## Incremental Distance Join Algorithms for Spatial Databases (1998)

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Citations: | 111 - 10 self |

### BibTeX

@MISC{Hjaltason98incrementaldistance,

author = {Gisli Hjaltason and Hanan Samet},

title = {Incremental Distance Join Algorithms for Spatial Databases},

year = {1998}

}

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### Abstract

Two new spatial join operations, distance join and distance semijoin, are introduced where the join output is ordered by the distance between the spatial attribute values of the joined tuples. Incremental algorithms are presented for computing these operations, which can be used in a pipelined fashion, thereby obviating the need to wait for their completion when only a few tuples are needed. The algorithms can be used with a large class of hierarchical spatial data structures and arbitrary spatial data types in any dimensions. In addition, any distance metric may be employed. A performance study using Rtrees shows that the incremental algorithms outperform non-incremental approaches by an order of magnitude if only a small part of the result is needed, while the penalty, if any, for the incremental processing is modest if the entire join result is required.

### Citations

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- Guttman
- 1984
(Show Context)
Citation Context ...ding its functionality as well as improving its performance. Section 2.3 presents modifications to the basic algorithm to enable it to compute the distance semi-join operation. 2.1 R-trees The R-tree =-=[15]-=- (see Figure 2) is one of many proposed spatial data structures. It is an object hierarchy in the form of a balanced structure inspired by the B + -tree [12]. Each R-tree node contains an array of (ke... |

1174 |
The Design and Analysis of Spatial Data Structures
- Samet
- 1990
(Show Context)
Citation Context ...wever, the algorithm can be easily adapted to handle most spatial data structures that do not satisfy these assumptions, such as the hB-tree [23] (which forms a directed acyclic graph), and quadtrees =-=[26, 27]-=- (where non-point objects may be stored in more than one leaf node). In the remainder of this section, we do not make a distinction between a node and the region that it represents; the meaning should... |

555 | The ubiquitous B-tree
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- 1979
(Show Context)
Citation Context ...emi-join operation. 2.1 R-trees The R-tree [15] (see Figure 2) is one of many proposed spatial data structures. It is an object hierarchy in the form of a balanced structure inspired by the B + -tree =-=[12]-=-. Each R-tree node contains an array of (key, pointer) entries where key is a hyper-rectangle that minimally bounds the data objects in the subtree pointed at by pointer. In an R-tree leaf node, the p... |

488 |
The R -tree: an efficient and robust access method for points and rectangles
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- 1990
(Show Context)
Citation Context ...tangles, and (b) a tree access structure for (a). Bounding rectangles for individual line segments are omitted from (a) in the interest of clarity. We make use of an R-tree variant called the R -tree =-=[5]-=-. It differs from the conventional R-tree in employing a more sophisticated insertion and node-splitting algorithms that attempt to minimize a combination of overlap and area increase between minimum ... |

484 | Nearest neighbor queries
- Roussopoulos, Kelley, et al.
- 1995
(Show Context)
Citation Context ...stance metric 3 But see Section 3.2 for a description of a priority queue implementation that puts part of the queue on disk if its size is too large to fit in memory. that has been termed MINMAXDIST =-=[25]-=-. The object bounding rectangles are required to minimally bound the objects. The key idea behind the MINMAXDIST metric is that if b is the ddimensional minimum bounding rectangle of object o, then ea... |

324 | Efficient processing of spatial joins using r-trees
- Brinkhoff, Kriegel, et al.
- 1993
(Show Context)
Citation Context ...edicate, which prescribes a certain spatial relationship between the objects in the result. The most common spatial predicate is intersect, i.e., the geometry of the objects are required to intersect =-=[1, 7, 8, 19, 21, 22]-=-. A generalization of this is within, where the objects are required to lie within some distance of each other [24, 29]. Other spatial predicates have been considered as well, and general methods to c... |

