R. Grossi and G. F. Italiano. Revised version of "efficient cross-trees for external memory". Technical Report TR-0016, Oct. 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....indexing structures often answer queries in much fewer I Os. However, their query performance can seriously deteriorate after a large number of updates. Recently, a number of linear space structures with guaranteed worst case efficient query and update performance have been developed (see e.g. [5, 15, 12]) The so called cross trees [12] and O trees [15] answer window queries in the optimal number of I Os and can be updated, theoretically, in I Os, but they are of limited practical interest because a theoretical analysis shows that their average query performance is close to the ....

....in much fewer I Os. However, their query performance can seriously deteriorate after a large number of updates. Recently, a number of linear space structures with guaranteed worst case efficient query and update performance have been developed (see e.g. 5, 15, 12] The so called cross trees [12] and O trees [15] answer window queries in the optimal number of I Os and can be updated, theoretically, in I Os, but they are of limited practical interest because a theoretical analysis shows that their average query performance is close to the worst case performance. See e.g. ....

R. Grossi and G. F. Italiano. Efficient cross-tree for external memory. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization, pages 87--106. American Mathematical Society, 1999. Revised version available at ftp://ftp.di.unipi.it/pub/techreports/TR-00-16.ps.Z.

....or rectangular objects. Aggregation over point objects is a special case of orthogonal range searching in computational geometry. Agarwal and Erickson [Agarwal and Erickson, 1999] provide a review of geometric range searching and its related topics. Grossi and Italiano [Grossi and Italiano, 1999, Grossi and Italiano, 2000] proposed the cross tree data structure, a generalized version of balanced tree, to speed up range searching in high dimensional space. Work has been reported on aggregation over point objects [Chan and Ioannidis, 1999, Geffner et al. 2000, Ho et al. 1997] and 1D intervals [Yang and Widom, ....

Grossi, R. and Italiano, G. F. (2000). Revised version of "efficient cross-trees for external memory". Technical Report TR-00-16.

....be point objects, intervals, or rectangular objects. Aggregation over point objects is a special case of orthogonal range searching in computational geometry. Agarwal and Erickson [Agarwal and Erickson, 1999] provide a review of geometric range searching and its related topics. Grossi and Italiano [Grossi and Italiano, 1999, Grossi and Italiano, 2000] proposed the cross tree data structure, a generalized version of balanced tree, to speed up range searching in high dimensional space. Work has been reported on aggregation over point objects [Chan and Ioannidis, 1999, Geffner et al. 2000, Ho et al. 1997] and 1D ....

Grossi, R. and Italiano, G. F. (1999). Efficient cross-trees for external memory. In Abello, J. and Vitter, J. S., editors, External Memory Algorithms and Visualization, pages 87--106. American Mathematical Society Press, Providence, RI.

....be maintained during updates (insertions) Unfortunately, a similar claim cannot be made about the underlying kd tree, and thus good query efficiency cannot be maintained. Recently, a number of theoretical worst case efficient dynamic external data structures have been developed. The cross tree [15] and the O tree [17] for example, both use linear space, answer range queries in the optimal number of I Os, and they can be updated I O efficiently. However, their practical efficiency has not been investigated, probably because a theoretical analysis shows that their average query performance ....

R. Grossi and G. F. Italiano. Efficient cross-trees for external memory. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization. American Mathematical Society, 1999.

....Department of Computer Science, University of Aarhus, Denmark and I.N.R.I.A. Sophia Antipolis, France. Email: jsv cs.duke.edu. 1 Introduction There has recently been much effort toward developing worst case I O efficient external memory data structures for range searching in two dimensions [1, 2, 4, 8, 12, 13, 20, 26, 28, 29]. In their pioneering work, Kanellakis et al. 13] showed that the problem of indexing in new data models (such as constraint, temporal, and object models) can be reduced to special cases of twodimensional indexing. Refer to Figure 1) In particular they identified the 3 sided range searching ....

R. Grossi and G. F. Italiano. Efficient cross-tree for external memory. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization. American Mathematical Society Press, 1999.

....B N) I Os (amortized) even if v has a large associated secondary structure that needs to be updated when a rebalance operation is performed on v, provided that the secondary structure can be updated in O(w) I Os. Weight balanced B trees have been used in numerous efficient data structure (see e.g. [30, 26, 89, 90, 38, 3, 28]) In some applications we need to be able to traverse a path in a B tree from a leaf to the root. To do so we need a parent pointer from each node to its parent. Such pointers can easily be maintained efficiently in normal B trees or weightbalanced B trees, but cannot be maintained efficiently ....

