A Load-Balanced Parallelization of AKS Algorithm

Ardhi Wiratama Baskara Yudha, Reza Pulungan

Abstract


The best known deterministic polynomial-time algorithm for primality testing right now is due to Agrawal, Kayal, and Saxena. This algorithm has a time complexity O(log^{15/2}(n)). Although this algorithm is polynomial, its reliance on the congruence of large polynomials results in enormous computational requirement. In this paper, we propose a parallelization technique for this algorithm based on message-passing parallelism together with four workload-distribution strategies. We perform a series of experiments on an implementation of this algorithm in a high-performance computing system consisting of 15 nodes, each with 4 CPU cores. The experiments indicate that our proposed parallelization technique introduce a significant speedup on existing implementations. Furthermore, the dynamic workload-distribution strategy performs better than the others. Overall, the experiments show that the parallelization obtains up to 36 times speedup.

 


Keywords


primality testing; AKS algorithm; parallelization; load balancing; high-performance computing;

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DOI: http://dx.doi.org/10.12928/telkomnika.v15i4.6049

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TELKOMNIKA Telecommunication, Computing, Electronics and Control
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