312 | Online aggregation
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- 1997
(Show Context)
Citation Context ..." pipelined join methods have recently become a focus of attention [3, 33]. They have become important in enabling the development of more user friendly and interactive interfaces to database sys=-=tems [16]-=-. Recent proposals for extending SQL [10] also benefit greatly from the presence of such algorithms. A variation of our incremental distance join algorithm can be used to compute intersecting pairs [3... |

181 | Dataflow Query Execution in a Parallel Main-Memory Environment
- Wilschut, Apers
- 1991
(Show Context)
Citation Context ...o use the algorithms in a pipelined fashion. Furthermore, the algorithms aim to deliver results as soon as possible. Such "fast first" pipelined join methods have recently become a focus of =-=attention [3, 33]-=-. They have become important in enabling the development of more user friendly and interactive interfaces to database systems [16]. Recent proposals for extending SQL [10] also benefit greatly from th... |

178 | Ranking in spatial databases
- Hjaltason, Samet
(Show Context)
Citation Context ...ea increase between minimum bounding rectangles. 2.2 Computing Distance Join Our incremental distance join algorithm may be viewed as simultaneously applying an incremental nearest neighbor algorithm =-=[18]-=- (see [17] for the application of a similar approach to the LSD tree) to the two spatial data structures corresponding to the spatial attributes of the joined relations. The algorithm works for any sp... |

136 | Multi-step processing of spatial joins - Kriegel, Schneider, et al. - 1994 |

92 | Efficient computation of spatial joins
- Gunther
- 1993
(Show Context)
Citation Context ...within, where the objects are required to lie within some distance of each other [24, 29]. Other spatial predicates have been considered as well, and general methods to computea spatial join proposed =-=[4, 14]. Some of -=-these methods involve special join indexes [14, 24]. In this paper, we define a "distance join" operation, which computes a subset of the Cartesian product of sets A and B, and speciThis wor... |

89 |
An O(n log n) Algorithm for the All-Nearest-Neighbor Problem
- Vaidya
- 1989
(Show Context)
Citation Context ...enefit greatly from the presence of such algorithms. A variation of our incremental distance join algorithm can be used to compute intersecting pairs [30], closest pair [6], and all nearest neighbors =-=[2, 11, 31]-=- in a set of objects. While our incremental distance join algorithm may not always be competitive with some of the above algorithms in terms of computational complexity, it may nevertheless bea reason... |

88 | Spatial joins using R-trees: breadth-first traversal with global optimizations
- Huang, Jing, et al.
- 1997
(Show Context)
Citation Context ...edicate, which prescribes a certain spatial relationship between the objects in the result. The most common spatial predicate is intersect, i.e., the geometry of the objects are required to intersect =-=[1, 7, 8, 19, 21, 22]-=-. A generalization of this is within, where the objects are required to lie within some distance of each other [24, 29]. Other spatial predicates have been considered as well, and general methods to c... |

75 |
Spatial Join Indices
- Rotem
(Show Context)
Citation Context ...ersect, i.e., the geometry of the objects are required to intersect [1, 7, 8, 19, 21, 22]. A generalization of this is within, where the objects are required to lie within some distance of each other =-=[24, 29]-=-. Other spatial predicates have been considered as well, and general methods to computea spatial join proposed [4, 14]. Some of these methods involve special join indexes [14, 24]. In this paper, we d... |

73 |
Applications of Spatial Data Structures: Computer Graphics, Image Processing and GIS
- Samet
- 1990
(Show Context)
Citation Context ...wever, the algorithm can be easily adapted to handle most spatial data structures that do not satisfy these assumptions, such as the hB-tree [23] (which forms a directed acyclic graph), and quadtrees =-=[26, 27]-=- (where non-point objects may be stored in more than one leaf node). In the remainder of this section, we do not make a distinction between a node and the region that it represents; the meaning should... |

