Lomet, D. Salzberg, B., "The hB-tree: A Multiattribute Indexing method with Good Guaranteed Performance", ACM Trans on Database Systems, vol. 15, no. 4, Dec. 1990, pp. 625-658.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[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 the references therein) These data structures are often the methods of choice in practical applications because they use linear space and reportedly perform well in practice. However, in a dynamic environment, the query time is high in the worst case. The ....

D. Lomet and B. Salzberg. The hB-tree: A multiattribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, 1990.

....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 the time. However, they all have highly suboptimal worst case performance, and ....

D. Lomet and B. Salzberg. The hB-tree: A multiattribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, 1990.

....and dimensionality reduction. Multidimensional indexing has been extensively researched in the database literature. There are numerous proposals for indexing techniques in multiple dimensions[5] A very good survey can be found in [11] Several 2 data structures such as R Trees [12] hB trees[17], TV Trees[16] SS trees[23] are designed for supporting fast searching in large multi dimensional databases. These trees have been shown to be efficient for small dimensions, and to be sensitive to dimensionality. Clustering algorithms have been studied recently in the domain of data mining [26] ....

D. B. Lomet and B. Salzberg. The hb-tree: A multi-attribute indexing method with good guaranteed performance. Proc. ACM Symp. on Transactions of Database Systems, 15(4):625--658, 1990.

....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 space containing the data points and data driven structures (like kd B ....

D. Lomet and B. Salzberg. The hB-tree: A multiattribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, 1990.

....under these constraints. Errors are minimal and the overall prediction time is up to two orders of magnitude below the time for building and probing the full index without sampling. 1. INTRODUCTION A large number of index structures for high dimensional data have been proposed in previous years [3, 7, 15, 20, 35, 26, 14, 24, 8, 6, 33]. These index structures have different characteristics and optimization strategies, making their analysis difficult. The indexed high dimensional datasets are also difficult to analyze because of their non trivial distribution in high dimensions. As a result of this complexity, the development of ....

D. B. Lomet and B. Salzberg. The hB-tree: A multiattribute indexing method with good guaranteed performance. TODS, 15(4):625--658, 1990.

....a point, deletion of a point, split and concatenate along one coordinate. In external memory, rectangular range queries on ordered decomposable problems can be done with quad trees [15] k d trees [7] and many other data structures, such as grid les [30] space lling curves, e.g. 32] hB trees [28], and R trees [20] just to cite a few (see the survey [16] for a more complete scenario and paper [24] for a discussion of their worst case complexity) These data structures were originally designed to support some operations for windowing problems in computer graphics and databases, and in ....

....to higher dimensions by carefully combining space driven and data driven partitions. As a result, the cross tree is competitive with other popular index data structures that require linear space, such as quad trees [15] k d trees [7] grid les [30] space lling curves, e.g. 32] hB trees [28], and R trees [20] We conclude this section with few remarks about the practicality of our approach. In our data structures, records are not replicated and the records satisfying a given query can be eciently scanned starting from their retrieved pointers. This is not always possible with known ....

D.B. Lomet and B. Salzberg. The hB-tree: A multiattribute indexing method with good guaranteed performance. ACM Transactions on Databases Systems 15 (1990), 625-658. 27

....5 concludes the paper. 2 Related Work Techniques for indexing multidimensional data (including spatial, temporal, and spatio temporal data) have been extensively studied in the literature. Example data structures developed include R tree and its family [3, 2, 15] Quadtree [14] and hB tree [6]. Specialized techniques to index temporal objects have also been proposed, including multi version index structures, e.g. Time Split B tree (TSBtree) 7] multi version B tree [1] and others, summarized in [13] While the focus of these data structures has been on indexing temporally changing ....

D. Lomet and B. Salzberg. The hB-Tree: A multiattribute indexing method with good guaranteed performance. ACM Trans. on Database Systems, 15(4):625--658, 1990.

....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 variants [22, 20, 38, 10, 25] These data structures are often the methods of choice in practical applications, because they use linear space and reportedly perform well in practice. However, in a highly dynamic environment they are all very query suboptimal in the worst case. The ....

D. Lomet and B. Salzberg. The hB-tree: A multiattribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, 1990.

....3.1.4 Example: K d tree Page Layout for GiST Based Spatial Indices The k d tree [Ben75] is a main memory multidimensional binary search tree that is very efficient for storing iso oriented rectangles that partition a given space. K d trees are 33 used as the layout of non leaf pages of hB trees [LS90] a multidimensional point access method that partitions the data space. Figure 3.4 shows an example of six rectangles in 2 dimensional space and their k d tree representation. By organizing rectangles into a tree structure, sides that are common to multiple rectangles need only be stored once, ....

