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12
On the limits of cacheobliviousness
 IN PROC. 35TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 2003
"... In this paper, we present lower bounds for permuting and sorting in the cacheoblivious model. We prove that (1) I/O optimal cacheoblivious comparison based sorting is not possible without a tall cache assumption, and (2) there does not exist an I/O optimalcacheoblivious algorithm for permuting, ..."
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Cited by 40 (7 self)
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In this paper, we present lower bounds for permuting and sorting in the cacheoblivious model. We prove that (1) I/O optimal cacheoblivious comparison based sorting is not possible without a tall cache assumption, and (2) there does not exist an I/O optimalcacheoblivious algorithm for permuting, not even in the presence of a tall cache assumption.Our results for sorting show the existence of an inherent tradeoff in the cacheoblivious model between the strength of the tall cache assumption and the overhead for the case M >> B, and show that Funnelsort and recursive binary mergesort are optimal algorithms in the sense that they attain this tradeoff.
Funnel heap  a cache oblivious priority queue
 In Proc. 13th Annual International Symposium on Algorithms and Computation, volume 2518 of LNCS
, 2002
"... Abstract The cache oblivious model of computation is a twolevel memory model with the assumption that the parameters of the model are unknown to the algorithms. A consequence of this assumption is that an algorithm efficient in the cache oblivious model is automatically efficient in a multilevel m ..."
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Cited by 34 (8 self)
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Abstract The cache oblivious model of computation is a twolevel memory model with the assumption that the parameters of the model are unknown to the algorithms. A consequence of this assumption is that an algorithm efficient in the cache oblivious model is automatically efficient in a multilevel memory model. Arge et al. recently presented the first optimal cache oblivious priority queue, and demonstrated the importance of this result by providing the first cache oblivious algorithms for graph problems. Their structure uses cache oblivious sorting and selection as subroutines. In this paper, we devise an alternative optimal cache oblivious priority queue based only on binary merging. We also show that our structure can be made adaptive to different usage profiles. 1
Dynamic Ordered Sets with Exponential Search Trees
 Combination of results presented in FOCS 1996, STOC 2000 and SODA
, 2001
"... We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fullydynamic linear space data structures. This leads to an optimal bound of O ( √ log n/log log n) for searching and updating a dynamic set of n integer keys i ..."
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Cited by 26 (1 self)
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We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fullydynamic linear space data structures. This leads to an optimal bound of O ( √ log n/log log n) for searching and updating a dynamic set of n integer keys in linear space. Here searching an integer y means finding the maximum key in the set which is smaller than or equal to y. This problem is equivalent to the standard text book problem of maintaining an ordered set (see, e.g., Cormen, Leiserson, Rivest, and Stein: Introduction to Algorithms, 2nd ed., MIT Press, 2001). The best previous deterministic linear space bound was O(log n/log log n) due Fredman and Willard from STOC 1990. No better deterministic search bound was known using polynomial space.
Engineering a cacheoblivious sorting algorithm
 In Proc. 6th Workshop on Algorithm Engineering and Experiments
, 2004
"... The cacheoblivious model of computation is a twolevel memory model with the assumption that the parameters of the model are unknown to the algorithms. A consequence of this assumption is that an algorithm efficient in the cache oblivious model is automatically efficient in a multilevel memory mod ..."
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Cited by 25 (1 self)
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The cacheoblivious model of computation is a twolevel memory model with the assumption that the parameters of the model are unknown to the algorithms. A consequence of this assumption is that an algorithm efficient in the cache oblivious model is automatically efficient in a multilevel memory model. Since the introduction of the cacheoblivious model by Frigo et al. in 1999, a number of algorithms and data structures in the model has been proposed and analyzed. However, less attention has been given to whether the nice theoretical proporities of cacheoblivious algorithms carry over into practice. This paper is an algorithmic engineering study of cacheoblivious sorting. We investigate a number of implementation issues and parameters choices for the cacheoblivious sorting algorithm Lazy Funnelsort by empirical methods, and compare the final algorithm with Quicksort, the established standard for comparison based sorting, as well as with recent cacheaware proposals. The main result is a carefully implemented cacheoblivious sorting algorithm, which we compare to the best implementation of Quicksort we can find, and find that it competes very well for input residing in RAM, and outperforms Quicksort for input on disk. 1
Cacheoblivious data structures for orthogonal range searching
 IN PROC. ACM SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 2003
"... We develop cacheoblivious data structures for orthogonal range searching, the problem of finding all T points in a set of N points in Rd lying in a query hyperrectangle. Cacheoblivious data structures are designed to be efficient in arbitrary memory hierarchies. We describe a dynamic linearsize ..."
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Cited by 23 (6 self)
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We develop cacheoblivious data structures for orthogonal range searching, the problem of finding all T points in a set of N points in Rd lying in a query hyperrectangle. Cacheoblivious data structures are designed to be efficient in arbitrary memory hierarchies. We describe a dynamic linearsize data structure that answers ddimensional queries in O((N/B)11/d + T/B) memory transfers, where B is the block size of any two levels of a multilevel memory hierarchy. A point can be inserted into or deleted from this data structure in O(log2B N) memory transfers. We also develop a static structure for the twodimensional case that answers queries in O(logB N + T /B) memory transfers using O(N log22 N) space. The analysis of the latter structure requires that B = 22 c for some nonnegative integer constant c.
