## Nearest Neighbor Queries (1995)

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Citations: | 484 - 1 self |

### BibTeX

@MISC{Roussopoulos95nearestneighbor,

author = {Nick Roussopoulos and Stephen Kelley and Frederic Vincent},

title = { Nearest Neighbor Queries},

year = {1995}

}

### Years of Citing Articles

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### Abstract

A frequently encountered type of query in Geographic Information Systems is to find the k nearest neighbor objects to a given point in space. Processing such queries requires substantially different search algorithms than those for location or range queries. In this paper we present an efficient branch-and-bound R-tree traversal algorithm to find the nearest neighbor object to a point, and then generalize it to finding the k nearest neighbors. We also discuss metrics for an optimistic and a pessimistic search ordering strategy as well as for pruning. Finally, we present the results of several experiments obtained using the implementation of our algorithm and examine the behavior of the metrics and the scalability of the algorithm.

### Citations

2219 | R-Trees: A Dynamic Index Structure for Spatial Searching
- Guttman
- 1984
(Show Context)
Citation Context ...racks and explores remaining subtrees which potentially contain NN until no subtree needs be visited. In [FBF77] a NN algorithm for k-d-trees was proposed which was later refined in [Spro91]. R-trees =-=[Gutt84]-=-, Packed R-trees [Rous85], [Kamel93], R-tree variations [SRF87], [Beck90] have been primarily used for overlap/containment range queries and spatial join queries [BKS93] based on overlap/containment. ... |

1174 |
The Design and Analysis of Spatial Data Structures
- Samet
- 1990
(Show Context)
Citation Context ...sing of NN queries requires spatial data structures which capitalize on the proximity of the objects to focus the search of potential neighbors only. There is a wide variety of spatial access methods =-=[Same89]-=-. However, very few have been used for NN. In [Same90], heuristics are provided to find objects in quadtrees. The exact k-NN problem, is also posed for hierarchical spatial data structures such as the... |

980 | The R*-tree: An efficient and robust access method for points and rectangles
- Beckmann, Kriegel, et al.
- 1990
(Show Context)
Citation Context ...no subtree needs be visited. In [FBF77] a NN algorithm for k-d-trees was proposed which was later refined in [Spro91]. R-trees [Gutt84], Packed R-trees [Rous85], [Kamel93], R-tree variations [SRF87], =-=[Beck90]-=- have been primarily used for overlap/containment range queries and spatial join queries [BKS93] based on overlap/containment. In this paper, we provide an efficient branch-and-bound search algorithm ... |

586 | An algorithm for finding best matches in logarithmic expected time
- Friedman, Bentley, et al.
- 1977
(Show Context)
Citation Context ...at contains the query point, in order to get a first estimate of the NN location. Then it backtracks and explores remaining subtrees which potentially contain NN until no subtree needs be visited. In =-=[FBF77]-=- a NN algorithm for k-d-trees was proposed which was later refined in [Spro91]. R-trees [Gutt84], Packed R-trees [Rous85], [Kamel93], R-tree variations [SRF87], [Beck90] have been primarily used for o... |

324 | Efficient processing of spatial joins using r-trees
- Brinkhoff, Kriegel, et al.
- 1993
(Show Context)
Citation Context ... refined in [Spro91]. R-trees [Gutt84], Packed R-trees [Rous85], [Kamel93], R-tree variations [SRF87], [Beck90] have been primarily used for overlap/containment range queries and spatial join queries =-=[BKS93]-=- based on overlap/containment. In this paper, we provide an efficient branch-and-bound search algorithm for processing exact k-NN queries for the R-trees, introduce several metrics for ordering and pr... |

262 | The R+-Tree: A Dynamic Index for Multi-Dimensional Objects," VLDB
- Sellis, Roussopoulos, et al.
- 1987
(Show Context)
Citation Context ...NN until no subtree needs be visited. In [FBF77] a NN algorithm for k-d-trees was proposed which was later refined in [Spro91]. R-trees [Gutt84], Packed R-trees [Rous85], [Kamel93], R-tree variations =-=[SRF87]-=-, [Beck90] have been primarily used for overlap/containment range queries and spatial join queries [BKS93] based on overlap/containment. In this paper, we provide an efficient branch-and-bound search ... |

194 |
Fundamentals of Computer Algorithms
- HOROWITZ, SAHNI
- 1978
(Show Context)
Citation Context ...k-NN. 3.1 MINDIST and MINMAXDIST for Ordering and Pruning the Search Branch-and-bound algorithms have been studied and used extensively in the areas of artificial intelligence and operations research =-=[HS78]-=-. If the ordering and pruning heuristics are chosen well, they can significantly reduce the number of nodes visited in a large search space. Search Ordering: The heuristics we use in our algorithm and... |