68 | On saying ”Enough Already - Carey, Kossmann - 1997 |

61 |
The Buddy-tree: an efficient and robust access method for spatial data base systems
- Seeger, Kriegel
- 1990
(Show Context)
Citation Context ... result would have to be computed and sorted before the first pair can be reported). Some widely used spatial data structures form unbalanced tree hierarchies (e.g., quadtrees [27] and the buddy-tree =-=[28]-=-). Bounding rectangles are not always present in the leaf nodes of these structures, even when objects are not represented directly in the leaves (i.e., the leaves only contain pointers to the objects... |

55 |
Fast algorithms for the all nearest neighbors problem
- Clarkson
- 1983
(Show Context)
Citation Context ...enefit greatly from the presence of such algorithms. A variation of our incremental distance join algorithm can be used to compute intersecting pairs [30], closest pair [6], and all nearest neighbors =-=[2, 11, 31]-=- in a set of objects. While our incremental distance join algorithm may not always be competitive with some of the above algorithms in terms of computational complexity, it may nevertheless bea reason... |

48 |
The pairing heap: A new form of self-adjusting heap
- Fredman, Sedgewick, et al.
- 1986
(Show Context)
Citation Context ...e, due to poor performance. In our experiments, we use a simple hybrid memory/disk scheme that stores parts of the priority queue in a memory-based heap structure (we chose the pairing heap structure =-=[13]-=-), while the rest is offloaded to disk. If a relatively small number of object pairs is requested, then the vast majority of pairs put on the priority queue will never be needed. Thus, our goal in dev... |

35 | An optimal algorithm for closest pair maintenance
- Bespamyatnikh
- 1995
(Show Context)
Citation Context ...s for extending SQL [10] also benefit greatly from the presence of such algorithms. A variation of our incremental distance join algorithm can be used to compute intersecting pairs [30], closest pair =-=[6]-=-, and all nearest neighbors [2, 11, 31] in a set of objects. While our incremental distance join algorithm may not always be competitive with some of the above algorithms in terms of computational com... |

33 | A cost model for estimating the performance of spatial joins using r-trees
- HUANG, JING, et al.
- 1997
(Show Context)
Citation Context .... More query plans may even exist, employing some other algorithm. To enable a query optimizer to choose between these options requires a cost model for the relevant algorithms (e.g., as developed in =-=[20]-=- for the traditional R-tree spatial join). Developing such cost models for the incremental distance join algorithms presented in this paper is a subject for further study. Other issues for further inv... |

32 |
On saying "enough already
- Carey, Kossmann
- 1997
(Show Context)
Citation Context ...A finds the nearest object in B. Figure 1 defines the distance join and distance semi-join operations using a syntax loosely adapted from SQL-92, including the STOP AFTER clause extension proposed in =-=[10]-=-. The WHERE and STOP AFTER clauses, specifying limits on the distance and/or the number of result tuples, are optional. These basic queries could be made more complicated by adding further selection c... |

30 | A distance-scan algorithm for spatial access structures
- Henrich
- 1994
(Show Context)
Citation Context ...e between minimum bounding rectangles. 2.2 Computing Distance Join Our incremental distance join algorithm may be viewed as simultaneously applying an incremental nearest neighbor algorithm [18] (see =-=[17]-=- for the application of a similar approach to the LSD tree) to the two spatial data structures corresponding to the spatial attributes of the joined relations. The algorithm works for any spatial data... |

29 |
A new algorithm for computing joins with grid files
- Becker, Hinrichs, et al.
- 1993
(Show Context)
Citation Context ...within, where the objects are required to lie within some distance of each other [24, 29]. Other spatial predicates have been considered as well, and general methods to computea spatial join proposed =-=[4, 14]. Some of -=-these methods involve special join indexes [14, 24]. In this paper, we define a "distance join" operation, which computes a subset of the Cartesian product of sets A and B, and speciThis wor... |

28 | Processing queries for the first few answers
- Bayardo, Miranker
- 1996
(Show Context)
Citation Context ...o use the algorithms in a pipelined fashion. Furthermore, the algorithms aim to deliver results as soon as possible. Such "fast first" pipelined join methods have recently become a focus of =-=attention [3, 33]-=-. They have become important in enabling the development of more user friendly and interactive interfaces to database systems [16]. Recent proposals for extending SQL [10] also benefit greatly from th... |

