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Faster Approximation of Minimum Enclosing Balls by Distance Filtering and GPU Parallelization

Publication Type:

Journal article


Journal of Graphics Tools


Taylor & Francis




Minimum enclosing balls are used extensively to speed up multidimensional data processing in, e.g., machine learning, spatial databases, and computer graphics. We present a case study of several acceleration techniques that are applicable in enclosing ball algorithms based on repeated farthest-point queries. Two different distance filtering heuristics are proposed aiming at reducing the cost of the farthest-point queries as much as possible by exploiting lower and upper distance bounds. Furthermore, auto-tunable GPU solutions using CUDA are developed for both low- and high-dimensional cases. Empirical tests apply these techniques to two recent algorithms and demonstrate substantial speedups of the ball computations. Our results also indicate that a combination of the approaches has the potential to give further performance improvements.


author = {Linus K{\"a}llberg and Thomas Larsson},
title = {Faster Approximation of Minimum Enclosing Balls by Distance Filtering and GPU Parallelization},
volume = {17},
number = {3},
pages = {67--84},
month = {July},
year = {2015},
journal = {Journal of Graphics Tools},
publisher = {Taylor {\&} Francis},
url = {}