An improved parallel algorithm for integer GCD
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We present a simple parallel algorithm for computing the greatest common divisor (gcd) of twon-bit integers in the Common version of the CRCW model of computation. The run-time of the algorithm in terms of bit operations isO(n/logn), usingn1+ɛ processors, where ɛ is any positive constant. This improves on the algorithm of Kannan, Miller, and Rudolph, the only sublinear algorithm known previously, both in run time and in number of processors; they requireO(n log logn/logn),n2 log2n, respectively, in the same CRCW model.
We give an alternative implementation of our algorithm in the CREW model. Its run-time isO(n log logn/logn), usingn1+ɛ processors. Both implementations can be modified to yield the extended gcd, within the same complexity bounds.
Key wordsGreatest common divisor Parallel algorithms
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