P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 381--392, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Note that the query bound consists of an O(log B N) search term corresponding to the familiar O(log N) internal memory search term, and an O(T=B) reporting term accounting for the O(T=B) I Os needed to report T elements. Recently, the above bounds have been obtained for a number of problems (e. g [30, 26, 149, 5, 47, 87]) but higher lower bounds have also been established for some problems [141, 26, 93, 101, 106, 135, 102] We discuss these results in later sections. B trees come in several variants, like B and B trees (see e.g. 35, 63, 95, 30, 104, 3] and their references) A basic B tree is a ....

....with this property were developed by Agarwal et al. 10] Proximity queries. Proximity queries such as nearest neighbor and closest pair queries have become increasingly important in recent years, for example because of their applications in similarity search and data mining. Callahan et al. [47] developed the first worst case efficient external proximity query data structures. Their structures are based on an external version of the topology trees of Frederickson [84] called topology B trees, which can be used to dynamically maintain arbitrary binary trees I O efficiently. Using ....

[Article contains additional citation context not shown here]

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 381--392, 1995.

....MTF ranks) and increment the (r) MTF ranks of all the items whose rank was smaller than r. The recomputation of these (r) MTF ranks is done implicitly by means of an additional MTF list. Consider generalizing the BSL for external memory operations. Say we adopt the bucketing strategy of [4] to make BSL work in external memory. BSL now consists of O(log B n) levels and seems to take (log B r) expected amortized I Os per operation. However this is not true because we need to update BSL 3 and MTF list consistently after a query operation, and this is a challenge since BSL and ....

....B k we also need to perform a promotion from band B k 1 by taking a random item from it. The cost of a deletion is then O(log n) expected time. 4 SASL in External Memory for Strings Skip lists can be easily adapted to work in external memory by setting the probability of ipping a head as (1=B) [4]. This way, the height of the skip list is O(log B n) It is not dicult to generalize the algorithms we designed for our SASL from the previous section to work in this context too. Just observe that any restructuring of our data structure is done during a downward traversal so that pointers and ....

P. B. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Algorithms and Data Structures, 4th International Workshop, volume 955 of Lecture Notes in Computer Science, pages 381-392, 1995.

.... which is expected to manipulate petabytes (thousands of terabytes, or millions of gigabytes) of data The effect of the I O bottleneck is getting more pronounced as internal computation gets faster, and especially as parallel computing gains popularity [107] Currently, technological 1 Cited in [34] 1 P M D M P D Figure 1.1: A RAM like machine model. Figure 1.2: A more realistic model. advances are increasing CPU speeds at an annual rate of 40 60 while disk transfer rates are only increasing by 7 10 annually [113] Internal memory sizes are also increasing, but not nearly fast ....

....papers also deal with fundamental problems such as permutation, sorting and matrix transposition. The problem of implementing various classes of permutations has been addressed in [47, 48, 50] More recently researchers have moved on to more specialized problems in the computational geometry [11, 15, 34, 40, 67, 74, 79, 110, 121, 130, 137], graph [12, 40, 42, 97] and string areas [44, 56, 57] As already mentioned the number of I O operations needed to read the entire input is N=B and for convenience we call this quotient n. We use the term scanning to describe the fundamental primitive of reading (or writing) all elements in a ....

[Article contains additional citation context not shown here]

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 381--392, 1995.

....algorithms that minimize the input output communication (I O) performed when solving a given problem. The area was effectively started in the late eighties by Aggarwal and Vitter [6] and subsequently I O algorithms have been developed for several problem domains, including computational geometry [29, 7, 13, 14, 4, 15, 31, 38, 39, 41, 3, 44, 2, 12, 13, 16, 28, 30, 44], graph algorithms [17, 7, 33, 1, 21, 8, 27, 35, 40] and string processing [25, 26, 11, 20] Also I O performance can often be improved if many disks can efficiently be used in parallel and the use of parallel disks has received a lot of theoretical attention. Recent surveys of theoretical ....

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 381--392, 1995.

....the K smallest interpoint distances in P; this takes O(sort(N K) I Os using O( N K) B) blocks of external memory. In Section 6.4, we present an algorithm to dynamically maintain the closest pair of P in O(log B N) I O s per insert or delete operation using O(N=B) blocks of external memory. In [5] an O(log B N) algorithm for the dynamic closest pair problem in higher dimensions is given. Their approach uses the Topology B tree data structure. For the remaining problems, our results are the only efficient external memory algorithms known in higher dimensions. For the K nearest neighbor and ....

....However, this does not give us an efficient way to find R(B) since the sequence of cuts may be long. In [8] it is shown that given the deepest node A, R(B) can be computed in constant time. We can compute A using O(log B N) I Os by posing it as a deepest intersect query on the Topology B tree [5]. Deletion: To delete a point a, delete the leaf a and compress the parent node p(a) Note that this preserves the invariants. Theorem 2. The fair split tree of a point set P can be maintained using O(N=B) disk blocks and O(log B N) I Os per insert or delete operation. Maintaining the pairs ....

[Article contains additional citation context not shown here]

P. B. Callahan, M. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. WADS'95, LNCS 955, pages 381--392, 1995.

....[26, 27] give efficient data structures for performing range searching in external memory. Very recently, a new data structure called buffer tree and its applications are given in [2, 3] and an external memory version of the directed topology tree ( 18] called topology B tree is given in [9]. For excellent examples of experimental work in computational geometry, see Bentley [5, 6, 7, 8] As for experimental work on I O efficient computation, very recently Vengroff has built an environment called TPIE for programming external memory algorithms as he proposed earlier in [29] and also ....

