## Filtering Search: A new approach to query-answering (1986)

Venue: | SIAM J. Comput |

Citations: | 107 - 8 self |

### BibTeX

@ARTICLE{Chazelle86filteringsearch:,

author = {Bernard Chazelle},

title = {Filtering Search: A new approach to query-answering},

journal = {SIAM J. Comput},

year = {1986},

volume = {15},

pages = {703--724}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. We introduce a new technique for solving problems of the following form: preprocess a set ofobjects so that those satisfying a given property with respect to a query object canbe listed very effectively. Well-known problems that fall into this category include range search, point enclosure, intersection, and near-neighbor problems. The approach which we take is very general and rests on a new concept called filtering search.We show on a number ofexamples how it can be used to improve the complexity ofknown algorithms and simplify their implementations as well. In particular, filtering search allows us to improve on the worst-case complexity ofthe best algorithms known so far for solving the problems mentioned above. Key words, computational geometry, database, data structures, filtering search, retrieval problems

### Citations

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(Show Context)
Citation Context ...so that any point can be efficiently located in its containing region. This planarpoint locationproblem canbe solved forgeneral planarsubdivisions in O(log n) query time, using O(n) space [15], [18], =-=[24]-=-, [28].We can now locate, say, the lowest endpoint, (x, Yl), of the query segment q, and proceed to "walk" along the edges of G, following the direction given by q. Without specifying the details, it ... |

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Citation Context ...ced, in the concept of the hive-graph, a novel technique for batching together binary searches by propagating fractional samples ofthe data to neighboring structures.We refer the interested reader to =-=[13]-=- for further developments and applications of this technique. Acknowledgments. I wish to thank Jon Bentley, Herbert Edelsbrunner, Janet Incerpi, and the anonymous referees for many valuable comments. ... |

124 |
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Citation Context ...ntain q (a d-range is the Cartesian product of d intervals) [31], [33]. 4. OrthogonalRange Search: Given a set S of n points inR a and a query d-range q, report the points of S that lie within q [1], =-=[2]-=-, [3], [5], [7], [9], [21], [22], [23], [26], [29], [31], [35], [36]. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report th... |

60 |
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Citation Context ... [26], [29], [31], [35], [36]. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report the/ points of S closest to q 11], [20], =-=[25]-=-. 6. Circular Range Search: Given a set $ of n points in the Euclidean plane and a query disk q, report the points of S that lie within q [4], [10], [11], [12], [16], [37]. * Received by the editors S... |

57 |
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Citation Context ...intervals) [31], [33]. 4. OrthogonalRange Search: Given a set S of n points inR a and a query d-range q, report the points of S that lie within q [1], [2], [3], [5], [7], [9], [21], [22], [23], [26], =-=[29]-=-, [31], [35], [36]. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report the/ points of S closest to q 11], [20], [25]. 6. Ci... |

49 |
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- 1986
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Citation Context ...reprocess G so that any point can be efficiently located in its containing region. This planarpoint locationproblem canbe solved forgeneral planarsubdivisions in O(log n) query time, using O(n) space =-=[15]-=-, [18], [24], [28].We can now locate, say, the lowest endpoint, (x, Yl), of the query segment q, and proceed to "walk" along the edges of G, following the direction given by q. Without specifying the ... |

31 |
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Citation Context ...sian product of d intervals) [31], [33]. 4. OrthogonalRange Search: Given a set S of n points inR a and a query d-range q, report the points of S that lie within q [1], [2], [3], [5], [7], [9], [21], =-=[22]-=-, [23], [26], [29], [31], [35], [36]. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report the/ points of S closest to q 11],... |

17 |
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Citation Context ...oints of S closest to q 11], [20], [25]. 6. Circular Range Search: Given a set $ of n points in the Euclidean plane and a query disk q, report the points of S that lie within q [4], [10], [11], [12], =-=[16]-=-, [37]. * Received by the editors September 15, 1983, and in final revised form April 20, 1985. This research was supported in part by the National Science Foundation under grants MCS 83-03925, and th... |

