3 Plaku, E. Kavraki, L. E. 2006 Workshop on Algorithmic Foundations of Robotics (WAFR) New York, NY proximity relations, path planning, project_Proximity We quantitatively analyze the performance of exact and approximate nearest-neighbors algorithms on increasingly high-dimensional problems in the context of sampling-based motion planning. We study the impact of the dimension, number of samples, distance metrics, and sampling schemes on the efficiency and accuracy of nearest-neighbors algorithms. Efficiency measures computation time and accuracy indicates similarity between exact and approximate nearest neighbors. Our analysis indicates that after a critical dimension, which varies between 15 and 30, exact nearest-neighbors algorithms examine almost all the samples. As a result, exact nearest-neighbors algorithms become impractical for sampling-based motion planners when a considerably large number of samples needs to be generated. The impracticality of exact nearest-neighbors algorithms motivates the use of approximate algorithms, which trade off accuracy for efficiency. We propose a simple algorithm, termed Distance-based Projection onto Euclidean Space (DPES), which computes approximate nearest neighbors by using a distance-based projection of high-dimensional metric spaces onto low-dimensional Euclidean spaces. Our results indicate DPES achieves high efficiency and only a negligible loss in accuracy. http://www.kavrakilab.org/sites/default/files/PaperWAFR_DPES-h.pdf