G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height (extended abstract). In Proc. 13th ACM-SIAM Symp. on Discrete Algorithms (SODA), 2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....They show how several basic problems namely matrix multiplication, matrix transpose, Fast Fourier Transform, and sorting have optimal algorithms that are cache oblivious. More recently, cache oblivious data structures matching the bounds of B trees, priority queues, and tries have been developed [2, 4 7]. Most memory models do not distinguish between random block transfers and sequential block transfers. The di erence in access times is caused by the seek times and latencies on disk and by prefetching in disk and main memory. The current di erence in speed between random access and sequential ....

....it seems that this improvement is marginal. Our results form a body of tools for manipulating dynamic data in unknown and multilevel memory hierarchies. In particular, they can be used to improve cache oblivious B trees. The only cache oblivious B tree structures that support traversals optimally [4, 6, 7] require O(log B N B ) amortized memory transfers per update. By applying the structure in Section 4, we obtain the following improvement: Corollary 1. There is a cache oblivious data structure that maintains an ordered set subject to searches in O(log B N ) memory transfers, insertions and ....

G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height (extended abstract). In SODA, 2002.

.... in [37] Generalizations of Hilbert curves to higher dimensions are given in [1] Specific applications include matrix multiplication [11, 20] domain decomposition [3, 25, 39] and image processing [2, 34, 4, 51, 31, 30] They are also a standard tool in the creation of cache oblivious algorithms [21, 40, 5, 41, 6, 10], which have asymptotically optimal memory performance on multilevel memory hierarchies while avoiding memory specific parameterization. There is a large body of work on scheduling and online scheduling, in particular. We do not attempt to review all this work here, but refer the reader to the ....

G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height (extended abstract). In Proc. 13th ACM-SIAM Symp. on Discrete Algorithms (SODA), 2002.

....Their structure does not allow the scan operation, unlike our structure. They provide the rst implementation of a cache oblivious dynamic dictionary, which performs better than an optimized B tree, because it interacts well with the translation lookaside bu er. Brodal, Fagerberg, and Jacob [14] independently developed a simpli ed cache oblivious search tree, whose bounds match those presented here. Their tree structure maintains a balanced tree of height log n O(1) which they lay out cache obliviously in an array of size O(n) They also present experimental results comparing memory ....

G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height (extended abstract). In Proc. ACM-SIAM Symp. on Discrete Algorithms, 2002.

.... in [37] Generalizations of Hilbert curves to higher dimensions are given in [1] Specific applications include matrix multiplication [11, 20] domain decomposition [3, 25, 39] and image processing [2, 34, 4, 51, 31, 30] They are also a standard tool in the creation of cacheoblivious algorithms [21, 40, 5, 41, 6, 10], which have asymptotically optimal memory performance on multilevel memory hierarchies while avoiding memory specific parameterization. There is a large body of work on scheduling and online scheduling, in particular. We do not attempt to review all this work here, but refer the reader to the ....

G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height (extended abstract). In Proc. 13th ACM-SIAM Symp. on Discrete Algorithms (SODA), 2002.

....into memory blocks, the algorithm does not achieve the perfect binary splitting into equal size subproblems. Cache aware algorithms have been studied in a number of di erent contexts [7, 8, 5, 10] The second approach to improving the memory performance of binary search is the cache oblivious [9, 4, 1, 2, 3] approach where the items are organized in a universal fashion so that items that are accessed closely in time are stored near each other. The method is called cache oblivious because knowledge of the memory block size is not needed to achieve the organization. The advantage of the cache oblivious ....

....the memory footprint of a single node, and thus increase the overall cache performance. However the computation of the implicit pointers at run time impacts the instruction count of the algorithm and can have a negative e ect on performance. In recent work Bender et al. [2] and Brodal et al. [3] have used the cache oblivious static search tree as the basis of a cache oblivious dynamic search structures that allow for insertions and deletions. In particular, Brodal et al. have discovered a very elegant and ecient way to calculate the pointers in the cache oblivious static search tree with ....

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Brodal, G.S.; Fagerberg, R.; Jacob, R. (2002): Cache oblivious search trees via binary trees of small height. SODA'02, Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 39-48

....to recent surveys for further I O model and hierarchical memory model results [6, 26] Frigo et al. 22] developed cache oblivious algorithms for sorting, Fast Fourier Transform, and matrix multiplication. Subsequently, a number of other results have been obtained in the cache oblivious model [7, 10, 11, 12, 13, 16, 17, 24], among them several cache oblivious B tree structure with O(log B N) search and update bounds [11, 12, 13, 17, 24] Several of these structures can also support one dimensional range queries in O(log B N T B) memory transfers [12, 13, 17] but at an increased amortized update cost of O(log B N ....