16 |
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Citation Context ...ort the intervals of S that intersect q [8], [17], [30], [31]. 2. Segment Intersection: Given a set S of n segments in the plane and a query segment q, report the segments of S that intersect q [19], =-=[34]-=-. 3. Point Enclosure: Given a set S of n d-ranges and a query point q inRd, report the d-ranges of S that contain q (a d-range is the Cartesian product of d intervals) [31], [33]. 4. OrthogonalRange S... |

15 |
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Citation Context ...of S closest to q 11], [20], [25]. 6. Circular Range Search: Given a set $ of n points in the Euclidean plane and a query disk q, report the points of S that lie within q [4], [10], [11], [12], [16], =-=[37]-=-. * Received by the editors September 15, 1983, and in final revised form April 20, 1985. This research was supported in part by the National Science Foundation under grants MCS 83-03925, and the Offi... |

13 |
Computing point enclosures
- Vaishnavi
- 1982
(Show Context)
Citation Context ...hat intersect q [19], [34]. 3. Point Enclosure: Given a set S of n d-ranges and a query point q inRd, report the d-ranges of S that contain q (a d-range is the Cartesian product of d intervals) [31], =-=[33]-=-. 4. OrthogonalRange Search: Given a set S of n points inR a and a query d-range q, report the points of S that lie within q [1], [2], [3], [5], [7], [9], [21], [22], [23], [26], [29], [31], [35], [36... |

12 | A problem in multivariate statistics: Algorithm, data structure, and applications
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Citation Context ...nge is the Cartesian product of d intervals) [31], [33]. 4. OrthogonalRange Search: Given a set S of n points inR a and a query d-range q, report the points of S that lie within q [1], [2], [3], [5], =-=[7]-=-, [9], [21], [22], [23], [26], [29], [31], [35], [36]. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report the/ points of S ... |

10 |
A note on Euclidean near neighbor searching
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Citation Context ...,/c =< n, report the/ points of S closest to q 11], [20], [25]. 6. Circular Range Search: Given a set $ of n points in the Euclidean plane and a query disk q, report the points of S that lie within q =-=[4]-=-, [10], [11], [12], [16], [37]. * Received by the editors September 15, 1983, and in final revised form April 20, 1985. This research was supported in part by the National Science Foundation under gra... |

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Citation Context ...ess G so that any point can be efficiently located in its containing region. This planarpoint locationproblem canbe solved forgeneral planarsubdivisions in O(log n) query time, using O(n) space [15], =-=[18]-=-, [24], [28].We can now locate, say, the lowest endpoint, (x, Yl), of the query segment q, and proceed to "walk" along the edges of G, following the direction given by q. Without specifying the detail... |

1 | A direct solution to range search and related problemsfor product regions - AVID, SHAMIR - 1981 |

1 |
Data structuresfor range searching
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Citation Context ... q (a d-range is the Cartesian product of d intervals) [31], [33]. 4. OrthogonalRange Search: Given a set S of n points inR a and a query d-range q, report the points of S that lie within q [1], [2], =-=[3]-=-, [5], [7], [9], [21], [22], [23], [26], [29], [31], [35], [36]. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report the/ po... |

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Citation Context ...h definitely deserves attention for its practical relevance, concerns the dynamic treatmerit of retrieval problems. There have been a number of interesting advances in the area of dynamization lately =-=[6]-=-, [32], [34], and investigating how these new techniques can take advantage of filtering search appears very useful. Also, the study of upper or lower bounds for orthogonal range search in two dimensi... |

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Citation Context ...More specifically,wepresentimproved algorithms forthefollowing retrieval problems: 1. Interval Overlap: Given a set S of n intervals and a query interval q, report the intervals of S that intersect q =-=[8]-=-, [17], [30], [31]. 2. Segment Intersection: Given a set S of n segments in the plane and a query segment q, report the segments of S that intersect q [19], [34]. 3. Point Enclosure: Given a set S of ... |

1 |
Optimal retrieval algorithmsfor small region queries
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Citation Context ...s the Cartesian product of d intervals) [31], [33]. 4. OrthogonalRange Search: Given a set S of n points inR a and a query d-range q, report the points of S that lie within q [1], [2], [3], [5], [7], =-=[9]-=-, [21], [22], [23], [26], [29], [31], [35], [36]. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report the/ points of S close... |

