Comer D. "The ubiquitous B-Tree." ACM Computing Surveys, vol. 11, no. 2, 121--137, Jun 1979  Home/Search   Document Not in Database   Summary   Related Articles   Check

....tree in which internal nodes contain references to next level nodes, and are used to direct the query evaluation. Leaf nodes hold the statistics or histograms for the data (e.g. SUM, COUNT, MIN, MAX values) and are linked together to facilitate scanning, similarly to the B tree data structure [7]. Statistics trees can also be called aggregation trees since they only store the aggregate information instead of the record details. 6 Each root to leaf path in a statistics tree represents a particular subcube of the underlying data set. In order to use an ST to answer cube queries against a ....

....proportional to the number of records in the table. The runtime of a bitmap based algorithm is much larger than the runtime of which has a runtime proportional to the number of dimensions of the data cube. A good alternative to encoded bitmaps for large domain sizes is the B tree index structure [7]. O Neil and Quass [27] provide an excellent overview of and detailed analyses for index structures which can be used to speed up OLAP queries. In decision support systems, a hybrid index combining bitmap and B tree technology is often used. When the number of distinct values in a dimension is ....

D. Comer, "The Ubiquitous Btree," ACM C. Surveys, vol. 11, pp. 121-137, Jun 1979.

....supports the operations insert , delete,andlookup. The basic structure and implementation of a B tree is similar to that of a balanced binary tree. However, unlike a binary tree, the allowed maximum number of children for each B tree node is not constrained to two; it can be much larger. Comer [27] presents a full discussion of the B tree and its common variants. Bayer and McCreight s original B tree [7] was designed to support sequential applications. Since then, researchers have proposed many di erent algorithms to support concurrent operations on the B tree (e.g. 8, 26, 53, 62, 63, ....

D. Comer. "The Ubiquitous B-Tree". ACM Computing Surveys, 11(2):121--128, June 1979.

....optimal. An example of this is the standard plane sweep algorithm for orthogonal segment intersection, where the dynamic data structure is an interval tree [30] An obvious way of implementing algorithms of this type in secondary memory is to replace the dynamic search tree with a dynamic B tree [6,9]. Unfortu nately, this requires O( N If)log ; O(B( log ; I O operations in the worst case, which is prohibitive. Previous work using lazy batched updates on the B tree yielded algorithms with O( I Os [34] Our new method uses an off line top down implementation of the sweep, ....

....the visibility from a point in the plane, finding pairwise rectangle intersections, computing the measure of a union of rectangles, and the 3 d maxima problem. These problems are discussed in greater detail in the full version of this paper. 3 Persistent B trees The B tree data structure [6,9] is a fundamental structure for maintaining a dynamically changing dictionary in external memory. In some cases, however, it may be advantageous to be able to access previous versions of the data structure. Being able to access such previous versions is known as pcrsistccc, and there exist very ....

D. Comer, "The Ubiquitous B-tree," Uomput. Surveys 11 (1979), 121 137.

....on by performing the opera tions chef2. crj. We assume, without loss of general ity, that the pi s are sorted by their j arguments. The problem is to determine the answer to each Pi query. One obvious external memory solution to this problem is to implement the search tree as a dynamic B tree [6,9] and to perform the queries in p in an on line fashion while performing the updates in or. Unfortu nately, this requires ( N Ix2)log ) B( n) log ) I O operations in the worst case, which is prohibitive. Previous work using lazy batched updates on the B tree yielded algorithms with ....

....the visibility from a point in the plane, finding pairwise rectangle intersections, computing the measure of a union of rectangles, and the 3 d maxima problem. These problems are discussed in greater detail in the full version of this paper. 3 Persistent B trees The B tree data structure [6,9] is a fundamental structure for maintaining a dynamically changing dictionary in external memory. In some cases, however, it may be advantageous to be able to access previous versions of the data structure. Being able to access such previous versions is known as persistence, and there exist very ....

D. Comer, "The ubiquitous B-tree," Coalput. Surveys 11(1979), 121 137.

....91 J 4052 ARPA Order No. 8225 declarative programming features (relational calculus and algebra) of the model are important, it is crucial to support these features by data structures for searching and updating that make optimal use of secondary storage. B trees and their variants B trees [BaM, Com] are examples of such data structures. They have been an unqualified success in supporting external dynamic 1 dimensional range searching in relational database systems. The general data structure problem underlying efficient secondary storage manipulation for many data models is external dynamic ....