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures (to appear), 1995.

.... which is expected to manipulate petabytes (thousands of terabytes, or millions of gigabytes) of data The e#ect of the I O bottleneck is getting more pronounced as internal computation gets faster, and especially as parallel computing gains popularity [107] Currently, technological 1 Cited in [34] 1 P M D M P D Figure 1.1: A RAM like machine model. Figure 1.2: A more realistic model. advances are increasing CPU speeds at an annual rate of 40 60 while disk transfer rates are only increasing by 7 10 annually [113] Internal memory sizes are also increasing, but not nearly fast ....

....papers also deal with fundamental problems such as permutation, sorting and matrix transposition. The problem of implementing various classes of permutations has been addressed in [47, 48, 50] More recently researchers have moved on to more specialized problems in the computational geometry [11, 15, 34, 40, 67, 74, 79, 110, 121, 130, 137], graph [12, 40, 42, 97] and string areas [44, 56, 57] As already mentioned the number of I O operations needed to read the entire input is N B and for convenience we call this quotient n. We use the term scanning to describe the fundamental primitive of reading (or writing) all elements in a ....

[Article contains additional citation context not shown here]

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 381--392, 1995.

....one disk block. Previous Related Work We first briefly review the work on I O techniques. In addition to early work on sorting and scientific computing [2, 28, 44] recently various researchers have been investigating external memory algorithms for graphs [1, 12] and for computational geometry [1, 3, 5, 6, 7, 10, 18, 21, 29, 38, 43]. As mentioned before, most of the results are theoretical, and yet the experiments of Chiang [11] Vengroff and Vitter [42] and Arge et al. 5] on some of these techniques show that they result in significant improvements over traditional algorithms in practice. As for isosurface extraction, ....

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, pages 381--392, 1995.

....for individual problems. The common approach is to re design the algorithm on one hand and the arrangement of data on the other, to extract such I O efficiency as the nature of the problem would allow. The design of data structures that facilitate the task has only recently been widely taken up [2, 3]. We feel that the design of general purpose I O efficient data structures is very important. The I O efficiency of a range of algorithms could be improved simply by replacing the data structures employed by their I O efficient versions, if such versions were to be available. Algorithms that use ....

Callahan, P., Goodrich, M.T. and Ramaiyer, K.: Topology B-Trees and Their Applications. In Proc. Fourth Workshop on Algorithms and Data Struc., pp. 381-392, 1995.

....and slower external memory (disk) becomes a major bottleneck. Algorithms specifically designed to reduce the I O bottleneck are called external memory algorithms. In recent years various researchers have been investigating external memory algorithms for graphs [10] and for computational geometry [2, 4, 5, 8, 13, 16, 23, 31, 34], in addition to early work on sorting and scientific computing [1, 21, 35] Although most of the results are theoretical, the experiments of Chiang [9] and of Vengroff and Vitter [33] on some of these techniques show that they result in significant improvements over traditional algorithms in ....

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, pages 381--392, 1995.

....data structures for performing range searching in external memory. Concurrent to the work in this paper, a new data structure called buffer tree and its applications are given in [2, 5] and an external memory version of the directed topology tree ( 21] called topology B tree is given in [11]. For excellent examples of experimental work in computational geometry, see Bentley [7, 8, 9, 10] As for experimental work on I O efficient computation, concurrent to our work Vengroff builds an environment called TPIE for programming external memory algorithms as he proposed earlier in [36] ....

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 381--392, 1995.

....bounds, but do have good average case behavior for common problems see [70, 61] Range searching is also considered in [74, 82, 83] where the problem of maintaining range trees in external memory is considered. However, the model used in this work is different from the one considered here. In [27] an external on line version of the topology tree is developed and this structure is used to obtain structures for a number of dynamic problems, including approximate nearest neighbor searching and closest pair maintenance. Very recently, an algorithm has been given [1] for preprocessing a TIN ....

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 381--392, 1995.

....bound for sorting in internal memory. Work has also been done on matrix algebra and related problems arising in scientific computation [3, 51, 52] More recently, researchers have designed external memory algorithms for a number of problems in different areas, such as in computational geometry [32, 5, 53, 31, 2, 11, 34, 44, 47, 12, 50, 17, 1], string processing [28, 29, 9] and graph theoretic computation [6, 24, 38, 35] Some encouraging experimental results regarding the practical merits of the developed algorithms have also been obtained [23, 51, 11, 33] Recent surveys can be found in [7, 8] 1.3 Our Results In this paper, we ....

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 381--392, 1995.

....[98, 106] give efficient data structures for performing range searching in external memory. Very recently, a new data structure called buffer tree and its applications are given in [5, 6] and an external memory version of the directed topology tree ( 52] called topology B tree is given in [17]. There has also been some work on selected graph problems, including the investigations by Ullman and Yannakakis [117] on transitive closure computations. This work, however, restricts its attention to problem instances where the set of vertices fits into main memory but the set of edges does ....

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures (to appear), 1995.

No context found.

P. Callahan, M. T. Goodrich, and K. Ramaiyer. Topology B-trees and their applications. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 381--392, 1995.

No context found.

P. Callahan, M.T. Goodrich and K. Ramaiyer. Topology B-Trees and Their Applications. Proc. WADS'94, LNCS 955, pp. 381-392, 1995.

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