1 |
An improved algorithmfor thefixed-radius neighborproblem, IPL 16(4
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Citation Context ...< n, report the/ points of S closest to q 11], [20], [25]. 6. Circular Range Search: Given a set $ of n points in the Euclidean plane and a query disk q, report the points of S that lie within q [4], =-=[10]-=-, [11], [12], [16], [37]. * Received by the editors September 15, 1983, and in final revised form April 20, 1985. This research was supported in part by the National Science Foundation under grants MC... |

1 |
Optimal solutions for a class ofpoint retrieval problems
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Citation Context ...the/ points of S closest to q 11], [20], [25]. 6. Circular Range Search: Given a set $ of n points in the Euclidean plane and a query disk q, report the points of S that lie within q [4], [10], [11], =-=[12]-=-, [16], [37]. * Received by the editors September 15, 1983, and in final revised form April 20, 1985. This research was supported in part by the National Science Foundation under grants MCS 83-03925, ... |

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Citation Context ... [23], [26], [29], [31], [35], [36]. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report the/ points of S closest to q 11], =-=[20]-=-, [25]. 6. Circular Range Search: Given a set $ of n points in the Euclidean plane and a query disk q, report the points of S that lie within q [4], [10], [11], [12], [16], [37]. * Received by the edi... |

1 | Quad-trees: a data structurefor retrieval on composite keys, Acta Informat - FINKEL, BENTLEY - 1974 |

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on the complexity ofsome optimaldata structures
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Citation Context ...roduct of d intervals) [31], [33]. 4. OrthogonalRange Search: Given a set S of n points inR a and a query d-range q, report the points of S that lie within q [1], [2], [3], [5], [7], [9], [21], [22], =-=[23]-=-, [26], [29], [31], [35], [36]. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report the/ points of S closest to q 11], [20],... |

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Quintary trees: A file structurefor multidimensional data base systems
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Citation Context ... of d intervals) [31], [33]. 4. OrthogonalRange Search: Given a set S of n points inR a and a query d-range q, report the points of S that lie within q [1], [2], [3], [5], [7], [9], [21], [22], [23], =-=[26]-=-, [29], [31], [35], [36]. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report the/ points of S closest to q 11], [20], [25].... |

1 |
TARJAN, Applications ofa planar separator theorein
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Citation Context ...t any point can be efficiently located in its containing region. This planarpoint locationproblem canbe solved forgeneral planarsubdivisions in O(log n) query time, using O(n) space [15], [18], [24], =-=[28]-=-.We can now locate, say, the lowest endpoint, (x, Yl), of the query segment q, and proceed to "walk" along the edges of G, following the direction given by q. Without specifying the details, it is eas... |

1 |
Efficient algorithmsfor enumerating intersecting intervalsand rectangles
- MCCREIGHT
- 1980
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Citation Context ...ically,wepresentimproved algorithms forthefollowing retrieval problems: 1. Interval Overlap: Given a set S of n intervals and a query interval q, report the intervals of S that intersect q [8], [17], =-=[30]-=-, [31]. 2. Segment Intersection: Given a set S of n segments in the plane and a query segment q, report the segments of S that intersect q [19], [34]. 3. Point Enclosure: Given a set S of n d-ranges a... |

1 |
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Citation Context ...initely deserves attention for its practical relevance, concerns the dynamic treatmerit of retrieval problems. There have been a number of interesting advances in the area of dynamization lately [6], =-=[32]-=-, [34], and investigating how these new techniques can take advantage of filtering search appears very useful. Also, the study of upper or lower bounds for orthogonal range search in two dimensions is... |

1 | New data structuresfor orthogonal range queries - WILLARD - 1985 |

1 |
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Citation Context ...33]. 4. OrthogonalRange Search: Given a set S of n points inR a and a query d-range q, report the points of S that lie within q [1], [2], [3], [5], [7], [9], [21], [22], [23], [26], [29], [31], [35], =-=[36]-=-. 5. k-Nearest-Neighbors" Given a set S of n points in the Euclidean plane E 2 and a query pair (q, k), with q E2,/c =< n, report the/ points of S closest to q 11], [20], [25]. 6. Circular Range Searc... |