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External Memory Algorithms and Data Structures
, 1998
"... Data sets in large applications are often too massive to fit completely inside the computer's internal memory. The resulting input/output communication (or I/O) between fast internal memory and slower external memory (such as disks) can be a major performance bottleneck. In this paper, we survey the ..."
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Cited by 320 (24 self)
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Data sets in large applications are often too massive to fit completely inside the computer's internal memory. The resulting input/output communication (or I/O) between fast internal memory and slower external memory (such as disks) can be a major performance bottleneck. In this paper, we survey the state of the art in the design and analysis of external memory algorithms and data structures (which are sometimes referred to as "EM" or "I/O" or "outofcore" algorithms and data structures). EM algorithms and data structures are often designed and analyzed using the parallel disk model (PDM). The three machineindependent measures of performance in PDM are the number of I/O operations, the CPU time, and the amount of disk space. PDM allows for multiple disks (or disk arrays) and parallel CPUs, and it can be generalized to handle tertiary storage and hierarchical memory. We discuss several important paradigms for how to solve batched and online problems efficiently in external memory. Programming tools and environments are available for simplifying the programming task. The TPIE system (Transparent Parallel I/O programming Environment) is both easy to use and efficient in terms of execution speed. We report on some experiments using TPIE in the domain of spatial databases. The newly developed EM algorithms and data structures that incorporate the paradigms we discuss are significantly faster than methods currently used in practice.
Cacheoblivious Btrees
, 2000
"... Abstract. This paper presents two dynamic search trees attaining nearoptimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e.g., the number of memory levels, the blocktransfer size at each level, and the relative speeds of me ..."
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Cited by 135 (22 self)
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Abstract. This paper presents two dynamic search trees attaining nearoptimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e.g., the number of memory levels, the blocktransfer size at each level, and the relative speeds of memory levels. The performance is analyzed in terms of the number of memory transfers between two memory levels with an arbitrary blocktransfer size of B; this analysis can then be applied to every adjacent pair of levels in a multilevel memory hierarchy. Both search trees match the optimal search bound of Θ(1+logB+1 N) memory transfers. This bound is also achieved by the classic Btree data structure on a twolevel memory hierarchy with a known blocktransfer size B. The first search tree supports insertions and deletions in Θ(1 + logB+1 N) amortized memory transfers, which matches the Btree’s worstcase bounds. The second search tree supports scanning S consecutive elements optimally in Θ(1 + S/B) memory transfers and supports insertions and deletions in Θ(1 + logB+1 N + log2 N) amortized memory transfers, matching the performance of the Btree for B = B Ω(log N log log N).
ExternalMemory Computational Geometry
, 1993
"... In this paper, we give new techniques for designing efficient algorithms for computational geometry problems that are too large to be solved in internal memory, and we use these techniques to develop optimal and practical algorithms for a number of important largescale problems. We discuss our algor ..."
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Cited by 121 (20 self)
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In this paper, we give new techniques for designing efficient algorithms for computational geometry problems that are too large to be solved in internal memory, and we use these techniques to develop optimal and practical algorithms for a number of important largescale problems. We discuss our algorithms primarily in the contex't of single processor/single disk machines, a domain in which they are not only the first known optimal results but also of tremendous practical value. Our methods also produce the first known optimal algorithms for a wide range of twolevel and hierarchical muir{level memory models, including parallel models. The algorithms are optimal both in terms of I/0 cost and internal computation.
The Uniform Memory Hierarchy Model of Computation
 Algorithmica
, 1992
"... The Uniform Memory Hierarchy (UMH) model introduced in this paper captures performancerelevant aspects of the hierarchical nature of computer memory. It is used to quantify architectural requirements of several algorithms and to ratify the faster speeds achieved by tuned implementations that use im ..."
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Cited by 116 (9 self)
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The Uniform Memory Hierarchy (UMH) model introduced in this paper captures performancerelevant aspects of the hierarchical nature of computer memory. It is used to quantify architectural requirements of several algorithms and to ratify the faster speeds achieved by tuned implementations that use improved datamovement strategies. A sequential computer's memory is modelled as a sequence hM 0 ; M 1 ; :::i of increasingly large memory modules. Computation takes place in M 0 . Thus, M 0 might model a computer's central processor, while M 1 might be cache memory, M 2 main memory, and so on. For each module M U , a bus B U connects it with the next larger module M U+1 . All buses may be active simultaneously. Data is transferred along a bus in fixedsized blocks. The size of these blocks, the time required to transfer a block, and the number of blocks that fit in a module are larger for modules farther from the processor. The UMH model is parameterized by the rate at which the blocksizes i...
CacheOblivious Algorithms
, 1999
"... This thesis presents "cacheoblivious" algorithms that use asymptotically optimal amounts of work, and move data asymptotically optimally among multiple levels of cache. An algorithm is cache oblivious if no program variables dependent on hardware configuration parameters, such as cache size and cac ..."