185 |
Linear clustering of objects with multiple attributes
- Jagadish
- 1990
(Show Context)
Citation Context ...using a different seed value for each data set. We then generated 100 equally spaced query points in the 8K by 8K space. We built the R-tree indexes by first presorting the data files using a Hilbert =-=[Jaga90]-=- number generating function, and then applying a modified version of [Rous85] R-tree packing technique according to the suggestion of [Kamel93]. The branching factor of both the terminal and non-termi... |

185 | Hilbert R-tree: An improved R-tree using fractals
- Kamel, Faloutsos
- 1994
(Show Context)
Citation Context ...es which potentially contain NN until no subtree needs be visited. In [FBF77] a NN algorithm for k-d-trees was proposed which was later refined in [Spro91]. R-trees [Gutt84], Packed R-trees [Rous85], =-=[Kamel93]-=-, R-tree variations [SRF87], [Beck90] have been primarily used for overlap/containment range queries and spatial join queries [BKS93] based on overlap/containment. In this paper, we provide an efficie... |

149 | D.Leifker “Direct spatial searche on pictorial databases using packed R Trees”, proc
- Roussopoulos
(Show Context)
Citation Context ...ing subtrees which potentially contain NN until no subtree needs be visited. In [FBF77] a NN algorithm for k-d-trees was proposed which was later refined in [Spro91]. R-trees [Gutt84], Packed R-trees =-=[Rous85]-=-, [Kamel93], R-tree variations [SRF87], [Beck90] have been primarily used for overlap/containment range queries and spatial join queries [BKS93] based on overlap/containment. In this paper, we provide... |

103 |
Refinements to Nearest-Neighbor Searching in k-Dimensional Trees
- Sproull
- 1987
(Show Context)
Citation Context ...ion. Then it backtracks and explores remaining subtrees which potentially contain NN until no subtree needs be visited. In [FBF77] a NN algorithm for k-d-trees was proposed which was later refined in =-=[Spro91]-=-. R-trees [Gutt84], Packed R-trees [Rous85], [Kamel93], R-tree variations [SRF87], [Beck90] have been primarily used for overlap/containment range queries and spatial join queries [BKS93] based on ove... |

73 |
Applications of Spatial Data Structures: Computer Graphics, Image Processing and GIS
- Samet
- 1990
(Show Context)
Citation Context ...ich capitalize on the proximity of the objects to focus the search of potential neighbors only. There is a wide variety of spatial access methods [Same89]. However, very few have been used for NN. In =-=[Same90]-=-, heuristics are provided to find objects in quadtrees. The exact k-NN problem, is also posed for hierarchical spatial data structures such as the PM quadtree. The proposed solution is a top-down recu... |

41 |
The R*-tree: An e cient and robust access method for points and rectangles
- Beckmann, Kriegel, et al.
(Show Context)
Citation Context ... no subtree needs be visited. In [FBF77] a NN algorithm for k-d-trees was proposed which was later re ned in [Spro91]. R-trees [Gutt84], Packed R-trees [Rous85], [Kamel93], R-tree variations [SRF87], =-=[Beck90]-=- have been primarily used for overlap/containment range queries and spatial join queries [BKS93] based on overlap/containment. In this paper, we provide an e cient branch-and-bound search algorithm fo... |

28 |
An algorithm for nding best matches in logarithmic expected time
- Friedman, Bentley, et al.
- 1977
(Show Context)
Citation Context ...that contains the query point, in order to get a rst estimate of the NN location. Then it backtracks and explores remaining subtrees which potentially contain NN until no subtree needs be visited. In =-=[FBF77]-=- a NN algorithm for k-d-trees was proposed which was later re ned in [Spro91]. R-trees [Gutt84], Packed R-trees [Rous85], [Kamel93], R-tree variations [SRF87], [Beck90] have been primarily used for ov... |

7 |
Re nements to nearest-neighbor searching in k-d trees. Algorithmica
- Sproull
- 1991
(Show Context)
Citation Context ...tion. Then it backtracks and explores remaining subtrees which potentially contain NN until no subtree needs be visited. In [FBF77] a NN algorithm for k-d-trees was proposed which was later re ned in =-=[Spro91]-=-. R-trees [Gutt84], Packed R-trees [Rous85], [Kamel93], R-tree variations [SRF87], [Beck90] have been primarily used for overlap/containment range queries and spatial join queries [BKS93] based on ove... |