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A Comparative Study of Box-assisted and Kd-tree Approaches for the False Nearest Neighbors Method

In different fields of science and engineering (medicine, economics, oceanography, biological systems, etc.) the False Nearest Neighbors (FNN) method has a special relevance. In some of these applications, it is important to provide the results in a reasonable time scale, thus the execution time of the FNN method has to be reduced. To achieve this goal, a multidisciplinary group formed by computer scientists and physicists are collaborative working on developing High Performance Computing implementations of one of the most popular algorithms that implement the FNN method: based on box-assisted algorithm and based on kd-tree data structure. In this paper, a comparative study of the distributed memory architecture implementations carried out in the framework of this collaboration, is presented. As a result, two parallel implementations for box-assisted algorithm and one parallel implementation for the kd-tree structure are compared in terms of execution time, speed-up and efficiency. In terms of execution time, the approaches presented here are from 2 to 16 times faster than the sequential implementation, and the kd-tree approach is from 3 to 7 times faster than the box-assisted approaches.