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Algorithms for Parallel Memory I: TwoLevel Memories
, 1992
"... We provide the first optimal algorithms in terms of the number of input/outputs (I/Os) required between internal memory and multiple secondary storage devices for the problems of sorting, FFT, matrix transposition, standard matrix multiplication, and related problems. Our twolevel memory model is n ..."
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Cited by 236 (32 self)
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We provide the first optimal algorithms in terms of the number of input/outputs (I/Os) required between internal memory and multiple secondary storage devices for the problems of sorting, FFT, matrix transposition, standard matrix multiplication, and related problems. Our twolevel memory model is new and gives a realistic treatment of parallel block transfer, in which during a single I/O each of the P secondary storage devices can simultaneously transfer a contiguous block of B records. The model pertains to a largescale uniprocessor system or parallel multiprocessor system with P disks. In addition, the sorting, FFT, permutation network, and standard matrix multiplication algorithms are typically optimal in terms of the amount of internal processing time. The difficulty in developing optimal algorithms is to cope with the partitioning of memory into P separate physical devices. Our algorithms' performance can be significantly better than those obtained by the wellknown but nonopti...
Data Cube Approximation and Histograms via Wavelets (Extended Abstract)
 In CIKM
, 1998
"... ) Jeffrey Scott Vitter Center for Geometric Computing and Department of Computer Science Duke University Durham, NC 277080129 USA jsv@cs.duke.edu Min Wang y Center for Geometric Computing and Department of Computer Science Duke University Durham, NC 277080129 USA minw@cs.duke.edu Bala Iyer ..."
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Cited by 92 (2 self)
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) Jeffrey Scott Vitter Center for Geometric Computing and Department of Computer Science Duke University Durham, NC 277080129 USA jsv@cs.duke.edu Min Wang y Center for Geometric Computing and Department of Computer Science Duke University Durham, NC 277080129 USA minw@cs.duke.edu Bala Iyer Database Technology Institute IBM Santa Teresa Laboratory P.O. Box 49023 San Jose, CA 95161 USA balaiyer@vnet.ibm.com Abstract There has recently been an explosion of interest in the analysis of data in data warehouses in the field of OnLine Analytical Processing (OLAP). Data warehouses can be extremely large, yet obtaining quick answers to queries is important. In many situations, obtaining the exact answer to an OLAP query is prohibitively expensive in terms of time and/or storage space. It can be advantageous to have fast, approximate answers to queries. In this paper, we present an I/Oefficient technique based upon a multiresolution wavelet decomposition that yields an approximate a...
Provably efficient scheduling for languages with finegrained parallelism
 IN PROC. SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 1995
"... Many highlevel parallel programming languages allow for finegrained parallelism. As in the popular worktime framework for parallel algorithm design, programs written in such languages can express the full parallelism in the program without specifying the mapping of program tasks to processors. A ..."
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Cited by 82 (25 self)
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Many highlevel parallel programming languages allow for finegrained parallelism. As in the popular worktime framework for parallel algorithm design, programs written in such languages can express the full parallelism in the program without specifying the mapping of program tasks to processors. A common concern in executing such programs is to schedule tasks to processors dynamically so as to minimize not only the execution time, but also the amount of space (memory) needed. Without careful scheduling, the parallel execution on p processors can use a factor of p or larger more space than a sequential implementation of the same program. This paper first identifies a class of parallel schedules that are provably efficient in both time and space. For any
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.
SpaceTime Tradeoffs in Memory Hierarchies
, 1993
"... The speed of CPUs is accelerating rapidly, outstripping that of peripheral storage devices and making it increasingly difficult to keep CPUs busy. Multilevel memory hierarchies, scaled to simulate singlelevel memories, are increasing in importance. In this paper we introduce the Memory Hierarchy ..."
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Cited by 9 (0 self)
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The speed of CPUs is accelerating rapidly, outstripping that of peripheral storage devices and making it increasingly difficult to keep CPUs busy. Multilevel memory hierarchies, scaled to simulate singlelevel memories, are increasing in importance. In this paper we introduce the Memory Hierarchy Game, a multilevel pebble game simulating data movement in memory hierarchies for straightline computations. This game provides a framework for deriving upper and lower bounds on computation time and the I/O time at each level in a memory hierarchy. We apply this framework to a representative set of problems including matrix multiplication and the Fourier transform. We also discuss conditions on hierarchies under which they act as fast flat memories.
External Memory Algorithms with Dynamically Changing Memory Allocations.
 DUKE UNIVERSITY
, 1998
"... We consider the problem of devising external memory algorithms whose memory allocations can change dynamically and unpredictably at runtime. The ..."
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Cited by 6 (3 self)
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We consider the problem of devising external memory algorithms whose memory allocations can change dynamically and unpredictably at runtime. The