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Cited by 79 (1 self)
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This thesis presents "cacheoblivious" algorithms that use asymptotically optimal amounts of work, and move data asymptotically optimally among multiple levels of cache. An algorithm is cache oblivious if no program variables dependent on hardware configuration parameters, such as cache size and cacheline length need to be tuned to minimize the number of cache misses. We show that the ordinary algorithms for matrix transposition, matrix multiplication, sorting, and Jacobistyle multipass filtering are not cache optimal. We present algorithms for rectangular matrix transposition, FFT, sorting, and multipass filters, which are asymptotically optimal on computers with multiple levels of caches. For a cache with size Z and cacheline length L, where Z =# (L 2 ), the number of cache misses for an m × n matrix transpose is #(1 + mn=L). The number of cache misses for either an npoint FFT or the sorting of n numbers is #(1 + (n=L)(1 + log Z n)). The cache complexity of computing n ...
A LocalityPreserving CacheOblivious Dynamic Dictionary
, 2002
"... This paper presents a simple dictionary structure designed for a hierarchical memory. The proposed data structure is cache oblivious and locality preserving. A cacheoblivious data structure has memory performance optimized for all levels of the memory hierarchy even though it has no memoryhierarc ..."
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Cited by 73 (21 self)
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This paper presents a simple dictionary structure designed for a hierarchical memory. The proposed data structure is cache oblivious and locality preserving. A cacheoblivious data structure has memory performance optimized for all levels of the memory hierarchy even though it has no memoryhierarchyspeci c parameterization. A localitypreserving dictionary maintains elements of similar key values stored close together for fast access to ranges of data with consecutive keys.
Cacheoblivious priority queue and graph algorithm applications
 In Proc. 34th Annual ACM Symposium on Theory of Computing
, 2002
"... In this paper we develop an optimal cacheoblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in O ( 1 B logM/B N) amortized memory B transfers, where M and B are the memory and block transfer sizes of any two consecutive levels of a multilevel memory hi ..."
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Cited by 68 (10 self)
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In this paper we develop an optimal cacheoblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in O ( 1 B logM/B N) amortized memory B 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. The bounds match the bounds of several previously developed externalmemory (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 externalmemory graph algorithms, and using our cacheoblivious priority queue we develop several cacheoblivious graph algorithms.
Algorithms for Parallel Memory II: Hierarchical Multilevel Memories
 ALGORITHMICA
, 1993
"... In this paper we introduce parallel versions of two hierarchical memory models and give optimal algorithms in these models for sorting, FFT, and matrix multiplication. In our parallel models, there are P memory hierarchies operating simultaneously; communication among the hierarchies takes place ..."
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Cited by 66 (5 self)
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In this paper we introduce parallel versions of two hierarchical memory models and give optimal algorithms in these models for sorting, FFT, and matrix multiplication. In our parallel models, there are P memory hierarchies operating simultaneously; communication among the hierarchies takes place at a base memory level. Our optimal sorting algorithm is randomized and is based upon the probabilistic partitioning technique developed in the companion paper for optimal disk sorting in a twolevel memory with parallel block transfer. The probability of using l times the optimal running time is exponentially small in l(log l) log P.
Asymptotically Tight Bounds for Performing BMMC Permutations on Parallel Disk Systems
, 1994
"... This paper presents asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform bitmatrixmultiply/complement (BMMC) permutations on the Parallel Disk Model proposed by Vitter and Shriver. A BMMC permutation maps a source index to a target index by an a ..."
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Cited by 61 (19 self)
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This paper presents asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform bitmatrixmultiply/complement (BMMC) permutations on the Parallel Disk Model proposed by Vitter and Shriver. A BMMC permutation maps a source index to a target index by an affine transformation over GF (2), where the source and target indices are treated as bit vectors. The class of BMMC permutations includes many common permutations, such as matrix transposition (when dimensions are powers of 2), bitreversal permutations, vectorreversal permutations, hypercube permutations, matrix reblocking, Graycode permutations, and inverse Graycode permutations. The upper bound improves upon the asymptotic bound in the previous best known BMMC algorithm and upon the constant factor in the previous best known bitpermute/complement (BPC) permutation algorithm. The algorithm achieving the upper bound uses basic linearalgebra techniques to factor the characteristic matrix...
Models of Computation  Exploring the Power of Computing
"... Theoretical computer science treats any computational subject for which a good model can be created. Research on formal models of computation was initiated in the 1930s and 1940s by Turing, Post, Kleene, Church, and others. In the 1950s and 1960s programming languages, language translators, and oper ..."
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Cited by 57 (7 self)
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Theoretical computer science treats any computational subject for which a good model can be created. Research on formal models of computation was initiated in the 1930s and 1940s by Turing, Post, Kleene, Church, and others. In the 1950s and 1960s programming languages, language translators, and operating systems were under development and therefore became both the subject and basis for a great deal of theoretical work. The power of computers of this period was limited by slow processors and small amounts of memory, and thus theories (models, algorithms, and analysis) were developed to explore the efficient use of computers as well as the inherent complexity of problems. The former subject is known today as algorithms and data structures, the latter computational complexity. The focus of theoretical computer scientists in the 1960s on languages is reflected in the first textbook on the subject, Formal Languages and Their Relation to Automata by John Hopcroft and Jeffrey Ullman. This influential book led to the creation of many languagecentered theoretical computer science courses; many introductory theory courses today continue to reflect the content of this book and the interests of theoreticians of the 1960s and early 1970s. Although