A Randomized Sublinear Time Parallel GCD Algorithm for the EREW PRAM

TL;DR

This paper introduces a novel randomized parallel algorithm for computing the greatest common divisor of two large integers, achieving sublinear expected time on the EREW PRAM model with a high probability of correctness.

Contribution

It presents the first known randomized sublinear time algorithm for GCD on the EREW PRAM, utilizing a large number of processors to significantly reduce computation time.

Findings

Expected time complexity is O(n loglog n / log n).

Algorithm succeeds with probability 1-o(1).

Uses n^{6+ε} processors.

Abstract

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 loglog n / log n) expected time using n^{6+\epsilon} processors on the EREW PRAM parallel model of computation. We believe this to be the first randomized sublinear time algorithm on the EREW PRAM for this problem.