R. Bayer and E. McCreight. Organization of large ordered indexes. Acta Inform., 1:173--189, 1972.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....computations that are fundamental for out of core scientific visualization and graphics: external merge sort [3] out of core pointer de referencing [14,17,18] and the meta cell technique [20] In Sec. 2. 3, we review some important data structures for on line computations, namely the B tree [9, 26] and B tree like data structures, and show a general method of converting a main memory, binary tree structure into a B tree like data structure. In particular, we review the BBIO tree [19, 20] which is an external memory version of the main memory interval tree [33] and is essential for ....

....) I O s. 2.3 On Line Computations: B Trees and B Tree Like Data Structures Tree based data structures arise naturally in the on line setting, since data items are stored sorted and queries can typically be performed by efficient searches on the trees. The well known balanced multiway B tree [9,26] (see also [27, Chapter 18] is the most widely used data structure in external memory. Each tree node corresponds to one disk block, capable of holding up to B items. The branching factor, Bf, defined as the number of children of each internal node, is #(B) except for the root) this guarantees ....

R. Bayer and McCreight. Organization of large ordered indexes. Acta Inform., 1:173--189, 1972.

....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 ....

R. Bayer and E. McCreight, "Organization of Large Ordered Indexes," Acta Iform. 1 (1972), 173 189.

....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 ....

R. Bayer & E. McCreight, "Organization of large ordered indexes," Acta Informatica 1 (1972), 173 189.

....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 ....

R. Bayer and E. McCreight, "Organization of Large Ordered Indexes," Acta Informatica 1 (1972), 173--189.

....have received much attention recently, but most of the results are known only for the planar case. The main idea underlying these structures is to construct high degree trees instead of binary trees. For example, variants of B trees are used to answer 1 dimensional range searching queries [35, 92]. A number of additional tricks are developed to optimize the size and the query time. See [21, 22, 210] for I O efficient data structures that have been used for answering range searching and related queries. Table 2 summarizes the known results on secondary memory structures for orthogonal ....

....the 12 Pankaj Agarwal and Jeff Erickson argument by Chazelle [57] they proved that any secondary memory data structure that answers a range reporting query in time O(polyLog n k=B) requires Omega Gamma N log N= log Log n) storage. d Range Size Query Time Source d = 1 Interval N Log n k=B [35, 92] Quadrant N log log B Log n k=B [220] d = 2 3 sided rectangle N Log n k=B log B [240] 3 sided rectangle N log B log log B Log n k=B [220] Rectangle N log N= log Log n Log n k=B log B [240] d = 3 Octant N log N fi(n) Log n k=B [245] Rectangle N log 4 N fi(n) Log n k=B ....

[Article contains additional citation context not shown here]

R. Bayer and McCreight, Organization of large ordered indexes, Acta Inform., 1 (1972), 173-- 189.

....computational geometry, and is optimal for this particular problem in terms 1 of internal computation [25] The three variations of plane sweep differ by the sorting methods (external merge sort [1] vs. internal merge sort) used in the preprocessing phase and the dynamic data structures (B tree [4, 11, 14] vs. 2 3 4 tree [14] used in the sweeping phase. We generate the test data by three programs that use a random number generator while producing some interesting properties that are predicted by our theoretical analysis. The sizes of the test data range from 250 thousand segments to 2.5 million ....

....phase. Using any dynamic balanced tree, plane sweep takes optimal O(N log N) time in terms of internal computation. Our three variations of plane sweep differ by the sorting methods and the dynamic data structures used. The first variation, B Tree, uses external merge sort [1] and a B tree [4, 11, 14]; this is a direct way to implement plane sweep in secondary memory. The number of I O operations performed in the first phase is optimal O( N B log M B N B ) 1] and in the second phase is O(N log B N B K B ) The second variation, 234 Tree, uses external merge sort and a 2 3 4 ....

R. Bayer and E. McCreight. Organization of large ordered indexes. Acta Inform., 1:173--189, 1972.

....data model of [8] While the declarative programming features (relational calculus and algebra) of the model are important, it is crucial to support these features with data structures for searching and updating that make optimal use of secondary storage. B trees and their variants B trees [1,9] 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 ....