The cost of cacheoblivious searching
 IN PROC. 44TH ANN. SYMP. ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
, 2003
"... This paper gives tight bounds on the cost of cacheoblivious searching. The paper shows that no cacheoblivious search structure can guarantee a search performance of fewer than lgelog B N memory transfers between any two levels of the memory hierarchy. This lower bound holds even if all of the bloc ..."
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Cited by 18 (8 self)
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This paper gives tight bounds on the cost of cacheoblivious searching. The paper shows that no cacheoblivious search structure can guarantee a search performance of fewer than lgelog B N memory transfers between any two levels of the memory hierarchy. This lower bound holds even if all of the block sizes are limited to be powers of 2. The paper gives modified versions of the van Emde Boas layout, where the expected number of memory transfers between any two levels of the memory hierarchy is arbitrarily close to [lge+O(lglgB/lgB)]log B N +O(1). This factor approaches lge ≈ 1.443 as B increases. The expectation is taken over the random placement in memory of the first element of the structure. Because searching in the diskaccess machine (DAM) model can be performed in log B N+O(1) block transfers, thisresultestablishes aseparation between the (2level) DAM model and cacheoblivious model. The DAM model naturally extends to k levels. The paper also shows that as k grows, the search costs of the optimal klevel DAM search structure and the optimal cacheoblivious search structure rapidly converge. This result demonstrates that for a multilevel memory hierarchy, a simple cacheoblivious structure almost replicates the performance of an optimal parameterized klevel DAM structure.
CacheOblivious Planar Orthogonal Range Searching and Counting
 In Proc. ACM Symposium on Computational Geometry
, 2005
"... We present the first cacheoblivious data structure for planar orthogonal range counting, and improve on previous results for cacheoblivious planar orthogonal range searching. Our range counting structure uses O(N log2 N) space and answers queries using O(logB N) memory transfers, where B is the bl ..."
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Cited by 15 (4 self)
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We present the first cacheoblivious data structure for planar orthogonal range counting, and improve on previous results for cacheoblivious planar orthogonal range searching. Our range counting structure uses O(N log2 N) space and answers queries using O(logB N) memory transfers, where B is the block size of any memory level in a multilevel memory hierarchy. Using bit manipulation techniques, the space can be further reduced to O(N). The structure can also be modified to support more general semigroup range sum queries in O(logB N) memory transfers, using O(N log2 N) space for threesided queries and O(N log 2 2 N / log2 log2 N)
CacheOblivious RTrees
, 2005
"... We develop a cacheoblivious data structure for storing a set S of N axisaligned rectangles in the plane, such that all rectangles in S intersecting a query rectangle or point can be found efficiently. Our structure is an axisaligned boundingbox hierarchy and as such it is the first cacheoblivio ..."
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Cited by 11 (3 self)
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We develop a cacheoblivious data structure for storing a set S of N axisaligned rectangles in the plane, such that all rectangles in S intersecting a query rectangle or point can be found efficiently. Our structure is an axisaligned boundingbox hierarchy and as such it is the first cacheoblivious Rtree with provable performance guarantees. If no point in the plane is contained in B or more rectangles in S, the structure answers a rectangle query using O(\sqrt{N/B} + T/B) memory transfers and a point query using O((N/B)^ε) memory transfers for any ε>0, where B is the block size of memory transfers between any two levels of a multilevel memory hierarchy. We also develop a variant of our structure that achieves the same performance on input sets with arbitrary overlap among the rectangles. The rectangle query bound matches the bound of the best known linearspace cacheaware structure.
Cacheoblivious algorithms and data structures
 IN SWAT
, 2004
"... Frigo, Leiserson, Prokop and Ramachandran in 1999 introduced the idealcache model as a formal model of computation for developing algorithms in environments with multiple levels of caching, and coined the terminology of cacheoblivious algorithms. Cacheoblivious algorithms are described as stand ..."
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Cited by 10 (1 self)
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Frigo, Leiserson, Prokop and Ramachandran in 1999 introduced the idealcache model as a formal model of computation for developing algorithms in environments with multiple levels of caching, and coined the terminology of cacheoblivious algorithms. Cacheoblivious algorithms are described as standard RAM algorithms with only one memory level, i.e. without any knowledge about memory hierarchies, but are analyzed in the twolevel I/O model of Aggarwal and Vitter for an arbitrary memory and block size and an optimal offline cache replacement strategy. The result are algorithms that automatically apply to multilevel memory hierarchies. This paper gives an overview of the results achieved on cacheoblivious algorithms and data structures since the seminal paper by Frigo et al.
An Optimal CacheOblivious Priority Queue and its Application to Graph Algorithms
 SIAM JOURNAL ON COMPUTING
, 2007
"... We develop an optimal cacheoblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in $O(\frac{1}{B}\log_{M/B}\frac{N}{B})$ amortized memory transfers, where $M$ and $B$ are the memory and block transfer sizes of any two consecutive levels of a multilevel ..."
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Cited by 5 (0 self)
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We develop an optimal cacheoblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in $O(\frac{1}{B}\log_{M/B}\frac{N}{B})$ amortized memory transfers, where $M$ and $B$ are the memory and block transfer sizes of any two consecutive levels of a multilevel memory hierarchy. In a cacheoblivious data structure, $M$ and $B$ are not used in the description of the structure. Our structure is as efficient as several previously developed external memory (cacheaware) priority queue data structures, which all rely crucially on knowledge about $M$ and $B$. Priority queues are a critical component in many of the best known external memory graph algorithms, and using our cacheoblivious priority queue we develop several cacheoblivious graph algorithms.