H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....subdivision is obtained. Examples of hierarchical constrained subdivision include quad trees [12] kd trees [9] and binary space partitions (BSP) 17] Motivated by various applications, constrained subdivisions have been extensively studied in computational geometry and related application areas [10, 16]. In a growing number of applications, we do not have one fixed set S because the objects move over time. This is the case, for instance, in video games, virtual reality, and dynamic simulations. The set S is now replaced by a continuous family S(t) indexed by time. A constrained subdivision Pi ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....geometry In the early days of computational geometry, multidimensional range search, also known as orthogonal range search, was one of the fundamental areas of interest. This interest produced a wealth of results, of which only few can be mentioned here. A number of books (e.g. Sam89a, Sam89b] and surveys (e.g. Meh84, Mat94, AE97] cover the subject very thoroughly. In the context of geometric range search, the term used is orthogonal range search. 13 2.1.1 Quadtree and kd tree One of the earliest data structures was the quad tree, proposed by Finkel and Bentley [FB74] In its ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....memory data structures most relevant to this paper. See [27, 2] for complete surveys of known results. One main challenge in the design of external data structures is obtaining good query performance in a dynamic environment. Early structures, such as the grid file [20] the various quad trees [21, 23], and the kdB tree [22] were poorly equipped to handle updates. Later structures tried to employ various (heuristic) techniques to preserve the query performance and space usage under updates. They include the LSD tree [16] the buddy tree [24] the hB tree [19] and R tree variants (see [14] and ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1990.

....a matching indexing scheme. External range search data structures: Background and outline of results Research on two dimensional external range searching has traditionally been concerned with the general 4sided problem. Many external data structures such as grid files [17] various quad trees [22, 23], z orders [18] and other space filling curves, k d B trees [21] hBtrees [15] and various R trees [9, 25] have been proposed. Often these structures are the data structures of choice in applications, because they are relatively simple, require linear space, and in practice perform well most of ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....have led to the development of a large number of general purpose data structures that often work well in practice, but which do not come with worst case performance guarantees. Below we quickly survey the major classes of such structures. The reader is referred to more complete surveys for details [12, 85, 121, 88, 124, 134]. Range searching in d dimensions is the most extensively researched problem. A large number of structures have been developed for this problem, including space filling curves (see e.g. 123, 1, 32] grid files [119, 94] various quadtrees [133, 134] kd B tress [128] and variants like ....

....complete surveys for details [12, 85, 121, 88, 124, 134] Range searching in d dimensions is the most extensively researched problem. A large number of structures have been developed for this problem, including space filling curves (see e.g. 123, 1, 32] grid files [119, 94] various quadtrees [133, 134], kd B tress [128] and variants like Buddy trees [138] hB trees [109, 75] and cell trees [91] and various R trees [92, 88, 139, 37, 100] Often these structures are broadly classified into two types, namely space driven structures (like quad trees and grid files) which partition the embedded ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1990.

....in practical applications. Refer to surveys by Vitter [42] and Arge [3] for references. One main challenge in the design of external indexing data structures is obtaining good query performance in a dynamic environment. Early structures, such as the grid file [32] the various quad trees [36, 33], and the kdB tree [34] were poorly equipped 1 to handle dynamic updates. Later structures tried to employ various (heuristic) techniques to preserve the query performance and space usage under dynamic updates. They include the LSD tree [23] the buddy tree [37] the hB tree [31] and R tree ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....success in supporting one dimensional range queries. B trees occupy O(n) space and answers queries in O(log B n t) I Os, which is optimal. Numerous structures have been proposed for range searching in two dimensions and higher dimensions, for example, grid files [35] various quad trees [40, 41, 8], k d B trees and variants [39, 26] hB trees [18, 30] and various Rtrees [7, 24, 28, 42, 9] Complete references can be found in the surveys [3, 23, 27, 36] Although these data structures have good average case query performance for common problems, their worstcase query performance is much ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....cases. These structures are not efficient when mapped to external memory. However, the practical need for I O support has led to the development of a large number of external data structures, which have good average case behavior for common problems but fail to be efficient in the worst case sense [68, 69, 86, 95, 103, 111, 114, 115, 117]. Recently some progress has been made on the construction of external two dimensional range searching structures with good worst case performance. In Figure 3.8 the different special cases of general two dimensional range searching are shown. As discussed in [79] it is easy to realize that the ....