R. Bayer and E. McCreight, "Organization of Large Ordered Indexes," Acta Informatica 1 (1972), 173--189.

....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]. Unfortunately, this requires Theta( N K) log ) Theta(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( log 2 ) I Os [34] Our new method uses an off line top down implementation of ....

....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 ....

R. Bayer and E. McCreight, "Organization of Large Ordered Indexes," Acta Inform. 1 (1972), 173--189.

....data model of [5] While the 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 [2, 6] are examples of such data structures. They have been an unqualified success in supporting external dynamic 1 dimensional range searching in relational database systems. This work was done while the author was at Bell Communications Research, Morristown, NJ 07960, USA. In this paper, we study ....

R. Bayer & E. McCreight, "Organization of Large Ordered Indexes," Acta Informatica1 (1972), 173--189.

....fixed relational calculus query can be evaluated in LOGSPACE and PTIME in the size of the input database. More importantly, these language features can be supported by data structures for searching and updating that make optimal use of secondary storage. B trees and their variants B trees [2,11] are examples of such data structures and have been an unqualified success in supporting external dynamic one dimensional range searching in relational database systems. The general data structure problem underlying efficient secondary storage manipulation for many data models is external dynamic ....

R. Bayer & E. McCreight, "Organization of Large Ordered Indexes," Acta Informatica 1 (1972), 173--189.

....model [1,16,32] We believe that efficient indexing is critical in making Object Oriented Databases (OODBs) competitive in terms of performance with relational technology. The principal motivation for our work is the development of indexing techniques to support OODBs as efficiently as B trees [2,8] support relations. We recall that B trees and their variants B trees are the canonical examples of relational database physical support and have been an unqualified success for external dynamic one dimensional range searching, which is the most common problem solved by indexing in relational ....

R. Bayer & E. McCreight, "Organization of Large Ordered Indexes," Acta Informatica 1 (1972), 173--189.

....every fixed relational calculus query is evaluable in LOGSPACE and PTIME in the size of the input database. More importantly, these language features can be supported by data structures for searching and updating that make optimal use of secondary storage. Btrees and their variants B trees [1,9] 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 ....

R. Bayer and E. McCreight, "Organization of Large Ordered Indexes," Acta Informatica 1 (1972), 173--189.

....have received much attention recently, but most of the results are known only for the planar case. The main idea underlying these structures is to construct high degree trees instead of binary trees. For example, variants of B trees are used to answer 1 dimensional rangesearching queries [35, 96]. A number of additional tricks are developed to optimize the size and the query time. See [20, 21, 232] for I O efficient data structures that have been used for answering range searching and related queries. Table 2 summarizes the known results on secondary memory structures for orthogonal range ....

....2. For a data structure to be used in real applications, its size should be at most cn, where c is a very small constant, the time to answer a typical query should be small the lower Geometric Range Searching and Its Relatives 13 d Range Size Query Time Source d = 1 Interval N Log n k=B [35, 96] Quadrant N log log B Log n k=B [244] 3 sided rectangle N Log n k=B log B [270] d = 2 3 sided rectangle N log B log log B Log n k=B [244] Rectangle N log N= log Log n Log n k=B log B [270] Rectangle cN k=B 1 Gamma1=2c [270] d = 3 Octant N log N fi(n) Log n k=B [277] ....

[Article contains additional citation context not shown here]

R. Bayer and McCreight, Organization of large ordered indexes, Acta Inform., 1 (1972), 173-- 189.

....improve the efficiency of query evaluation. A typical problem in query evaluation is 1 dimensional range searching, which asks to return all tuples that have an x attribute with values between two constants. Range searching on regular relations can be implemented by B trees and and B trees [17, 46] which are good in minimizing the number of accesses to secondary storage. Range searching requires O(log B N K=B) secondary memory accesses in the worst case, where B is the number of tuples in a block, N is the total number of tuples in the relation searched, and K is the number of tuples ....