....in the context of the GiST, they can also be applied individually to any particular access method that complies with the GiST structure. This is not a very restrictive requirement, because it only excludes access methods that are either not proper trees (e.g. the hB tree, as described in [LS90] or that have other structural peculiarities (for instance, R trees, described in [SRF87] replicate leaf entries) Although the GiST structure is similar to that of a B tree, it generalizes the B tree structure in a way which makes most of the extensively researched concurrency control ....

D. Lomet and B. Salzberg. The hB-Tree: A Multiattribute Indexing Method with Good Guaranteed Performance. ACM TODS, 15(4):625--685, December 1990. 151

....In essence, our index consists of large I O pages that are supported by an additional search structure to speed up the main memory operations. A few index structures with supporting search structures have already been previously proposed. For instance, Lomet and Salzberg propose the hB tree [28] which uses a kd tree like structure to organize directory pages. Their objective is improve the insert operations in order to achieve an overlap free space decomposition in their index, not a separate optimization of CPU and I O operations. Also, some quad tree based structures can be used in ....

Lomet D., Salzberg B.: The hB-Tree: A Multiattribute Indexing Method with Good Guaranteed Performance, ACM Transactions on Database Systems (TODS), Vol. 15, No. 4, 1990.

....is that, they are neigher paginated nor balanced. An advantage of a balanced index tree is the consistency in good performance for all queries independent of their access patterns. Other index structures based on the idea of domain decomposition include k d tree [8] K D B tree [9] hB tree [10], etc. Again, none of these techniques are designed for regional data. Furthermore, all of these trees split a domain according to the value of the inserting data. As a result, the shape of their trees is highly dependent on the insertion order of the data points. As a contrast, we will see that ....

David B. Lomet and Betty Salzberg. The hb-tree: A multiattribute indexing method with good guaranteed performance. ACM Trans. on Database Systems, 15(2):625--658, June 1990. Query window R-tree D-tree: number of nodes accessed X size, Y size Total Domain Data R-tree Total Saving

....B tree, extending its basic ideas to n dimensions. With the aim of transforming the mQ tree into a new structure that can be stored in secondary memory, we have thoroughly analyzed the pagination mechanisms developed in these structures. The ideas we will use have been mainly taken from hb tree [8] and Q tree [1] Bang file [5] and BV tree [6] Access methods that manage complex spatial objects such as R tree, R tree, SS tree, X tree, Pyramid tree, etc. have also been studied, 7] 2] in order to get a complete background of these kinds of structures and to grasp new ideas that may ....

Lomet, D., Salzberg, B., "The hB-tree: A Multi-attribute Indexing Method with Good Guaranteed Performance". ACM Transactions on Database Systems, Vol. 15, no. 4, December 1990.

....databases a practical possibility. In order to make transaction time systems practical, the hardware advances must be combined with advances in query processing techniques. Research focus has spread from conceptual data modeling aspects to also include implementationrelated aspects [15] [16], 29] and significant effort has recently been devoted to implementation related topics (e.g. see [18] 21] 28] 32] The timeslice operator [1] 25] is one of the central operators in temporal database systems. Indeed, most temporal relational algebras [19] proposed to date contain a K. ....

D. Lomet and B. Salzberg. The hB-Tree: A Multiattribute Indexing Method with Good Guaranteed Performance. ACM Transaction on Database Systems. Vol. 15, No. 4, pp. 625--658, December 1990.

....models is reported in [15] A number of approaches exist to the storage of data in data warehouses. 21] contrasts the performance of value based (ROLAP) and multidimensional (MOLAP) implementations. The data structures used include grid files [6] B trees, R trees [1] X trees, HB trees [14], GiST [8] arrays and sets based data structures. The data model and query evaluation algorithm presented in this paper are based on (ordered) sets [11,12,20] We argue in favor of using sets for the consistent representation of data within the OLAP system. Sets can be implemented efficiently ....

D. B. Lomet and B. Salzberg. The HB-tree: A multi-attribute indexing method with good guaranteed performance. In Proc. ACM Symposium on Transactions of Database Systems, volume 15, pages 625-- 658, 1990.

....and the dotted lines illustrate the extended boundaries. The shaded area contains screened points. 2.2 Other Index Structures kdB tree [Rob81] is similar to the R tree. The main difference is that the bounding rectangles cover the entire space, unlike the MBRs of the R tree. hB tree [LS09] is similar to the kdB tree except that bounding rectangles of the children of an internal node are organized as a K D tree [Ben75] rather than as a list of MBRs. The K D tree is a binary tree for multi dimensional points. In each level of the K D tree, only one dimension, chosen cyclically, is ....