D. Comer, "The Ubiquitous B-tree," Computing Surveys 11(2) (1979), 121--137.

....a number of node entries, E = p, ptr , where p is a predicate that describes the subtree indicated by ptr. The subtrees recursively partition the data records. However, they do not necessarily partition the data space. GiST can therefore model ordered, space partitioning trees (e.g. B trees [COME79]) as well as unordered, non spacepartitioning trees (e.g. R trees [GUTT84] 2 For consistency with [HELL95] we call each datum stored in p a predicate. 1 We use the term key only when it is part of a standard phrase in database terminology. In the remainder of this paper, we describe ....

D. Comer, "The Ubiquitous B-tree," Computing Surveys 11, 2 (1979), 122-137.

....a number of node entries, e = p, ptr , where each predicate, p, describes the subtree indicated by ptr. The subtrees recursively partition the data records. However, they do not necessarily partition the data space. GiST can therefore model ordered, space partitioning trees (e.g. B trees [COME79]) as well as unordered, non space partitioning trees (e.g. R trees [GUTT84] The original GiST framework of [HELL95] consists of (1) a set of common internal methods provided by GiST and (2) a set of extension methods provided by the user. The internal methods generally correspond to the ....

D. Comer, "The Ubiquitous B-tree," Computing Surveys 11, 2 (June 1979), 122-137.

....in which internal nodes contain references to next level nodes and are used to direct the query evaluation. Leave nodes hold the statistics or histograms for the data (e.g. SUM, COUNT, MIN, MAX values) and are linked together to facilitate scanning, similarly to the B B Tree data structure [9]. Each root to leaf path in a statistics tree represents a particular subcube of underlying data set. In order to use an ST to answer cube queries over a particular data set, one must first pre compute the aggregations on all subcubes by scanning the detailed data set. Statistics trees can also be ....

....Later in the report, we show that the runtime of a bitmap based algorithm is much larger than the runtime of CubiST which has a worst case runtime proportional to the number of dimensions of the data cube. A good alternative to encoded bitmaps for large domain sizes is the B Tree index structure [9]. O Neil and Quass [25] provide an excellent overview of and detailed analyses for index structures which can be used to speed up OLAP queries. 2.4. View Materialization View materialization in decision support systems refers to the pre computing of partial query results which may be used to ....

D. Comer, "The Ubiquitous Btree," ACM Computing Surveys, 11:2, pp. 121-137, 1979.

....nearest neighbor search, we can retrieve similar data objects easily. For the multimedia databases with nearest neighbor retrieval, a good indexing method is a key component for efficient and accurate retrieval. Nowadays, alphanumeric data indexing techniques are already well developed such as [5, 16]. However, these databases make use of features for retrieval. The alphanumeric indexing methods are not particularly suitable for indexing features because they are designed for one dimensional vectors, but not multi dimensional vectors like the ones used in databases. Therefore, people have ....

....indexing and partition based indexing. Rectangle based Indexing The rectangle based indexing methods make use of rectangles to organize the features into groups for indexing. Examples are R tree, R tree, R tree, and SR tree. R tree R tree [33] is a generalization version of the B tree [5, 16] for multi dimensional data indexing. It uses rectangles to partition the data into groups. The partition process will proceed hierarchically and an indexing tree will then be produced. ffl Properties: R tree is a height balanced tree and it has two kinds of nodes: Leaf Node and Non leaf Node. ....

D. Comer. "The Ubiquitous B-tree". ACM Computing Surveys, 11(2):121-- 137, June 1979.

...., c) Estimation of the number of page accesses for index lookup If the predicate in the query involves an instance variable associated with an index, we can make use of this index to expedite the loading of root class objects. For clustered index B tree with average fan out b [3, 9], the number of page accesses required is # # # # # # # # # = 1 0 , 1 1 log q k k k b NP C SEL to lookup a clustered index, where 1 SEL is the selectivity of the predicate on the root class and k NP 1 is the number of objects (of the k th subclass of the root class) per page. ....

