A randomized sublinear time parallel GCD algorithm for the EREW PRAM

We present a randomized parallel algorithm that computes the greatest common divisor of two integers of n bits in length with probability 1 − o ( 1 ) that takes O ( n log log n / log n ) time using O ( n 6 + ϵ ) processors for any ϵ > 0 on the EREW PRAM parallel model of computation. The algorith...

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Bibliographic Details
Published in:Information processing letters Vol. 110; no. 5; pp. 198 - 201
Main Author: Sorenson, Jonathan P.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.02.2010
Elsevier
Elsevier Sequoia S.A
Subjects:
Algorithm analysis
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computation
Computer science; control theory; systems
Exact sciences and technology
Failure
Greatest common divisor
Integers
Mathematical models
Miscellaneous
Number theoretic algorithms
Parallel algorithms
Probability
Processors
Randomized algorithms
Smooth numbers
Studies
Theoretical computing
Randomized algorithms
Greatest common divisor
Parallel algorithms
Smooth numbers
Algorithm analysis
Number theoretic algorithms
Parallel algorithm
Processor
Computer theory
Probability
Probability distribution
Failures
Integer
Information processing
Parallel computation
Failure
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Description
Summary:We present a randomized parallel algorithm that computes the greatest common divisor of two integers of n bits in length with probability 1 − o ( 1 ) that takes O ( n log log n / log n ) time using O ( n 6 + ϵ ) processors for any ϵ > 0 on the EREW PRAM parallel model of computation. The algorithm either gives a correct answer or reports failure. We believe this to be the first randomized sublinear time algorithm on the EREW PRAM for this problem.
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2009.12.008