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Author Vitter, Jeffrey,S. ♦ Aggarwal, Alok
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Abstract We provide tight upper and lower bounds, up to a constant factor, for the number of inputs and outputs (I/OS) between internal memory and secondary storage required for five sorting-related problems: sorting, the fast Fourier transform (FFT), permutation networks, permuting, and matrix transposition. The bounds hold both in the worst case and in the average case, and in several situations the constant factors match. Secondary storage is modeled as a magnetic disk capable of transferring P blocks each containing B records in a single time unit; the records in each block must be input from or output to B contiguous locations on the disk. We give two optimal algorithms for the problems, which are variants of merge sorting and distribution sorting. In particular we show for P = 1 that the standard merge sorting algorithm is an optimal external sorting method, up to a constant factor in the number of I/Os. Our sorting algorithms use the same number of I/Os as does the permutation phase of key sorting, except when the internal memory size is extremely small, thus affirming the popular adage that key sorting is not faster. We also give a simpler and more direct derivation of Hong and Kung's lower bound for the FFT for the special case B = P = O(1).
Description Affiliation: Brown Univ., Providence, RI (Vitter, Jeffrey,S.) || IBM Watson Research Center, Yorktown Heights, NY (Aggarwal, Alok)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 31
Issue Number 9
Page Count 12
Starting Page 1116
Ending Page 1127

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Source: ACM Digital Library