Cache-Oblivious R-Trees

Arge, Lars; Berg, Mark de; Haverkort, Herman

doi:10.1007/s00453-007-9007-8

Cited by 10 publications

(7 citation statements)

References 28 publications

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“…A number of linear-space data structures have been proposed that achieve a query bound of O( √ N/B + K/B) block transfers in two dimensions and O((N/B) 1−1/d + K/B) block transfers in higher dimensions [9,19,20,22,26,28], where K is the number of reported points. The same bounds have been obtained in the cache-oblivious model [5,11]. In 2-d, Arge et al [8] showed that Θ(N log N/ log log B N) space is sufficient and necessary to obtain a query bound of O(log B N + K/B) block transfers for orthogonal range reporting in the I/O model.…”

Section: Related Worksupporting

confidence: 55%

Cache-Oblivious Range Reporting with Optimal Queries Requires Superlinear Space

Afshani

Hamilton

Zeh

2011

Discrete Comput Geom

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We consider a number of range reporting problems in two and three dimensions and prove lower bounds on the amount of space used by any cacheoblivious data structure for these problems that achieves the optimal query bound of O(log B N + K/B) block transfers, where K is the size of the query output.The problems we study are three-sided range reporting, 3-d dominance reporting, and 3-d halfspace range reporting. We prove that, in order to achieve the above query bound or even a bound of f (log B N, K/B), for any monotonically increasing function f (·, ·), the data structure has to use Ω(N(log log N) ε ) space. This lower bound holds also for the expected size of any Las-Vegas-type data structure that achieves an expected query bound of at most f (log B N, K/B) block transfers. The exponent ε depends on the function f (·, ·) and on the range of permissible block sizes.Our result has a number of interesting consequences. The first one is a new type of separation between the I/O model and the cache-oblivious model, as deterministic I/O-efficient data structures with the optimal query bound in the worst case and using linear or O(N log * N) space are known for the above problems. The second conse- Discrete Comput Geom (2011) 45: 824-850 825 quence is the non-existence of linear-space cache-oblivious persistent B-trees with optimal 1-d range reporting queries.

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Section: Related Worksupporting

confidence: 55%

Cache-Oblivious Range Reporting with Optimal Queries Requires Superlinear Space

Afshani

Hamilton

Zeh

2011

Discrete Comput Geom

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“…Subsequently, a number of other results have been obtained in this model [1,5,6,7,10,11,12,13,14,17,18,19,20,28], among them several cacheoblivious B-tree structures with O(log B N ) search and update bounds [12,13,14,20,28]. Several of these structures also support one-dimensional range queries in O(log B N + T /B) memory transfers [13,14,20] (but at an increased update cost of O(log B N + 1 B log 2 2 N ) = O(log 2 B N ) amortized memory transfers).…”

Section: Previous Resultsmentioning

confidence: 94%

Simple and semi-dynamic structures for cache-oblivious planar orthogonal range searching

Arge

Zeh

2006

Proceedings of the Twenty-Second Annual Symposium on Computational Geometry

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In this paper, we develop improved cache-oblivious data structures for two-and three-sided planar orthogonal range searching. Our main result is an optimal static structure for two-sided range searching that uses linear space and supports queries in O(log B N + T /B) memory transfers, where B is the block size of any level in a multi-level memory hierarchy and T is the number of reported points. Our structure is the first linear-space cache-oblivious structure for a planar range searching problem with the optimal O(log B N + T /B) query bound. The structure is very simple, and we believe it to be of practical interest.We also show that our two-sided range search structure can be constructed cache-obliviously in O(N log B N ) memory transfers. Using the logarithmic method and fractional cascading, this leads to a semi-dynamic linear-space structure that supports two-sided range queries in O(log 2 N + T /B) memory transfers and insertions in O(log 2 N · log B N ) memory transfers amortized. This structure is the first (semi-)dynamic structure for any planar range searching problem with a query bound that is logarithmic in the number of elements in the structure and linear in the output size.Finally, using a simple standard construction, we also obtain a static O(N log 2 N )-space structure for three-sided range searching that supports queries in the optimal bound of O(log B N +T /B) memory transfers. These bounds match the bounds of the best previously known structure for this *

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“…To date, representatives of capacity oblivious algorithms include matrix multiplication and transposition [17], funnel sort and distribution sort [12,17]. Representatives of block size oblivious algorithms are cache-oblivious B-trees [4,5,11] and Rtrees [3]. The cache-oblivious non-indexed NLJ we propose is capacity oblivious, and our indexed NLJ is both capacity oblivious and block size oblivious.…”

Section: Cache-conscious and Cache-oblivious Algorithmsmentioning

confidence: 98%

“…Since then, a few cache-oblivious algorithms and data structures [3,4,5,6,10,11,12,17] have been studied. The most interesting feature of this line of work is that, even though the model has no knowledge about the capacity and block size of each level of a multi-level memory hierarchy, a cache-oblivious algorithm has a provable upper bound on the number of block transfers for any two adjacent levels of the hierarchy.…”

Section: Introductionmentioning

confidence: 99%

Cache-oblivious nested-loop joins

Luo

2006

Proceedings of the 15th ACM International Conference on Information and Knowledge Management - CIKM '06

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We propose to adapt the newly emerged cache-oblivious model to relational query processing. Our goal is to automatically achieve an overall performance comparable to that of fine-tuned algorithms on a multi-level memory hierarchy. This automaticity is because cache-oblivious algorithms assume no knowledge about any specific parameter values, such as the capacity and block size of each level of the hierarchy. As a first step, we propose recursive partitioning to implement cache-oblivious nested-loop joins (NLJs) without indexes, and recursive clustering and buffering to implement cache-oblivious NLJs with indexes. Our theoretical results and empirical evaluation on three different architectures show that our cache-oblivious NLJs match the performance of their manually optimized, cache-conscious counterparts.

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Cache-Oblivious R-Trees

Cited by 10 publications

References 28 publications

Cache-Oblivious Range Reporting with Optimal Queries Requires Superlinear Space

Cache-Oblivious Range Reporting with Optimal Queries Requires Superlinear Space

Simple and semi-dynamic structures for cache-oblivious planar orthogonal range searching

Cache-oblivious nested-loop joins

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