Computational geometry: an introduction
Computational geometry: an introduction
K-d trees for semidynamic point sets
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Parallel Construction of Multidimensional Binary Search Trees
IEEE Transactions on Parallel and Distributed Systems
Lecture Notes on Bucket Algorithms
Lecture Notes on Bucket Algorithms
Algorithms in C
Nonlinear Time Series Analysis
Nonlinear Time Series Analysis
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
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The False Nearest Neighbors (FNN) method is particularly relevant in several fields of science and engineering (medicine, economics, oceanography, biological systems, etc.). In some of these applications, it is important to give results within a reasonable time scale, so the execution time of the FNN method has to be reduced. This paper describes two parallel implementations of the FNN method based on the distribution of embedding dimensions for distributed memory architectures. A "Single-Program, Multiple Data" (SPMD) paradigm is employed using a simple data decomposition approach where each processor runs the same program but acts on a different subset of the data. The computationally intensive part of the method lies mainly in the neighbor search and this task is therefore parallelized and executed using 4 to 64 processors. The accuracy and performance of the two parallel approaches are then assessed and compared to the best sequential implementation of the FNN method which appears in the TISEAN project. The results indicate that the two parallel approaches, when the method is run using 64 processors on the MareNostrum supercomputer, are between 17 and 37 times faster than the sequential one. Efficiency is between 26% and 59%.