Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Multidimensional binary search trees used for associative searching

Multidimensional binary search trees used for associative searching This paper develops the multidimensional binary search tree (or k -d tree, where k is the dimensionality of the search space) as a data structure for storage of information to be retrieved by associative searches. The k -d tree is defined and examples are given. It is shown to be quite efficient in its storage requirements. A significant advantage of this structure is that a single data structure can handle many types of queries very efficiently. Various utility algorithms are developed; their proven average running times in an n record file are: insertion, O (log n ); deletion of the root, O ( n ( k -1)/ k ); deletion of a random node, O (log n ); and optimization (guarantees logarithmic performance of searches), O ( n log n ). Search algorithms are given for partial match queries with t keys specified proven maximum running time of O ( n ( k - t )/ k ) and for nearest neighbor queries empirically observed average running time of O (log n ). These performances far surpass the best currently known algorithms for these tasks. An algorithm is presented to handle any general intersection query. The main focus of this paper is theoretical. It is felt, however, that k -d trees could be quite useful in many applications, and examples of potential uses are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications of the ACM Association for Computing Machinery

Multidimensional binary search trees used for associative searching

Communications of the ACM , Volume 18 (9) – Sep 1, 1975

Loading next page...
 
/lp/association-for-computing-machinery/multidimensional-binary-search-trees-used-for-associative-searching-q0wcUnKQw0

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
Association for Computing Machinery
Copyright
Copyright © 1975 by ACM Inc.
ISSN
0001-0782
DOI
10.1145/361002.361007
Publisher site
See Article on Publisher Site

Abstract

This paper develops the multidimensional binary search tree (or k -d tree, where k is the dimensionality of the search space) as a data structure for storage of information to be retrieved by associative searches. The k -d tree is defined and examples are given. It is shown to be quite efficient in its storage requirements. A significant advantage of this structure is that a single data structure can handle many types of queries very efficiently. Various utility algorithms are developed; their proven average running times in an n record file are: insertion, O (log n ); deletion of the root, O ( n ( k -1)/ k ); deletion of a random node, O (log n ); and optimization (guarantees logarithmic performance of searches), O ( n log n ). Search algorithms are given for partial match queries with t keys specified proven maximum running time of O ( n ( k - t )/ k ) and for nearest neighbor queries empirically observed average running time of O (log n ). These performances far surpass the best currently known algorithms for these tasks. An algorithm is presented to handle any general intersection query. The main focus of this paper is theoretical. It is felt, however, that k -d trees could be quite useful in many applications, and examples of potential uses are given.

Journal

Communications of the ACMAssociation for Computing Machinery

Published: Sep 1, 1975

There are no references for this article.