22 |
A robust multi-attribute search structure
- Lomet, Salzberg
- 1989
(Show Context)
Citation Context ...et of assumptions was chosen as it holds for the R-tree. However, the algorithm can be easily adapted to handle most spatial data structures that do not satisfy these assumptions, such as the hB-tree =-=[23]-=- (which forms a directed acyclic graph), and quadtrees [26, 27] (where non-point objects may be stored in more than one leaf node). In the remainder of this section, we do not make a distinction betwe... |

22 |
Counting and reporting intersections of d-ranges
- Six, Wood
- 1982
(Show Context)
Citation Context ...6]. Recent proposals for extending SQL [10] also benefit greatly from the presence of such algorithms. A variation of our incremental distance join algorithm can be used to compute intersecting pairs =-=[30]-=-, closest pair [6], and all nearest neighbors [2, 11, 31] in a set of objects. While our incremental distance join algorithm may not always be competitive with some of the above algorithms in terms of... |

21 | Query processing for distance metrics
- Wang, Shasha
- 1990
(Show Context)
Citation Context ...ot symmetric. In particular, the result of computing the distance semi-join of the warehouse relation and the stores relation is that for each warehouse, we get the closest store. The clustering join =-=[32]-=- is similar to the distance semi-join with the difference being that the clustering join is symmetric. An algorithm for computing the clustering join is also given in [32]. However, that algorithm is ... |

17 | R.: Parallel algorithms for high-dimensional similarity joins for data mining applications
- Shafer, Agrawal
- 1997
(Show Context)
Citation Context ...ersect, i.e., the geometry of the objects are required to intersect [1, 7, 8, 19, 21, 22]. A generalization of this is within, where the objects are required to lie within some distance of each other =-=[24, 29]-=-. Other spatial predicates have been considered as well, and general methods to computea spatial join proposed [4, 14]. Some of these methods involve special join indexes [14, 24]. In this paper, we d... |

15 | Data-parallel spatial join algorithms
- Hoel, Samet
- 1994
(Show Context)
Citation Context ...edicate, which prescribes a certain spatial relationship between the objects in the result. The most common spatial predicate is intersect, i.e., the geometry of the objects are required to intersect =-=[1, 7, 8, 19, 21, 22]-=-. A generalization of this is within, where the objects are required to lie within some distance of each other [24, 29]. Other spatial predicates have been considered as well, and general methods to c... |

14 |
The Spatial Filter Revisited
- Aref, Samet
- 1994
(Show Context)
Citation Context |

10 | Join strategies on KD-tree indexed relations - Kitsuregawa, Harada, et al. - 1989 |

9 |
of Census., “Tiger/Lines Precensus Files
- Bureau
- 1990
(Show Context)
Citation Context ...aximum optimization (--O3). The distance functions were based on the Euclidean metric. As in other evaluations of spatial algorithms (e.g., [8, 21]), we derived our test data from the TIGER/Line File =-=[9]-=-. We used two sets of points from the coverage of the Washington, DC area: Water contains the centroids of water features (37,495 points), and Roads contains the centroids of road features (200,482 po... |

3 |
Probabilistic analysis of an algorithm for solving the k-dimensional all-nearest-neighbors problem by projection
- Bartling, Hinrichs
- 1991
(Show Context)
Citation Context ...enefit greatly from the presence of such algorithms. A variation of our incremental distance join algorithm can be used to compute intersecting pairs [30], closest pair [6], and all nearest neighbors =-=[2, 11, 31]-=- in a set of objects. While our incremental distance join algorithm may not always be competitive with some of the above algorithms in terms of computational complexity, it may nevertheless bea reason... |

2 |
Multistep Processing of Spatial Joins
- Seeger
- 1994
(Show Context)
Citation Context |

2 | of the Census. Tiger/Line precensusfiles - Bureau - 1989 |