D. Lomet and B. Salzberg. The hB-tree: A multiattribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, 1909.

....are typically represented by multi dimensional feature vectors. A similarity function between these feature vectors is defined and is used as a measure for the similarity between the corresponding data objects. Several indexing techniques have been proposed for multidimensional Euclidean spaces [20, 29, 28, 25, 21, 2, 34, 24, 5, 4]. Most of these structures are optimized specifically for point, range, and nearest neighbor queries with Euclidean distance as the similarity metric between feature vectors. Conical queries are a novel type of query with an increasing number of applications. Traditional index structures and ....

D. B. Lomet and B. Salzberg. The hb-tree: A multi-attribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, December 1990.

....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 worse than the O(log B n t) I O bound obtained in one ....

D. Lomet and B. Salzberg. The hB-tree: A multiattribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, 1990.

....been proposals for GIS applications to handle queries with more complex and accurate structures, such as polygons. Numerous index structures have been developed to facilitate range searching in two and higher dimensions including grid files [NHK84] quadtrees [Sam89] kdb trees [Rob81] hB trees [LS90] R trees and variants [Gut84, BKSS90, BKK96] Another very important class of queries in applications that involve spatial data is that of nearest neighbor (NN) queries [RKV95] Similar to range queries, nearest neighbor queries are also commonly used in spatial applications. In general, the ....

D. B. Lomet and B. Salzberg. The hb-tree: A multi-attribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, December 1990.

....Instead of n objects, the query retrieves a set of s objects, which is a subset of these n objects. The better the index structure, the smaller the size of s. There have been several approaches to organize and partition a multi dimensional data set for indexing including kdb trees [37] hB tree [31], R tree [23] R tree [5] SS tree [43] TV tree [28] X tree [8] Pyramid Technique [7] Hybrid Tree [12] There are also techniques that are proposed to reduce the size of the retrieved set in multiple disk architectures [16, 19, 20] All these index structures focus mainly on finding the exact ....

D. B. Lomet and B. Salzberg. The hb-tree: A multi-attribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, December 1990. 19

....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 ....

....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 (see [79] for a complete reference on the field) Recently some progress has been ....

D. Lomet and B. Salzberg. The hB-tree: A multiattribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, 1990.

....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 [23] for a complete reference on the field) Recently some progress has been ....

D. Lomet and B. Salzberg. The hB-tree: A multiattribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, 1990.

....Instead of n objects, the query retrieves a set of s objects, which is a subset of these n objects. The better the index structure, the smaller the size of s. There have been several approaches to organize and partition a multi dimensional data set for indexing including kdb trees [35] hB tree [29], R tree [22] R tree [5] SS tree [41] TV tree [26] X tree [8] Pyramid Technique [7] Hybrid Tree [12] There are also techniques that are proposed to reduce the size of the retrieved set in multiple disk architectures [15, 18, 19] All these index structures focus mainly on finding the exact ....

D. B. Lomet and B. Salzberg. The hb-tree: A multi-attribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625--658, December 1990.

.... index structures exist that facilitate search and retrieval of two dimensional data or spatial databases [20, 12, 13] With the proliferation of multimedia data these index structures have been extended and new ones are being proposed to deal with the high dimensional nature of information [16, 5, 22, 17, 14]. In fact, Berchtold et al. 4] have argued that using multidimensional index structures for searching beyond a certain dimension becomes worse than a sequential scan. Besides being inecient in high dimensions, it is hard to achieve optimal parallelism for these index structures. We therefore need ....

D. B. Lomet and B. Salzberg. The hb-tree: A multiattribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625-658, December 1990.

....database transactions only in that the structure changes may commit without the transaction committing. Although the most important application of our new method will undoubtedly be in its use in B trees, it can be extended to other structures. In particular, it can be used with the hB tree [LoSa3,LoSa4], a spatial database structure. We are working on the details of this extension [ELS] Again, quoting the Lagunita report [SSU] Many scientific databases have two or three dimensional points, lines and polygons as data elements. A typical search is to find the ten closest neighbors to some data ....

....which are an integral part of all modern DBMSs, we can also apply the algorithm to other search structures. Along with Georgio Evangelidis, a student at Northeastern, we have begun some work in applying our concurrency algorithm to our multiattribute structure, the Holey Brick Tree or hB tree [LoSa3, LoSa4]. We are implementing the hB tree in a slightly different way from the original papers. Specifically, in [LoSa3, LoSa4] external markers were used to show that a contained node had been extracted from a containing node. In [ELS] we replace these external markers with addresses of contained ....

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Lomet, D. Salzberg, B., "The hB-tree: A Multiattribute Indexing method with Good Guaranteed Performance", ACM Trans on Database Systems, vol. 15, no. 4, Dec. 1990, pp. 625-658.

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D.B. Lomet, and B. Salzberg. The hb-tree: a multiattribute indexing method with good guaranteed performance. ACM Transactions on Database Systems, 15(4):625-658, December 1990.

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