....algorithms for sorting, Fast Fourier Transform, and matrix multiplication. Subsequently, a number of other results have been obtained in the cache oblivious model [7, 10, 11, 12, 13, 16, 17, 24] among them several cache oblivious B tree structure with O(log B N) search and update bounds [11, 12, 13, 17, 24]. Several of these structures can also support one dimensional range queries in O(log B N T B) memory transfers [12, 13, 17] but at an increased amortized update cost of O(log B N B N) memory transfers. To our knowledge, no cache oblivious structures for higher dimensional orthogonal range ....

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 39--48, 2002.

....hierarchy. Frigo et al. 25] developed optimal cache oblivious algorithms for matrix multiplication, matrix transposition, Fast Fourier Transform, and sorting. Optimal cache oblivious algorithms have also been found for LU decomposition [15, 35] Bender et al. 13] and subsequently Brodal et al. [16], Bender et al. 14] and Rahman et al. 32] developed cacheoblivious B trees with a search cost of O(log B N) matching the standard (cache aware) B tree. The practical eciency of the developed algorithms have been investigated in [32, 16, 14] 1.1.3 Priority queues. A priority queue maintains a ....

....[15, 35] Bender et al. 13] and subsequently Brodal et al. 16] Bender et al. 14] and Rahman et al. 32] developed cacheoblivious B trees with a search cost of O(log B N) matching the standard (cache aware) B tree. The practical eciency of the developed algorithms have been investigated in [32, 16, 14]. 1.1.3 Priority queues. A priority queue maintains a set of elements each with a priority (or key) under the operations insert, delete, and deletemin, where a deletemin operation nds and deletes the minimum key element in the queue. The heap data structure is a standard implementation of a ....

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 39-48, 2002.

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height. In Proc. 13th Ann. ACM-SIAM Symp. on Discrete Algorithms (SODA), pages 39-48, 2002.

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height. In Proc. 13th Ann. ACM-SIAM Symp. on Discrete Algorithms, pages 39--48, 2002.

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height. In Proc. 13th Ann. ACM-SIAM Symp. on Discrete Algorithms, pages 39--48, 2002.

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height. In Proc. 13th Ann. ACM-SIAM Symp. on Discrete Algorithms, pages 39--48, 2002.

....model is automatically e#cient on each level of a multi level memory model. They also presented optimal cache oblivious algorithms for matrix transposition, FFT, and sorting. Cache oblivious search trees which match the search cost of the standard (cache aware) B trees [4] were presented in [6,8,9,11]. Cache oblivious algorithms have also been given for problems in computational geometry [6,10] for scanning dynamic sets [5] and for layout of static trees [7] Recently, the first Partially supported by the Future and Emerging Technologies programme of the EU under contract number ....

G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height. In Proc. 13th Ann. ACM-SIAM Symp. on Discrete Algorithms, pages 39--48, 2002.

.... algorithms for matrix transposition, FFT, and sorting [13] Bender et al. 7] gave a proposal for cache oblivious search trees with search cost matching that of standard (cache aware) B trees [5] Simpler cache oblivious search trees with complexities matching that of [7] were presented in [8, 11]. Cache oblivious data structures based on on exponential structures are presented in [6] Recently, a cache oblivious priority queue has been developed [3] which in turn gives rise to several cacheoblivious graph algorithms. We consider cache oblivious algorithms within the field of ....

G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height. In Proc. 13th Ann. ACM-SIAM Symp. on Discrete Algorithms, pages 39--48, 2002.

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height (extended abstract). In Proc. 13th ACM-SIAM Symp. on Discrete Algorithms (SODA), 2002.

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache-oblivious search trees via binary trees of small height. In Proc. 13th ACM-SIAM Ann. Symp. on Discrete Algorithms, pages 39--48, 2002.

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G. S. Brodal, R. Fagerberg and R. Jacob. Cache oblivious search trees via binary trees of small height. In Proc. 13th Annu. ACM-SIAM Symp. on Discrete Algorithms, 39--48, 2002.

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height. In 13th SODA, pages 39-48, 2002.

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache-oblivious search trees via binary trees of small height. In Proc. 13th ACM-SIAM Ann. Symp. on Discrete Algorithms, pages 39--48, 2002.

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height (extended abstract). In Proc. 18th Annual ACM-SIAM Symposium on Discrete Algorithms, 2002.

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G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height (extended abstract). In Proc. ACM-SIAM Symp. on Discrete Algorithms (SODA), pages 39-48, January 2002. 13

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