....practical need for I O support has led to the development of a large number of external data structures that do not have good theoretical worst case update and query I O bounds, but do have good average case behavior for common problems. Such methods include the grid file [95] various quad trees [114, 115], z orders [103] and other space filling curves, k d B tress [111] hB trees [86] cell trees [68] and various R trees [69, 117] The worst case performance of these data structures is much worse than the optimal bounds achievable for dynamic external 1 dimensional range searching using B trees ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....practical need for I O support has led to the development of a large number of external data structures that do not have good theoretical worstcase update and query I O bounds, but do have good average case behavior for common problems. Such methods include the grid file [29] various quad trees [38, 39], z orders [31] and other space filling curves, k d B tress [36] hB trees [26] cell trees [17] and various R trees [18, 40] The worstcase performance of these data structures is much worse than the optimal bounds achievable for dynamic external 1 dimensional range searching using B trees (see ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....subdivision is obtained. Examples of hierarchical constrained subdivision include quadtrees [12] kd trees [9] and binary space partitions (BSP) 17] Motivated by various applications, constrained subdivisions have been extensively studied in computational geometry and related application areas [10, 16]. In a growing number of applications, we do not have one fixed set S because the objects move over time. This is the case, for instance, in video games, virtual reality, and dynamic simulations. The set S is now replaced by a family S(t) indexed by time. A constrained subdivision Pi computed ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....based on the join index of Valduriez [Val87] The join index used in [Rot91] partially computes the result of the spatial join using a grid file. There has recently been much interest in using spatial index structures like the R tree [Gut85] R tree [SRF87] R tree [BKSS90] and PMR quadtree [Sam89] to speed up the filter step of the spatial join. Brinkhoff, Kriegel, and Seeger [BKS93] propose a spatial join algorithm based on R trees. Their algorithm is a carefully synchronized depth first traversal of the two trees to be joined. An improvement of this algorithm was recently reported in ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....subdivision is obtained. Examples of hierarchical constrained subdivision include quad trees [12] kd trees [9] and binary space partitions (BSP) 17] Motivated by various applications, constrained subdivisions have been extensively studied in computational geometry and related application areas [10, 16]. In a growing number of applications, we do not have one xed set S because the objects move over time. This is the case, for instance, in video games, virtual reality, and dynamic simulations. The set S is now replaced by a continuous family S(t) indexed by time. A constrained subdivision ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....on the join index of Valduriez [Val87] The join index used in [Rot91] partially computes the result of the spatial join using a grid file. There has recently been much interest in using spatial index structures like the R tree [Gut85] R tree [SRF87] R tree [BKSS90] and PMR quadtree [Sam89] to speed up the filter step of the spatial join. Brinkhoff, Kriegel, and Seeger [BKS93] propose a spatial join algorithm based on R trees. Their algorithm is a carefully synchronized depth first traversal of the two trees to be joined. An improvement of this algorithm was recently reported in ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....17] have been an unquali ed success in supporting one dimensional range queries. B trees occupy O(n) space and answer queries in O(log # n t) I Os, which is optimal. Numerous structures have been proposed for range searching in two and higher dimensions, for example, grid les [41] quad trees [46, 47], k d B trees and variants [45, 31] hB trees [23, 35] and R trees and variants [9, 29, 33, 48, 10] More references can be found in the surveys [3, 28, 32, 42] Although these data structures have good average case query performance for common geometric searching problems, their worst case ....

H. Samet, The Design and Analyses of Spatial Data Structures, Addison Wesley, MA, 1989.

....17] have been an unquali ed success in supporting one dimensional range queries. B trees occupy O(n) space and answer queries in O(log B n t) I Os, which is optimal. Numerous structures have been proposed for range searching in two and higher dimensions, for example, grid les [41] quad trees [46, 47], k d B trees and variants [45, 31] hB trees [23, 35] and R trees and variants [9, 29, 33, 48, 10] More references can be found in the surveys [3, 28, 32, 42] Although these data structures have good average case query performance for common geometric searching problems, their worst case ....

H. Samet, The Design and Analyses of Spatial Data Structures, Addison Wesley, MA, 1989.

....Alto CA 94303. Appears in the Proceedings of ACM SIGMOD Conference, Philadelphia, June 1999. either offer some kind of support for spatial data or are in the process of providing such support. GISs have also been the focus of much research, mostly towards efficient manipulation and access[Sam89a, Sam89b] and more recently, towards research prototypes[DeW94, GRSS97] As in relational database systems, there are many modules of a spatial database system that require accurate estimates of query result sizes. Such estimates are used in a variety of ways. For example, query optimizers use query ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....[Ube94] GISs typically store and manage spatial data such as points, lines, poly lines, polygons, and surfaces. Since the amount of data that they manage is quite large, GISs typically tend to be disk based systems. Efficient retrieval of spatial data from disk has been studied extensively [Sam89b, Sam89a] An extremely important problem on spatial data is the spatial join, where two spatial relations are combined together based on some spatial criteria. A typical use for spatial join is the map overlay operation that combines two maps of different types of objects. For example, the query ....

....along a single dimension using space filling curves. The I O complexity of the spatial join problem was studied in [GS87] There has been a series of papers [BKS93, HJR97, Gun93, HS92] on using spatial indexes such as the R tree [Gut85] R tree [SRF87] R tree [BKSS90] and PMR quad tree [Sam89b] to speed up the filtering step of the spatial join. Others [LR94, LR95] have focused on the case where one or both of the input relations to the spatial join do not have an index available. Recently, two join algorithms based on spatial hashing [LR96, PD96] have been proposed for the spatial ....

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H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

....dynamic problem to obtain a number of new d dimensional algorithms. One prominent example of the problems we consider is the rectangle intersection problem, which is a key component in VLSI design rule checking [31] and in the extremely important database operation spatial join [34]. We illustrate the practical significance of our algorithms by comparing the empirical performance of our algorithm for this problem with the well known sweepline algorithm developed for internal memory. 1.1 Problem definition and memory model A searching problem involves a question asked about ....

.... all intersecting pairs among a set of axis parallel hyperrectangles in d dimensional space [15, 17, 16, 35, 9] The problem is a key component in VLSI design rule checking [31] and in databases it is a component in the fundamental join operator in relational [19] temporal [36] spatial [33, 34], and constraint [22] models. 1.2 Previous related results As mentioned, considerable attention has recently been given to the development of provably I O efficient algorithms. Aggarwal and Vitter [2] considered sorting and permutation related problems in the two level I O model and proved that ....

H. Samet. The Design and Analyses of Spatial Data Structures. Addison Wesley, MA, 1989.

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