....In practical applications involving massive datasets it is often crucial that external data structures use linear space. We discuss this further in Section 7. Grossi and Italiano developed the elegant linear space cross tree data structure which answers planar range queries in O( p N=B T=B) I Os [89, 90]. This is optimal for linear space data structures as e.g. proven by Kanth and Singh [102] The O tree of Kanth and Singh [102] obtains the same bounds using ideas similar to the ones used by van Kreveld and Overmars in divided k d trees [146] In Section 5.2 below we discuss the cross tree ....

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R. Grossi and G. F. Italiano. Efficient cross-tree for external memory. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization, pages 87--106. American Mathematical Society, DIMACS series in Discrete Mathematics and Theoretical Computer Science, 1999. Revised version available at ftp://ftp.di.unipi.it/pub/techreports/TR-00-16.ps.Z.

....B tree to be maintained during updates (insertions) Unfortunately, a similar claim cannot be made about the underlying kd tree and thus good query efficiency cannot be maintained. Recently, a number of theoretical worst case efficient dynamic data structures have been developed. The cross tree [21] and the O tree [27] for example, both use linearspace, answer range queries in the optimal number of I Os, and they can be updated I O efficiently. However, their practical efficiency has not been investigated, probably because a careful theoretical analysis shows that their average query ....

R. Grossi and G. F. Italiano. Efficient cross-trees for external memory. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization, DIMACS Series 13 in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society Press, 1999.

....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 ....

R. Grossi and G. F. Italiano. Efficient cross-tree for external memory. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization. American Mathematical Society Press, Providence, RI, 1999.

....all commercial DBMS because of its optimal performance. Lately some extensions of the Btree have been proposed for multi dimensional access methods. The BV tree[Fre95] is an attempt to generalize the B tree to higher dimensions. A weight balanced Btree is proposed in [AV96] The Cross Tree [GI98] is a multidimensional version of a Btree that combines the Btree data driven partition of data with the quadtree space driven partitioning. PAMs index points and therefore do not need a decomposition in two steps: filter step and refinement step. In contrast SAMs deal with lines and regions, 50 ....

R. Grossi and G.F. Italiano. Efficient Cross-Trees for External Memory. In J. Abello and J.S. Vitter, editors, External Memory Algorithms and Visualization, DIMACS. American Mathematical Society, 1998.

....a dynamic set S. Splits and concatenates are useful and alternative operations to slide window R over the items in S instead of performing many single insertions and deletions of items. Furthermore, our technique for order decomposable problems is suitable for efficient external memory algorithms [15]. The remainder of this paper is organized as follows. In Section 2 we describe our technique for the case d = 2 and a single set S. In Section 3 we list some applications of this technique to concatenable data structures. General order decomposable problems of dimension d 2 are considered in ....

R. Grossi and G.F. Italiano, Efficient cross-trees for external memory. Unpublished manuscript, 1998.

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R. Grossi and G. F. Italiano. Revised version of "efficient cross-trees for external memory". Technical Report TR-0016, Oct. 2000.

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R. Grossi and G. F. Italiano. Efficient cross-trees for external memory. In James Abello and Jeffrey Scott Vitter, editors, External Memory Algorithms and Visualization, pages 87--106. American Mathematical Society Press, Providence, RI, 1999.

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R. Grossi and G. F. Italiano. Revised version of "efficient cross-trees for external memory". Technical Report TR-00-16, Oct. 2000.

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R. Grossi and G. F. Italiano. Efficient cross-trees for external memory. In James Abello and Jeffrey Scott Vitter, editors, External Memory Algorithms and Visualization, pages 87--106. American Mathematical Society Press, Providence, RI, 1999.

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R. Grossi and G. F. Italiano. Revised version of "efficient cross-trees for external memory". Technical Report TR-0016, Oct. 2000.

No context found.

R. Grossi and G. F. Italiano. Efficient cross-trees for external memory. In James Abello and Jeffrey Scott Vitter, editors, External Memory Algorithms and Visualization, pages 87--106. American Mathematical Society Press, Providence, RI, 1999.

No context found.

R. Grossi and G. F. Italiano. Revised version of "efficient cross-trees for external memory". Technical Report TR-00-16, Oct. 2000.

No context found.

R. Grossi and G. F. Italiano. Efficient cross-trees for external memory. In James Abello and Jeffrey Scott Vitter, editors, External Memory Algorithms and Visualization, pages 87--106. American Mathematical Society Press, Providence, RI, 1999.

No context found.

R. Grossi and G. F. Italiano. Revised version of "efficient cross-trees for external memory". Technical Report TR-0016, 10 2000.

No context found.

R. Grossi and G. F. Italiano. Efficient cross-trees for external memory. In James Abello and Jeffrey Scott Vitter, editors, External Memory Algorithms and Visualization, pages 87-- 106. American Mathematical Society Press, Providence, RI, 1999.

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