number of algorithms and data structures for multidimensional problems. We use this… (More)

- Harold N. Gabow, Jon Louis Bentley, Robert E. Tarjan
- STOC
- 1984

Three techniques in computational geometry are explored: <italic>Scaling</italic> solves a problem by viewing it at increasing levels of numerical precision; <italic>activation</italic> is a restricted type of update operation, useful in sweep algorithms; the <italic>Cartesian tree</italic> is a data structure for problems involving maximums and minimums.… (More)

- Jon Louis Bentley, Robert Sedgewick
- SODA
- 1997

We present theoretical algorithms for sorting and searching multikey data, and derive from them practical C implementations for applications in which keys are character strings. The sorting algorithm blends Quicksort and radix sort; it is competitive with the best known C sort codes. The searching algorithm blends tries and binary search trees; it is faster… (More)

- Jon Louis Bentley, Daniel Dominic Sleator, Robert E. Tarjan, Victor K.-W. Wei
- Commun. ACM
- 1986

- Jon Louis Bentley, James B. Saxe
- J. Algorithms
- 1980