R. Bayer, E. McCreight. Organization of Large Ordered Indexes. Acta Informatica, 1:173--189, 1972.

....storage is an additional requirement, beyond low data complexity or strong polynomiality of operations, whose satisfaction greatly contributes to relational technology. B trees (and their variants B trees) are examples of important data structures for implementing relational databases (see Bayer and McCreight, 1972). Let each secondary memory access transmit B units of data, let r be a relation with N tuples, and let us have a B tree on the attribute x of r. The space used in this case is O(N=B) The following operations define (dynamic) one dimensional searching on relational attribute x, with the ....

R. Bayer, E. McCreight. Organization of Large Ordered Indexes. Acta Informatica, 1:173--189, 1972.

....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 ....

R. Bayer and E. McCreight, "Organization of Large Ordered Indexes," Acta Informatica 1 (1972), 173--189.

....list. We avoid this inefficiency by representing each list as a search tree. For definiteness, we shall describe a solution based on splay trees [21] a form of self adjusting binary search tree, although any kind of search tree, such as red black trees [15, 24] AVL trees [1] or B trees [2], will suffice. Since the required operations on search trees are well known and straightforward, we shall be very sketchy in the presentation. Detailed discussions of splay trees can be found in [21, 24] Each arc in an Euler tour list becomes a node in the splay tree representing the list. ....

R. Bayer and E. McCreight, "Organization of large ordered indexes," Acta Inform. 1 (1972), 173--189.

....every fixed relational calculus query is evaluable in LOGSPACE and PTIME in the size of the input database. More importantly, these language features can be supported by data structures for searching and updating that make optimal use of secondary storage. Btrees and their variants B trees [1,10] 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 ....

R. Bayer and E. McCreight, "Organization of Large Ordered Indexes," Acta Informatica 1 (1972), 173--189.

....databases on secondary storage would have been impractical. I O efficient (i.e. logarithmic or constant) use of secondary storage is an additional requirement, beyond low data complexity, whose satisfaction greatly contributes to relational technology. B trees and their variants B trees, [7, 24], are examples of important data structures for implementing relational databases. In particular, let each secondary memory access transmit B units of data, let r be a relation with N tuples, and let us have a B tree on the attribute x of r. The space used in this case is O(N=B) The ....

R. Bayer, E. McCreight. Organization of Large Ordered Indexes. Acta Informatica, 1:173--189, 1972.

....in computational geometry, and is optimal for this particular problem in terms of internal computation [29] The three variations of plane sweep differ by the sorting methods (external merge sort [1] vs. internal merge sort) used in the preprocessing phase and the dynamic data structures (B tree [6, 13, 16] vs. 2 3 4 tree [16] used in the sweeping phase. Intuitively, the four algorithms are spread along a design spectrum from an algorithm designed exclusively for external memory (distribution sweep) to one designed exclusively for internal memory using an infinite size virtual memory assumption. We ....

....can each be performed in O(log N) time, plane sweep takes optimal Theta(N log N K) time in terms of internal computation. Our three variations of plane sweep differ by the sorting methods and the dynamic data structures used. The first variation, B Tree, uses external merge sort [1] and a B tree [6, 13, 16]; this is a direct way to implement plane sweep in secondary memory. In the first phase, the number of I O operations performed is optimal Theta(sort(N ) Theta( N B log M B N B ) 1] In the second phase, insertions, deletions and searches in a B tree can each be performed in O(log B N B ....

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R. Bayer and E. McCreight. Organization of large ordered indexes. Acta Inform., 1:173--189, 1972.

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R. Bayer and E. McCreight. Organization of large ordered indexes. Acta Inform., 1:173--189, 1972.

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R. Bayer, E. McCreight. Organization of Large Ordered Indexes. Acta Informatica, 1:173--189, 1972. 102

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R. Bayer and McCreight. Organization of large ordered indexes. Acta Inform., 1:173--189, 1972.

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R. Bayer and E. McCreight. Organization of large ordered indexes. Acta Inform., 1, 173#189, 1972.

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Bayer, R., and McCreight, E., "Organization of large ordered indexes", Acta Inform., pp 173-189, 1, 1972.

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