....required is # # # # # # # # # = 1 0 , 1 1 log q k k k b NP C SEL to lookup a clustered index, where 1 SEL is the selectivity of the predicate on the root class and k NP 1 is the number of objects (of the k th subclass of the root class) per page. For non clustered index [3, 9], the number of page 5 accesses required is # # # # # # # # # = 1 0 1 log q k k b C SEL . d) Estimation of the number of object references We need to estimate the number of object references during predicate evaluation (along the class composition hierarchy) For sequential ....

Douglas Comer, "The Ubiquitous B-Tree", in ACM Computing Surveys, Vol. 11, No. 2, pages 121--137, 1979.

....a number of entries, E = p, ptr , where p is a predicate that describes the subtree indicated by ptr. The subtrees recursively partition the data records. However, they do not necessarily partition the data space. GiST can therefore model ordered, space partitioning trees (e.g. B trees [COME79]) as well as unordered, non space partitioning trees (e.g. R trees [GUTT84] Two terms will be used in this paper that require additional explanation. First, for consistency with [HELL95] we call each datum stored in p a predicate rather than a key or index column. Second, we describe ....

D. Comer, "The Ubiquitous B-tree," Computing Surveys 11, 2 (1979), 122-137.

....coverage minimal. Resulting from this, the HG tree guarantees the worst cast storage utilization is more than 66.7 (2 3) of full capacity. Our experimental results in section 4 show that the average storage utilization is more than 80 . This concept is similar to that used with the B tree [4]. However, the B tree operates on 1dimensional space and the HG tree can be viewed as a generalization. The Hilbert R tree [14] also has a similar scheme, but it is a SAM for non point (geometric) data. Contrary to the HGtree, its directory regions may be overlapped with each other. The more the ....

D. Comer, "The Ubiquitous B-tree," ACM Computing Surveys, Vol. 11, No. 2, pp. 121-137, 1979. 20

....on the other hand, the semantic features or keywords obtained only by human sense cannot be quantified by any metric function. Indexing tabular data for exact match search or range search in traditional databases is a well understood problem, and the index structures like B tree family [6] provide efficient access mechanisms. However, they are not likely to provide enough information to deal with complex image contents. The one dimensional B tree does not usually reflect the n dimensional domain space, where n is the number of image features to index, and thus the B tree ....

D. Comer, "The Ubiquitous B-tree," ACM Computing Surveys, 11(2), 1979, 121-137.

.... relation manager (MMM) of the Starburst system from IBM Almaden Research Center [17] and the Dali system from the AT T Bell Laboratories [11, 4, 22] The work reported in this paper is motivated by our observation that, in contrast to a large amount of research work on the concurrent B tree [5, 19, 23, 18, 20, 12, 13, 24], little work has been reported on the study of the concurrent T tree [14, 17, 8] As pointed by Lehman et al. 17] and Gottemukkala et al. 8] once the I O bottleneck of paging data into and out of the main memory are removed, some other factors such as latching and locking dominate the cost of ....

....the T tree index and its variation, the T tail tree. Afterwards, we propose two mechanisms that allow concurrent operations including both search and modification on the tree while maintaining the consistency. 2.1. T tree and T tail tree The T tree [15] rooted in the AVL tree [2] and the Btree [5], is a balanced binary tree whose nodes contain more than one item. Figure 2.1 (a) depicts a T node, a node of a T tree. A T node consists of a number of data pointers, three data fields, 1 parent pointer, 0 1 tail pointer, and 0 2 child pointers. An internal T node has two child pointers pointing ....

[Article contains additional citation context not shown here]

D. Comer, "The Ubiquitous B-tree", ACM Computer Surveys, Volume 11, Number 2, June 1979, pp. 121-137.

....since the size of the memory being moved grows accordingly. Multi user or multi threaded systems are even more vulnerable since memory resources must be shared with other processes. 1. 3 Problem Definition: Impact of Large Pages on B Tree Performance The above clearly points out that the B tree [15] needs to be reexamined to prevent it from being too memory intensive for a system that uses large pages. Various organizations have been attempted for B tree leaf pages, including sorted array, partitioned, hashing, and unorganized tuples [20] By far the most popular organization is the sorted ....

D. Comer. "The Ubiquitous B-tree." ACM Computing Surveys, Volume 11, Issue 2, 1979: 121-137.

....well represented by point 9 locations. It is very important for a database system to have an index mechanism to handle spatial data efficiently, as required in computer aided design, geo data applications, and multimedia applications. R tree [10] was proposed as a natural extension of B trees [2] [7] and combines the nice features of both B trees and quadtrees. R tree is a height balanced tree similar to a B tree. The spatial objects are stored in the leaf level and are not further decomposed into their pictorial primitives, i.e. into quadrants, line streams, or pixels. We call this spatial ....

