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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 ..."
Abstract

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...
A Randomized LinearTime Algorithm to Find Minimum Spanning Trees
, 1994
"... We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost ra ..."
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Cited by 115 (7 self)
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We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost randomaccess machine with the restriction that the only operations allowed on edge weights are binary comparisons.
Approximate Medians and other Quantiles in One Pass and with Limited Memory
, 1998
"... We present new algorithms for computing approximate quantiles of large datasets in a single pass. The approximation guarantees are explicit, and apply without regard to the value distribution or the arrival distributions of the dataset. The main memory requirements are smaller than those reported ea ..."
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Cited by 113 (2 self)
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We present new algorithms for computing approximate quantiles of large datasets in a single pass. The approximation guarantees are explicit, and apply without regard to the value distribution or the arrival distributions of the dataset. The main memory requirements are smaller than those reported earlier by an order of magnitude. We also discuss methods that couple the approximation algorithms with random sampling to further reduce memory requirements. With sampling, the approximation guarantees are explicit but probabilistic, i.e., they apply with respect to a (user controlled) confidence parameter. We present the algorithms, their theoretical analysis and simulation results. 1 Introduction This article studies the problem of computing order statistics of large sequences of online or diskresident data using as little main memory as possible. We focus on computing quantiles, which are elements at specific positions in the sorted order of the input. The OEquantile, for OE 2 [0; ...
Fast Exchange Sorts
"... We present three variations of the following new sorting theme: Throughout the sort, the arrayismaintained in piles of sorted elements. Ateach step, the piles are split into two parts, so that the elements of the left piles are smaller than #or equal to# the elements of the right piles. Then, th ..."
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We present three variations of the following new sorting theme: Throughout the sort, the arrayismaintained in piles of sorted elements. Ateach step, the piles are split into two parts, so that the elements of the left piles are smaller than #or equal to# the elements of the right piles. Then, the two parts are each sorted, recursively. The theme, then, is a combination of Hoare's Quicksort idea, and the Pick algorithm, by Blum, et al., for linear selection. The variations arise from the possible choices of splitting method. Twovariations attempt to minimize the average number of comparisons. The better of these has an average performance of 1:075n lg n comparisons. The third variation sacri#ces the average case for a worstcase performance of 1:756n lg n, which is better than Heapsort. They all require minimal extra space and about as manydatamoves as comparisons. 1 Introduction The sorting problem is: Given an array a 1 ;a 2 ; ###;a n of elements, rearrange them so t...