Cache Oblivious Distribution Sweeping

Brodal, Gerth Stølting; Fagerberg, Rolf

doi:10.1007/3-540-45465-9_37

Cited by 44 publications

(43 citation statements)

References 14 publications

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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: 93%

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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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Section: Previous Resultsmentioning

confidence: 93%

“…In [17], an algorithm for batched planar orthogonal range searching was developed. This algorithm answers a set of…”

Section: Previous Resultsmentioning

confidence: 99%

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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“…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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“…We now argue that this distribution can be run cache-obliviously in a manner similar to lazy funnelsort [7]. Lazy funnelsort is based on k-mergers: a k-merger takes as input k sorted sequences and merges them into a sorted sequence.…”

Section: Proofmentioning

confidence: 99%

Star-quadtrees and guard-quadtrees: I/O-efficient indexes for fat triangulations and low-density planar subdivisions

Berg¹,

Haverkort²,

Thite³

et al. 2010

Computational Geometry

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We present a new I/O-efficient index structure for storing planar subdivisions. This socalled guard-quadtree is a compressed linear quadtree, which is provably efficient for map overlay, point location, and range queries in low-density subdivisions. In particular, we can preprocess a low-density subdivision with n edges, in O (sort(n)) I/Os, to build a guardquadtree that allows us to:(i) compute the intersections between the edges of two such preprocessed subdivisions in O (scan(n)) I/Os, where n is the total number of edges in the two subdivisions;(ii) answer a single point location query in O (log B n) I/Os, and k batched point location queries in O (scan(n) + sort(k)) I/Os; and (iii) answer range queries for any constant-complexity query range Q in O ( 1 ε (log B n) + scan(k ε )) I/Os for every ε > 0, where k ε is the number of edges of the subdivision within distance ε · diam(Q ) from Q .For the special case where the subdivision is a fat triangulation, we show how to obtain the same results with an ordinary (uncompressed) linear quadtree, which we call the starquadtree. The star-quadtree is fully dynamic and needs only O (log B n) I/Os per update.Our algorithms and data structures improve on the previous best known bounds for overlaying general subdivisions, both in the number of I/Os and space usage. The constants in the asymptotic bounds are small, which makes our results applicable in practice. Moreover, our algorithms are simpler than previous approaches and almost all of them are cache-oblivious.

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Cache Oblivious Distribution Sweeping

Cited by 44 publications

References 14 publications

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

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

Cache-oblivious nested-loop joins

Star-quadtrees and guard-quadtrees: I/O-efficient indexes for fat triangulations and low-density planar subdivisions

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