D. Comer, "The Ubiquitous B-tree," Computing Surveys, 11:2, pp. 121-138, June 1979.

....and terabytes of disk capacity. In this paper we describe the XFS file system with a focus on the mechanisms it uses to manage large file systems on large computer systems. The most notable mechanism used by XFS to increase the scalability of the file system is the pervasive use of B trees [Comer79]. B trees are used for tracking free extents in the file system rather than bitmaps. B trees are used to index directory entries rather than using linear lookup structures. B trees are used to manage file extent maps that overflow the number of direct pointers kept in the inodes. Finally, B ....

Comer, D., "The Ubiquitous B-Tree," Computing Surveys, Vol. 11, No. 2, June 1979 121-137.

....could to the same bucket) Nevertheless, practice has shown that in the absence of pathological data, good hashing schemes with few overflows and constant average case query performance exist. This is a major difference between hashing and indexing schemes. With a balanced index (like a B tree [C79]) answering a membership query takes logarithmic time on the size of the set. For many applications (for example in joins [SD90, LR96] a hashing scheme with constant average case query performance (one or two I O s) is preferable to the logarithmic worst case query performance (four or more ....

D. Comer, "The Ubiquitous B-Tree", ACM Computing Surveys, 11(2), pp121-137,1979.

....a database. To facilitate this functionality, the index manager chooses one or more attributes as a key and builds an index from them. There have been many research efforts to devise efficient index structures for database systems. The binary search tree [12] AVL tree [15] T tree [16] B tree [3], chained bucket hashing [15] extensible hashing [7] and linear hashing [18] are the typical examples. Previous research efforts mainly focus on designing efficient index structures appropriate for their own application domains. However, they rarely dealt with the practical issues occurred in ....

....the structure and the balancing scheme that are identical to those of the AVL tree, the T tree stores multiple entries in a node. As a result, storage overhead for each key entry gets smaller. This also reduces the number of rotation operations significantly in dynamic environment. The B tree [3] is a completely balanced index structure widely used in disk based DBMSs. It maximizes the fan out of a node to reduce the height of a tree, and thus minimizes the number of disk accesses in tree traverse. A leaf node stores multiple entries of the form hK i ; P i i, where K i is a key value and ....

D. Comer, "The ubiquitous B-Trees," ACM Computing Surveys, Vol. 11, No. 2, pp. 121-137, 1979.

....(i.e. duplications are not allowed) Like the clipping technique, the MBRs are represented in a file and may be organized by any multidimensional PAM. The most popular SAM using the overlapping technique is the R tree [Gutt84] R tree is a balanced tree generalizing the B tree concept [Come79] to spatial objects. The advantage of the overlapping technique is that the storage utilization depends only on the PAM, since every MBR is uniquely represented in the file. For instance, the space utilization in the R tree is at least 50 , due to the underlying B tree structure. However, ....

....At the moment, all tests are confined in the two dimensional space. The structure chosen to play the role of the underlying PAM in the experiments is the KDB tree [Robi81] The KDB tree is a very efficient multidimensional PAM which combines the properties of both KD tree [Bent75] and B tree [Come79]. A Composite KDB tree has been implemented to support the object overhead elimination for data sets consisting of various MBR sizes. What differentiates it from the KDB tree is the structure of the leaf node entries, where points are accompanied with two attribute values conveying information ....

D. Comer: `The Ubiquitous B-tree', Computing Surveys, Vol.11, No.2, 121-137, 1979.

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Comer D. "The ubiquitous B-Tree." ACM Computing Surveys, vol. 11, no. 2, 121--137, Jun 1979

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D. Comer, "The Ubiquitous B-tree", ACM Computing Surveys 1(2):121-137, 1979.

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Comer D. "The ubiquitous B-Tree." ACM Computing Surveys, vol. 11, no. 2, 121--137, Jun 1979

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D. Comer: "The Ubiquitous B-tree", ACM Computing Surveys, Vol.11, No.2, pp.121-137, 1979.

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D. Comer, "The Ubiquitous B-tree", in ACM Computing Surveys,vol- ume 11, pages 121--137, 1979.

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